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. 1· I �'--/' _,..)', Standards and Specifications for Geodetic Control .Networks

···:=· Federal Geodetic Control Committee Rear Adm. John D. Bossler, Chairman

Rockville, Maryland September 1984 FGCC Standards� 1and Specifications for Geodetic Control Networks

Federal Geodetic Control Committee John D. Bossler, Chairman September 1984

For information write: Chairman Federal Geodetic Control Coinmittee 6001 Executive Boulevard Rockville, Maryland 20852

For sale by the National GeodeticInformation Branch (N/CG17x2), NOAA, Rockville, MD 20852

j (

, Libraryof CongressCataloging in PublicationData United States. Federal Geodetic Control Committee. Standard and specificationsfor geodetic control networks. Replaces both "Classification, standards .of accuracy, and general specifications of ieodetic control surveys," issued February 1974 and "Specifications to support classification, standards of accuracy, and general specifications of geodetic contrcii surveys," revised June 1980 Pref. c� "September 1984." ( 1. Geodesy-Standards-United States. I. Bossler, John D. II. Title. QB296.U89U5 1984 526.3'3 84-600257

ii Preface

This single publication is designed to replace both "Classification, Standards of Accuracy and General Specifications of Geodetic Control Surveys," issued February 1974, and "Specifications to Support Classification, Standards of Accuracy, and General Specifications of Geodetic Control Sur­ veys," issued June 1980. Because requirements and methods for acquisition of geodetic control are changing rapidly, this publication is being released in loose-leaf format so that it can be updated more conveniently and efficiently. Recipients of this publication wishing to receive updated information should complete and mail the form below. Comments on the contents and format of the publication are welcomed and should be addressed to:

FGCC Secretariat, Code N/CG1x5 National Geodetic Survey, NOAA , Rockville,Maryland 20852

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Please inform me of updated information for "Standards and Specifications for Geodetic Control c�'· Networks." Name: ------

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iii Contents

Preface ...... iii 1. Introduction...... 1-1 2 Standards ...... · ...... 2-1 2.1 Horizontal control network standards ...... 2-1 2.2 Vertical control network standards ...... 2-2 2.3 Gravity control network standards ...... 2-3 ,,:-; 3. Specifications...... 3-1 3.1 Introduction ...... 3-1 3.2 Triangulation...... 3-1 3.3 Traverse ...... 3-3 3.4 Inertial surveying ...... 3-5 3.5 Geodetic leveling ...... 3-6 3.6 Photogrammetry...... : ...... 3-8 3.7 Satellite Doppler positioning...... 3-9 3.8 Absolute gravimetry...... 3-12 3.9 Relative gravimetry...... : ...... 3-13- 4. Infonnation...... ·...... 4-1 5. References ...... 5-1 Appendix A. Governmentalauthority ...... , ...... ,...... A-1 A.I Authority...... A-1 A.2 References ...... A-1 Appendix B. Variance factor estimation...... B-1 B.1 Introduction...... B-1 B.2 Global variance factor estimation...... B-2 B.3 Local variance factor estimation ...... �...... B-2 B.4 Iterated almost unbiased estimation ...... B-3 B.5 References...... B-4 Appendix C. Procedures forsubm itting data to theNational GeodeticSurvey ...... C-1

V ,!) (-(J 1. Introduction

The Government of the United States makes nation­ vertical standards are defined in reasonable conformance wide surveys, maps, and charts of various kinds. These are with past practice. The recent development of highly necessary to support the conduct of public business at all accurate absolute gravity instrumentation now allows a levels of government, for planning and carrying out nationai. gravity reference standard. In the section on "Standards," and local projects, the development and utilization of the classification standards for each of the control net­ natural resources, national defense, land management, works are described, sample computations performed, and monitoring crustal motion. Requirements for geo­ and monumentation requirements given. detic control surveys are most critical where intense devel­ Control networks can be produced only by making very opment is taking place, particularly offshore areas, where accurate measurements which are referred to identifiable surveys are used in the exploration and development of control points. The combination of survey design, instru­ natural resources, and in delineation of state and interna­ mentation, calibration procedures, observational techniques, tional boundaries. and data reduction methods is known as a measurement State and local governments and industry regularly system. The section on "Specifications" describes impor­ cooperate in various parts of the total surveying and tant components and states permissible tolerances for a mapping program. In surveying and mapping large areas: variety of measurement systems. it is first necessary to establish frameworks·of horizontal, Clearly, the control networks would be of little use if vertical, and gravity control. These provide a common the datum values were not published. The section entitled basis forall surveying and mapping operations to ensure a "Information" describes the various products and for­ coherent product. A reference system, or datum, is the set mats of available geodeticdata. of numerical quantities that serves as a common basis. Upon request, the National Geodetic Survey will accept Three National Geodetic Control Networks have been data submitted in the correct formats with the proper created by the Government to provide the datums. It is supporting documentation (appendix C) for incorpora­ the responsibility of the National Geodetic Survey (NGS) to tion into the national networks. When a survey is submit­ actively maintain the National Geodetic Control Net­ ted for inclusion into the national networks, the survey works (appendix A). measurements are processed in a quality control proce­ These control networks consist of stable, identifiable dure that leads to their classification of accuracy and points tied together by extremely accurate observations. storage in the National Geodetic Survey data base. To From these observations, datum values (coordinates or fully explain the process we shall trace a survey from the gravity) are computed and published. These datum values planning stage to admission into the data base. This example provide the common basis that is so important to survey­ will provide an overview of the standards and specifica­ ing and mapping activities. tions, and how they work together. As stated, the United States maintains three control The user should first compare the distribution and networks. A horizontal network provides geodetic lati­ accuracy of current geodetic control withboth' immediate tudes and longitudes in the North American Datum ref­ and long-term needs. From this basis, requirements for erence system; a vertical network furnishes elevations in the extent and accuracy of the planned survey are deter­ the National Geodetic Vertical Datum reference system; mined. The classification standards of the control net­ and a gravity network supplies gravity values in the U.S. works will help in this formulation. Hereafter, the require­ absolute gravity reference system. A given station may be ments for the accuracy of the planned survey will be a control point in one, two, or all three control networks. referred to as the "intended accuracy" of the survey. A It is not feasible for all points in the control networks to measurement system is then chosen, based on various be of the highest possible accuracy. Different levels of factors such as: distribution and accuracy of present con­ accuracy are referred to as the "order" of a point. Orders trol; region of the country; extent, distribution, and accu­ a,re often subdivided farther by a "class" dt;signation, racy of the desired control; terrain and accessibility of Datum values for a station are assigned an order (and control; and economic factors. class) based upon the appropriate classification standard Upon selection of the measurement system, a survey for each of the three control networks. Horizontal and design can be started. The design will be strongly depen-

1-1 dent upon the "Network Geometry" specifications for procedure to make sure that all users may place confi­ 0 that measurement system. Of particular importance is the dence in the new survey points. First, the data and docu­ \....._ ·,,_ ••. requirement to connect to previously established control mentation are examined for compliance with the mea­ LI points. If this is not done, then the survey cannot be placed surement system specifications for the intended accuracy on the national datum. An adequate number of existing of the new survey. Then office computations are performed, control point connections are of ten required in the speci­ including a minimally constrained least squares adjust­ fications in order to ensure strong network geometry for ment. (See appendix B for details.) From this adjustment, other users of the control, and to provide several closure accuracy measures can be computed by error propaga­ checks to help measure accuracy. NGS can certify the tion. The accuracy classification thus computed is called results of a survey only if it is connected to the national the "provisional accuracy" of the survey. network. The provisional accuracy is compared to the intended Situations will arise where one cannot, or prefers not to, accuracy. The difference indicates the departure of the conform to the specifications. NGS may downgrade the accuracy of the survey from the specifications. If the classification of a survey based upon failup; to adhere to difference is small, the intended accuracy has precedence the measurement system specifications if the departure because a possible shift in classification is not warranted. degrades the precision, accuracy, or utility of the survey. However, if the difference is substantial, the provisional On the other hand, if specification requirements for the accuracy will supersede the intended accuracy, either as a desired level of accuracy are exceeded, it may be possible downgrade or an upgrade. to upgrade a surveyto a higher classification. As the final step in the quality control procedure, the Depending upon circumstances, one may wish to go variance factor ratio computation using established con­ into the field to recover old control and perform recon­ trol, as explained in the section on "Standards," is deter­ naissance and site inspection for the new survey. Monu­ mined for the new survey. If this result meets the criteria mentation may be performed at this stage. Instruments stated there, then the survey is classified in accordance should be checked to conform to the "Instrumentation" with the provisional accuracy (or intended accuracy, which- specifications, and to meet the "Calibration Procedures" ever has precedence). specifications. Frequent calibration is an excellent method to Cases arise where the variance factor ratio is signifi­ help ensure accurate surveys. cantly larger than expected. Then the control network is In the field, the "Field Procedures" specifications are at fault, or the new survey is subject to some unmodeled used to guide the methods for taking survey measure­ error source which degrades its accuracy. Both the estab­ c� ments. It must be stressed that the "Field Procedures" lished control measurements and the new survey mea­ ( section is not an exhaustive account of how to perform surements will be scrutinized by NGS to determine the observations. Reference should be made also to the appropri­ source of the problem. In difficult cases, NGS may make ate manuals of observation methods and instruments. diagnostic measurements in the field. Computational checks can be found in the "Field Pro­ cedures" as well as in the "Office Procedures" specifica­ Upon completion of the quality control check, the sur­ tions, since one will probably want to perform some of the vey measurements and datum values are placed into the computations in the field to detect blunders. It is not data base. They become immediately available for elec­ necessary for the userto do the computations described in tronic retrieval, and will be distributed in the next publi­ the "Office Procedures" specifications, since they will be cation cycle by the National Geodetic Information Branchof done by NGS. However, it is certainly in the interest of NGS. the user to compute these checks before leaving the field, A final remark bears on the relationship between the in case reobservations are necessary. With the tremen­ classification standards and measurement system speci­ dous increase in programmable calculator and small com­ fications. Specifications are combinations of rules of thumb puter technology, any of the computations in the "Office and studies of error propagation, based upon experience, Procedures" specifications could be done with ease in the of how to best achieve a desired level of quality. Unfortu­ field. nately, there is no guarantee that a particular standard At this point the survey measurements have been col­ will be met if the associated specifications are followed. lected, together with the new description and recovery However, the situation is ameliorated by a safety factorof notes of the stations in the new survey. They are then two incorporated in the standards and specifications. placed into the formats specified in the Federal Geodetic Because of this safety factor, it is possible that one may Control Committee (FGCC) publications Input Formats fail to meet the specifications and still satisfy the desired and Specifications of the National Geodetic Survey Data standard. This is why the geodetic control is not automat­ Base. Further details of this process can be found in ically downgraded when one does not adhere to the speci­ appendix C, "Procedures for Submitting Data to the fications. Slight departures from the specifications can be National Geodetic Survey." accommodated. In practice, one should always strive to The data and supporting documentation, after being meet the measurement system specifications whenextending received at NGS, are processed through a quality control a National Geodetic ControlNetwork.

1-2 2. Standards

· The classification standards of the National Geodetic relation of specific accuracy to the coordinates of all other Control Networks are based on accuracy. This means that points in the horizontal control network. This relation is when control points in a particular survey are classified, expressed as a distance accuracy, 1:a. A distance accu­ . they are certified as having datum values consistent with racy is the ratio of the relative positional error of a pair of all other points in the network, not merely those within control points to the horizontal separation of those points. that particular survey. It is not observation closures within a survey which are used to classify control points, but the Table 2.1-Distanceaccuracy standards ability of that survey to duplicate already established control values. This comparison takes into account mod­ Minimum els of crustal motion, refraction, and any other systematic Classification distance accuracy effectsknown to influencethe survey measurements. 1:100,000 The NGS procedure leading to classification covers First-order...... Second-order, classI ...... 1: 50,000 , foursteps: Second-order, classII ...... 1: 20,000 1. The survey measurements, field records, sketches, Third-order, class I ...... 1: 10,000 and other documentation are examined to verify Third-order, classII ...... 1: 5,000 compliance with the specifications for the intended accuracy of the survey. This examination may lead to a modificationof the intended accuracy. A distance accuracy, 1:a, is computed from a mini­ 2. Results of a minimally constrained least squares mally constrained, correctly weighted, least squares adjust­ adjustment of the survey measurements are exam­ ment by: ined to ensure correct weighting of the observations and freedomfrom blunders. a = d/s 3. Accuracy measures computed by random error propa­ gation determine the provisional accuracy. If the where provisional accuracy is substantially different from a=distance accuracy denominator the intended accuracy of the survey, then the provi­ s = propagated standard deviation of distance between sional accuracy supersedes theintended accuracy. survey points obtained from the least squares adjust­ 4. A variance factor ratio for the new survey combined ment with network data is computed by the Iterated Almost d=distance betweensurvey points Unbiased Estimator (!AUE) method (appendix B). If the variance factor ratio is reasonably close to 1.0 The distance accuracy pertains to all pairs of points (typically less than 1.5), then the survey is consid­ (but in practice is computed for a sampling of pairs of ered to check with the network, and the survey is points). The worst distance accuracy (smallest denominator) classified with the provisional (or intended) accura­ is taken as the provisional accuracy. If this is substan­ cy. If the variance factor ratio is much greater than tially large� or smaller than the intended accuracy, then 1.0 (typically 1.5 or greater), then the survey is con­ the provisionalaccuracy takes precedence. sidered to not check with the network, and both the As a test for systematic errors, the variance factor ratio survey and network measurements will be scruti­ of the new survey is computed by the Iterated Almost nized forthe source of the problem. Unbiased Estimator (IAUE) method described in appen­ dix B. This computation combines the new survey mea­ surements with existing network data, which are assumed 2.1 Horizontal Control NetworkStandards to be correctly weighted and free of systematic error. If the variance factor ratio is substantially greater than When a horizontal control point is classified with a unity then the survey does not . check with the network, particular order and· class, NGS certifies that the geo­ and both the survey and the network data will be exam­ detic latitude and longitude of that control point bear a ined byNGS.

2-l Computer simulations performed by 'NGS have shown horizontal location which can be defined as a point. A 30- that a variance factor ratio greater than ·1;5 typically centimeter-long wooden stake driven into the ground, for indicates systematic errors between the survey and the example, would lack both permanence and horizontal network. Setting a cutoff value higher than this could stability. A mountain peak is difficult to define asa point. allow undetected systematic error to propagate into the Typically, corrosion resistant metal disks set in a large national network. On the other hand, a higher cutoff value concrete mass have the necessary qualities. First-order might be considered if the survey has only a small number and second-order, class I, control points should have an of connections to th� network, because this circumstance underground mark, at least two monumented reference would tend to increase the variance factorratio. marks at right angles to one another, and at least one In some situations, a survey has been designed in which monumented azimuth mark no less than 400 m from the different sections provide different orders of control. For control point. Replacement of a temporary mark by a these multi-order surveys, the computed distance accu­ more permanent mark is not acceptable unless the two racy denominators should be grouped into sets appropri­ marks are connected in timely fashion by survey observations ate to the different parts of the survey. Then, the smallest of sufficient accuracy. Detailed information may be found in value of a in each set is used to classify the control points C&GS Special Publication 247, "Manual of geodetic of· that portion, as discussed above. If there are sufficient triangulation." connections to the network, several: variance factor ratios, one foreach section of the survey, should be computed. 2.2 VerticalControl NetworkStandards HorizontalExample When a vertical control point is classifiedwith a particular Suppose a survey with an intended accuracy of first­ order arid class, NGS certifies that the orthometric elevation order (1:100,000) has been performed. A series of propa­ at that point bears a relation of specific accuracy to the gated distance accuracies from a minimally constrained · · elevations of all other points in the vertical control net­ adjustment is now computed. work. That relati9n is expressed as an elevation difference accuracy, b. An elevation difference accuracy· is the rela­ tive elevation ·error between a pair of control points that is s d J:a scaled by the square root of their horizontal separation line (m) (m) traced along existing level routes. 1-2 ...... 0.141 17,107 1:121,326 1-3 ... : ... : ...... 0.170 20,123 1:118,371 2-3 ...... 0;164 • 15,505 1: 94,543 Table 2.2-Elevationaccuracy standards (

Maximum elevation Classification differenceaccuracy First-

2-2 as the provisional accuracy. If this is substantially larger that a variance factor ratio of 1.2 was computed for the or smaller than the intended accuracy, then the provi­ survey. This would be reasonably close to unity and would sional accuracy takes precedence. indicate that the survey checks with the network. The As a test for systematic errors, the variance factor ratio survey would then be classified as second-order, class II, of the new survey is computed by the Iterated Almost using the intended accuracy of 1.3. Unbiased Estimator (IAUE) method described in appen­ However, if a survey variance factor ratio of, say, 1.9 dix B. This computation combines the new survey mea­ was computed, the survey would not check with the net­ surements with existing network data, which are assumed work. Both the survey and network measurements then to be correctly weighted and free of systematic error. If would have to be scrutinizedto findthe problem. the variance factor ratio is substantially greater than unity, then the survey does not check with the network, Monwnentation and both the survey and the network data will be exam- Control points should be part of the National Geodetic ined byNGS. Vertical Network only if they possess permanence, verti­ Computer simulations performed by NGS have shown cal stability with respect to the Earth's crust, and a verti­ that a variance factor ratio greater than 1.5 typically cal location that can be defined as a point. A 30-centime­ indicates systematic errors between the survey and the ter-long wooden stake driven into the ground, for example, network. Setting a cutoff value higher than this. could would lack both permanence and vertical stability. A allow undetected systematic error to propagate into the rooftop lacks' stability and is difficult to define as a point. national network. On the other hand, a higher cutoff value• Typically, corrosion resistant metal disks set in large rock might be considered if the survey has only a small number outcrops or long metal rods driven deep into the ground of connections to the network, because this circumstance have the necessary qualities. Replacement of a temporary would tend to increase the variance factorratio . .mark by a more permanent mark is not acceptable unless . In some situations, a survey has been designed in which the two marks are connected in timely fashion by survey different sections provide different orders of control. For observations of sufficient accuracy. Detailed information these multi-order surveys, the computed elevation. difference may be found in NOAA Manual NOS NGS 1, "Geodetic accuracies should be grouped into sets appropriate to the bench marks." different parts of the survey. Then, the largest vaiue of b in each set is used to classify the control points of that portion, as discussed above. If there are sufficient connec­ 2.3 GravityControl NetworkStandards tions to the network, several variance factor ratios, one for When a gravitycontrol point is classified with a particular each section of the survey, should be computed. order and class, NGS certifies that the gravity value at that control point possessesa specific accuracy. Gravity is commonly expressed in units of milligals VerticalExample 5 Suppose a survey with an intended accuracy of second­ (mGal) or microgals (µGal) equal, respectively, to (10- ) 2 -s 2 order, class II has been performed. A series of propagated meters/sec , and (10 ) meters/sec • Classification order elevation difference accuracies from a minimally con­ refers to measurement accuracies and class to site stabili­ strained adjustment is now computed. ty. Table 2.3-Gravityaccuracy standards d b s Gravity accuracy line (mm) (km) (mm)/y (km) Classification (µ.Gal) 1-2 ...... 1.574 1.718 1.20 First-order,class · I ...... 20 (subject to stability 1-3 ...... 1.743 2.321 1.14 verification) 2-3 ...... 2.647 4.039 1.32 First-order,class II ...... 20 Second-order...... 50 Third-order ...... :...... ::...... 100

When a survey establishes only new points, and where Suppose that the worst elevation difference accuracy is only absolute measurements are observed, then each sur­ 1.32. This is not substantially different from the intended vey point is classified independently. The standard devia­ accuracy of 1.3 which would therefore have precedence tion from the mean of measurements observed at that for classification. It is not feasible to precisely quantify point is corrected by the error budget for noise sources in "substantially different." Judgment and experience·· are accordance with the followingformula: determining factors. Nowiassume that a solution combining survey and network datahas been obtained (as per appendix B), and 2-3 where GravityExamples c =gravity accuracy Example A. Suppose a gravity survey using absolute r1 Xi=:=gravity measurement measurement techniques has been perfonned. These points ---cp.=number of measurements are then unrelated. Consider one of these surveypoints. n ( x m = (};t=l x.)/n t Assume n = 7 50 750 2 2 m e=externalrandom error i=�l (x. I - x ) = .169 mGal

The value obtained for c is then compared directly against e = 5 µGal the gravity accuracy standards table. 0.169 When a survey establishes points at which both abso­ c2 = + (.005)2 lute and relative measurements are made, the absolute 750-1 determination ordinarily takes precedence and the point is classified accordingly. (However, see Example D below c = 16 µGal foran exception.) The point is then classifiedas first-order,class II. When a survey establishes points where only relative Example B. Suppose a relative gravity survey with an measurements are observed, and where the survey is tied . intended accuracy of second-order (50 µGal) has been per­ to the National Geodetic GravityNetwork, then the gravity fonned. A series of propagated gravity accuracies from a accuracy is identified with the propagated gravity stan­ minimally constrained adjustment is now computed. dard deviation from a minimally constrained, correctly weighted, least squares adjustment. The worst gravity accuracy of all the points in the Gravity standard t survey is taken· as the . provisional accuracy. If the provi­ Station deviation (µGal) sional accuracy exceeds the gravity accuracy- limit set for 1 38 the intended survey clru;sification, then the survey is clas­ 2 ,. 44 sifiedusing the provisional accuracy. 3 55 As a test for systematic errors, the variance factor ratio �of the new survey is computed by the_ Iterated Almost C--.__../'Unbiased Estimator (IAUE) method described in appen­ dix B. This computation combines the new survey mea- ( surements with existing network data which are assumed Suppose that the worst gravity accuracy was 55 µGal. to be correctly weighted and free of systematic error. If This is worse than the intended accuracy of 50 µGal. the variance factor ratio is substantially greater than Therefore, the provisional accuracy of 55 µGal would unity, then the survey does not check with the network, have precedence for classification, which would be set to and both the survey and the network data will be exam­ third-order. Now assume that a solution combining survey and ined byNGS. B) Computer simulations performed by NGS have shown network data has been obtained (as per appendix. and that a variance factor ratio greater than 1.5 typically that a variance factor of 1.2 was computed for the survey. This would be· reasonably close to unity, and would indi­ indicates systematic errors between the survey and the cate that the survey checks with the network. The survey network. Setting a cutoff value higher than this could would then be classified as third-order using the provi­ allow undetected systematic error to propagate into the sional accuracyof 55 µGal. national network. On the other hand, a higher cutoff value However, if a variance factor of, say, 1.9 was computed, might be considered if the survey has only a minimal the survey· would not check with the network. Both the number of connections to the network, because this cir­ survey and network measurements then would have to be cumstance wouid tend to increase the variance factor scrutinized to findthe problem. ratio. Example C. Suppose a survey consisting of both abso­ In 'some situations, a survey has been designed in which lute and relative measurements has been made at the different sections provide different orders of control. For same points. Assume the absolute observation at one of these multi-order surveys, the computed gravity accura­ the points yielded a classification of first-order, class II, cies should be grouped into sets appropriate to the differ­ whereas the relative measurements produced a value to ent parts of the survey. Then, the largest value of c in each second-order standards. The point in question would be set is used to classify the control points of that portion,. as classified as first-order, class II, in accordance with the r discussed above. If there are sufficient connections to the absolute observation. G.__/rtetwork, several variance factor ratios, one for each part Example D. Suppose we have a survey similar to Case of the survey, should be computed. C, where the absolute measurements at a particular point 2-4 yielded a third-order classification due to an unusually checked at least twice for the first year to ensure stability. noisy observation session, but the relative measurements For first-order, class II stations, the platform should be still satisfied the ·second-order standard. The point in located in an extremely stable environment, such as the question would be classified as second-order, in accor­ concrete floor of a mature structure. For second and dance with the relative measurements. third-order stations, standard bench mark monumentation is adequate. Replacement of a temporary mark by a more Monument.ati on permanent mark is not acceptable unless the two marks Control points should be part of the National Geodetic are connected in timely fashion by survey observations of Grayity Network only if they possess permanence, hori­ sufficient accuracy. Detailed information is given in NOAA zontal and vertical stability with respect to the Earth's Manual NOS NGS 1, "Geodetic bench marks." Monu­ ments should not be near sources of electromagnetic crust, and a horizontal and vertical location which can be interference. defined as a point. For all orders of accuracy, the mark It is recommended, but not necessary, to monument should be imbedded in a stable platform such as flat, third-order stations. However, the location associated horizontal concrete. For first-order, class I stations, the with the. gravity value should be recoverable, based upon platform should be imbedded in stable, hard rock, and the station description.

,·r /,,- \._)___)

2-5 l . ------3. Specifications

3.1 Introduction. performed by NGS will use models of error sources, such as crustal motion, when they are judged to be significant All measurement systems regardless of their nature to the level of -accuracyof the survey. have certain common qualities. Because of this, the mea­ surement system specifications follow a prescribed struc­ ture as outlined below. These specifications describe the 3.2 Triangulation important components and state permissible tolerances used in a general context of accurate surveying methods. Triangulation is a measurement system comprised of The user is cautioned that these specifications are not joined or overlapping triangles of angular observations substitutes for manuals that detail recommended field supported by occasional distance and astronomic obser­ operations and procedures. vations.Triangulation is usedto extendhorizontal control The observations will have spatial or temporal relation­ ships with one another as given in the "Network Geome­ NetworkGeometry try" section. In addition, this section specifies the fre­ quency of incorporation of old control into the survey. Order First Second Second Third Third Computer simulations could be performed instead of fol­ Class I II I II lowing the "Network Geometry" and "Field Procedures" Station spacing not less specifications. However, the user should consult theNational than (km)...... 15 10 5 0.5 0.5 Geodetic Survey before undertaking such a departure Averageminimwn distance from thespecifications: anglet of figuresnot less than ...... 40° 30° 30° 25° The "Instrumentation" section describes the types and Minimum distanceanglet characteristics of the instruments used to make observations.· of all figuresnot An instrument must be able to attain the precision require­ lessthan ...... 30° 25° 20° 20° ments given in "Field Procedures." Baseline spacing not The section "Calibration Procedures" specifies the nature more than (triangles) ...... 5 , 10 12 15 15 Astronomic azimuth and frequency of instrument calibration. An instrument spacing not more • must be calibrated whenever it has been damaged or than (triangles)...... 8 10 10 12 15 repaired. The "Field Procedures" section specifies particular rules t Distanceangle is angle opposite the side through which distanceis propagated. and limitsto bemet while followingan appropriate method of ob�ervation. For a detailed account of how to perform The new survey is required to tie to at least four net­ observations, the user should consult the appropriate work control points spaced well apart. These network points must have datum values equivalent to or better manuals. than the intended order (and class) of the new survey. For Since NGS will perform _the computations described example, in an arc of triangulation, at least two network under "Office Procedures," it is not necessary forthe user control points should be occupied at each end of the arc. to do them. However, these computations provide valu- Whenever the distance between two new unconnected . able checks on the survey measurements that could indi­ survey pomtsis less than 20 percent of the distance between cate the need for some reobservations. This section speci­ those points traced along existing or new connections, fies commonly applied corrections to observations, and then a direct connection should be made between those computations which ·'monitor the precision and accuracy two survey points. In addition, the survey should tie into of the survey. It also discusses the correctly weighted, any sufficiently accurate network control points within minimally constrained least squares adjustment used to the station .spacing distance of the survey. These network ensure that the survey work is free from blunders and able stations should be occupied and sufficient observations to achieve the intended accuracy. Results of the least taken to make these stations integral parts -of the survey. squares adjustment are used in the quality control and Nonredundant geodetic connections to the network sta­ accuracy classification procedures. The adjustment tions are not considered sufficient ties. Nonredundantly

3-1 determined stations are not allowed. Control stations should Order First Second Second Third Third not be determined by intersection or resection methods; Class I II I i Simultaneous reciprocal vertical angles or geodetic level- II CL � ing are observed along base lines. A base line need not be Standard deviation of observed if other base lines of sufficient accuracy were mean not to exceed ...... 0.4" 0.5'' 0.8" 1.2" 2.0" observed within the base line spacing sp,ecification in the Rejection limit from (: the mean ...... 4" 4" 5" 5" 5" network, and similarly for astronomic azimuths. Reciprocal Vertical Angles (along distance sight path) Instrumentation Number of independent :: Only properly maintained theodolites are adequate for observations observing directions and azimuths for triangulation. Only direct/reverse ...... 3 3 2 2 2 precisely marked targets, mounted stably op. tripods or Maximum spread ...... 10" 10" 10" 10" �" supported towers, should be employed. The target should Maximum time interval have a clearly defined center, resolvable at the minimum between reciprocal angles (hr) ...... ·.... 1 control spacing. Optical plummets or collimators are required to ensure that the theodolites and targets are AstronomicAzimuths centered over the marks. Microwave-type electronic dis- Observationsper night ...... 16 16 16 8 4 Number of nights ...... 2 2 1 I 1 tance measurement (EDM) equipment is not sufficiently Standard deviation of accurate for measuring higher-orderbase lines. mean not to exceed ...... 0.45" 0.45" 0.6" 1.0" 1.7'' Rejection limit from the mean ...... 5" 5" 5" 6" 6" First Second Second Third Third Order Electro-OpticalDistances Class I II I II Minimum number of days .. 2* 2• 1 1 Minimum number of Theodolite,least count ...... 0.2!' 0.2" 1.0" 1.0" 1.0" measurements/day .;...... 2§ 2§ 2§ 1 Minimum number of con- Calibration Procedures centric observations/ Each year and whenever the difference between direct measurement ...... 2 2 Minimum numberof offset and reverse readings of the theodolite depart from 180 • observations/ by more than 30", the instrument should be adjusted c) measurement ...... 2 2 2 �.J for collimation error. Readjustment of the cross hairs Maximum difference from and the level bubble -should be done whenever their mis- mean of observations ( .:: adjustments affect the instrument reading by the amount (mm) ...... 40 40 50 60 60 Minimum number of of the least count. readings/ observation All EDM devices and retroreflectors should be serviced ( or equivalent) ...... 10 10 10 10 10 regularly and checked frequently over lines of known Maximum differencefrom distances. The National Geodetic Survey has established mean of readings (mm) .. :j: :j: :j: :j: :j: specific calibration base lines for this purpose. EDM InfraredDi,stances instruments should be calibrated annually, and frequency Minimum number of days .. 2* 1 checks made semiannually. Minimum number of measurements ...... 2§ 2§ FieldProcedures Minimum number of con- centric observations/ Theodolite observations for first-order and second-order, measurement ...... class I surveys may only be made at night. Reciprocal Minimum numberof offset vertical angles should be observed at times of best atmo- observations/ spheric conditions (between noon and late afternoon) for measurement ...... 2 Maximum differencefrom all orders of accuracy. Electronic distance measurements mean of observations need a record at both ends of the line of wet and dry bulb (mm) ...... 5 5 10 10 temperatures to ± 1 · C, and barometric pressure to ± 5 Minimum number of mm of mercury. The theodolite and targets should be readings/obs ervation ( or equivalent) ...... 10 10 10 10 centered to within 1 mm over the survey mark or eccentric Maximum difference from point. mean of readings (mm) .. :j: :j: :j: :j: Microwave Distances Order First Second Second Third Third Minimum number of (�\ Class I II I . II measurements ...... ) Minimum time span \ G- Directions between measurements Number ofpositions ...... 16 16 8 or 12t 4 2 (hr) ...... 8

3-2 arc correction Order First Second Second Third Third geoid height correction Class I II I II second velocitycorrection crustal motion -----, Maximum difference C\,/_,,,,( j between measurements "-j l, (mm) ...... 100 3.3 Traverse Minimum number of con­ centric observations/ measurement ...... 2** 1** Traverse is a measurement system comprised of joined Maximum difference from distance and theodolite observations supported by occasional mean of observations astronomic observations. Traverse is used to densify hori- (mm) ...... 100 150 zontal control. Minimum number of readings/obs ervation (or equivalent) ...... 20 20 NetworkGeometry Maximum difference from mean of readings (mm) .. Order First Second Second Third Third + + Class I II I II t 8 if 0.2", 12 if 1.0" resolution. * two or more instruments. Station spacing not less § one measurementat each end of the line. than (km) ...... 10 4 2 0.5 0.5 i as specifiedby manufacturer. Maximum deviation of •• carriedout at bothends of the line. main traverse from straight line ...... 20° 20° 25° 30° 40° Measurements of astronomic latitude and longitude Minimum number of are not required in the United States, except perhaps for bench mark ties ...... 2 2 2 2 2 first-0rder work, because sufficient information for deter­ Bench mark tie spacing mining deflections of the vertical exists. Detailed proce­ not more than (segments) ...... , ...... 6 8 10 15 20 dures can be found in Hoskinson and Duerksen (1952). Astronomic azimuth spacing not more than OfficeProcedures (segments) ...... 6 12 20 25 40 Minimum number of network control points...... 4 3 2 2 Order First Second Second Third Third 2 Class I II I II Triangle Oosure The new survey is required to tie to a minimum number Average not to exceed ...... LO" 1.2" 2.0" 3.0" 5.0" of network control points spaced well apart. These net­ Maximum not to exceed .... 3" 3" 5" 5" 10" work points must have datum values equivalent tp or Side Checks better than the· intended order (and class) of the new Mean absolute correction survey. Whenever the distance between two new uncon­ by side equation not nected survey points is less than 20 percent of the distance to exceed ...... 0.3" 0.4" 0.6" 0.8" 2.0" between those points traced along existing or new connec­ tions, then a direct connection must be made between A minimally constrained least squares adjustment will those two survey points. In addition, the survey should tie be checked for blunders by examining the normalized into any sufficiently accurate network control points within residuals. The observation weights will be checked by the station spacing distance of the survey. These ties must inspecting the postadjustment estimate of the variance of include EDM or taped distances. Nonredundant geodetic unit weight. Distance standard errors · computed by error connections to the network stations are not considered sufficient ties. Nonredundantly determined stations are propagation in this correctly weighted least squares adjust­ not allowed. Reciprocal vertical angles or geodetic level­ ment will indicate the provisional accuracy classification. ing are observed along all traverse lines. A survey variance factor ratio will be computed to check for systematic error. The least squares. adjustment will Instrumentation use models which acC?untfor the following: Only properly maintained theodolites are adequate for semimajor axis of the ellipsoid ...... (a = 6378137 m) observing directions and azimuths for traverse. Only pre­ reciprocal flatteningof the ellipsoid ...... (1 /f = 298.257222)" cisely marked targets, mounted stably on tripods or sup­ mark elevation above mean sea level...... (known to ± 1 m) ported towers, should be employed. The target should geoid heights ...... (known to ± 6 m) have a clearly defined center, resolvable at the minimum deflections of the vertical ...... (known to ± 3") control spacing. Optical plummets or collimators are geodesic correction skew normal correction required to ensure that the theodolites and targets are 0 height of instrument centered over the marks. Microwave type electronic dis­ height of target tance measurement equipment is not sufficiently accu­ sea level correction rate forJ?easuring first-order traverses.

3-3 Order First Second Second Third Third Order First Second Second Third Third ,� Class I II I II Class I II I II 1 1' , - '-,, Theodo 1· 1te, I east count ...... 0. 2" 1.0" 1.0" 1.0" 1.0" Minimum number of readings/ (�/ ------observation(or equivalent)..... 10 10 10 10 10 Maximum differencefrom CalibrationProcedures meanof readings(mm) ...... § § § § § c· Each year and whenever the difference between direct Infrared Distances and reverse readings of the theodolite depart from 180 • Minimum number of by more than 30", the instrument should be adjusted for measurements...... 1 collimation error. Readjustment of the cross hairs and the Minimum number of concentric observations/measurement...... 1 1 level bubble should be done whenever their misadjustments Minimum numberof offset affect the instrument reading by the amount of the least observations/measurement...... 1 1:j: count. Maximum differencefrom All electronic distance measuring devices and retrore- meanof observations(mm) ..... 10 10 10:j: flectors should be serviced regularly and checked fre­ Minimum number of readings/ observation...... 10 10 10 10 10 quently over lines of known distances. The National Geo­ Maximumdifferen:ce from detic Survey has established specific. calibration base mean of readings(mm} ...... § § § § § lines for this purpose. EDM instruments should be cali­ Microwave Distances brated annually, and frequencychecks made semiannually. Minimum number of measurciments...... Field Procedures Minimum number of concentric Theodolite observations for first-order and second-order, observations/measurement...... 2•• 1 •• 1 •• 1 •• class I surveys may be made only. at night. Electronic Maximumdifference from meanof observations(mm)..... 150 150 200 200 distance measurements need a record at both ends . of the Minimumnumber of readings/ line of wet and dry bulb temperatures to :l;: 1 • C and observation...... 20 20 10 JO barometric pressure to ±5 mm of mercury. The theodo­ Maximumdifference from lite, EDM, and targets should be centered to within 1 mm meanof readings(mm) ...... § § § § over the survey mark or eccentric point. t 8 if 0.2", 12 if 1.0" resolution. • 6 if 0.2", 8 if 1.0" resolution. '---./�/-) § as specifiedby manufacturer. r ; only if decimalreading near O or high 9'.s. Order First Second Second T�itd · Third •• carried out at both ends of the line. (. Class I II I II Measurements of astronomic •latitude and longitude Directions Number ofpositions ...... 16 8 or 12t 6 ors• 4 2 are not required in the United States, except perhaps for Standarddeviation of mean first-order work, because sufficient information for deter­ not to exceed...... 0.4" 0.5'' 0.8" 1.2" 2.0" mining deflections of the vertical exists. Detailed proce­ Rejection limitfrom themean .... 4" 5" 5" 5" 5" dures can be found in Hoskinson and Duerksen (1952). ReciprocalVertical Angles (along distance sight path) Office Procedures Number of independent observationsdirect/reverse ..... 3 3 2 2 2 Order First Second Second Third Third Maximum spread...... 10" 10" . 10''. io" 20" Class I II I II Maximumtime interval between reciprocal angles(hr) ...... Azimuthclosure at azimuth AstronomicAzimuths checkpoint Observationsper night ...... 16 16 12 8 4 (seconds of arc) . 1.7yN 3.0yN 4.SyN 10.0yN 120yN Number of nights ...... 2 2 1 1 1 , Positionclosure .... 0.04yK 0.08yK 0.20yK 0.40yK 0.80yK Standarddeviation of mean after azimuth... or or or or or not to exceed...... 0.45" 0.45" 0.6" 1.0" 1.7" adjustmentt ..... 1:100,000 1:50,000 1:20,000 1:10,000 1:5,000 Rejection limit fromthe mean.... 5" 5" 5" 6" 6" (N is numberof segments, K is routedistance in km) Electro-OpticalDistances t The expression containing the square root is designed for longer lines where Minimum numberof higher proportional accuracy is required. Use the formula that gives the smallest measurements ...... permissible closure. The closure (e.g., 1:100,000) is obtained by computing the Minimum numberof concentric differencebet.ween computed the and fJXCdvalues, and dividing this difference by K Note: Donot confuseclosure with distanceaccuracy of thesurvey. observations/measurement...... ·1 Minimum numberof offset A minimally constrained least squares·adjustment will r�'-1 observations/measurement...... r �-/ Maxi�um differencefrom be checked for blunder_s by examining the nonpalized 0 meanof observations(mm) ..... 60 60 residuals. The observation weights will be checked by

3-4 inspecting the postadjustment estimate of the variance of receive an accuracy classification, it must be permanently unit weight Distance standard errors computed by error monumented. propagation in a correctly weighted least squares adjust­ A grid of intersecting lines should . contain a minimum ment will indicate the provisional accuracy classification. of eight network points, and should have a network con­ A survey variance factor ratio will be computed to check trol point at each corner. The remaining network control for systematic error. The least squares adjustment will points may be distributed about the interior or the periphery use modelswhich account forthe following: of the grid. However, there should be at least one network control point at an intersection of the grid lines near the semimajoraxis of the ellipsoid (a = 6378137 m) reciprocalflattening of the el!ipsoid (1/f = 298.257222) center of the grid. If the required network points are not mark elevation abovemean sea level · (knownto ± 1 m) available, then they should be established by some other geoid heights (knownto ±6 m) measurement system. Again, the horizontal datum values deflections of the vertical (knownto ±3") of these network control points must have an order (and geodesic correction skew normalcorrection class) better than the intended order (and class) of the height of instrument new survey. height of target sea level correction Instrumentation arc correction geoidheight correction ISS equipment fallsinto twotypes: analytic (or strapdown) second velocitycorrection and semianalytic. Analytic inertial units are not consid­ crustalmotion ered to possess geodetic accuracy. Semianalytic units are either "space stable" or "local level." Space stable sys­ tems maintain the orientation of the platform with respect 3.4 InertialSurveying to inertial space. Local level systems continuously torque Inertial surveying is a measurement system comprised the accelerometers to account for Earth rotation and of lines, or a grid, of Inertial Surveying System (ISS) movement of the.inertial unit, and also torque the platform to observations. These specifications cover use of .inertial . coincide with the local level. This may be done on com­ systems only for horizontal control mand at a coordinate update, or whenever the unit achieves zero velocity (Zero velocity UPdaTe, or "ZUPT"). Inde­ Network Geometry pendently of the measurement technique, the recorded Order Second Second - Third Third data mayc be filtered by an onboard computer. Because (,./'J Class I II I II of the variable quality of individual ISS instruments, the user should test an instrument with existing geodetic Station spacing not lessthan (km).... 10 4 2 1 Maximum deviation from straight control beforehand. line connectingendpoints ...... 20° 25° 30° 35° An offset measurement device accurate to within. 5 mm should be affixedto the inertial unitor the vehicle.

Each inertial survey line is required to tie into a mini­ CalibrationProcedures mum of four horizontal network control points spaced. A static calibration should be performed yearly and well apart and should begin and end at network control immediately after repairs affecting the platform, gyro­ points. These network control points must have horizontal scopes, or accelerometers. datum values better than the intended order (and class) of A dynamic or field calibration should be performed the new survey. Whenever the shortest distance between prior to each project or subsequent to a static calibration. two new unconnected survey points is Jess than 20 percent of the distance between those points traced along existing The dynamic calibration should be performed only between or new connections, then a direct connection should be horizontal control points of first-order accuracy and in made between those two survey . points. In addition, the each cardinal direction. The accelerometer scale factors survey should connect to any· sufficiently accurate net­ from this calibration should be recorded and, if possible, work control points within the distance specified by the stored in the onboard computer of the inertial unit. station spacing. The connections may be measured by Before each project or after repairs affecting the offset EDM or tape traverse, or by another ISS line. If an ISS measurement device or the inertial unit, the relation between line is used, then these lines should follow the same speci- the center of the inertial unit and the zero point of the ficationsas all other ISS lines in the survey. offset measurement device should be established. For extended area surveys by ISS, a grid of intersecting lines that satisfies the 20 percent rule stated above can be FieldProcedures designed. There must bea mark at each intersection of the When sur,veying in a helicopter, the helicopter must lines. This mark need not be · l:l permanent monument; it come to rest on the ground for all ZUPT's and all may be a stake driven into the ground. For a position to measurements.

3-5 Order Second Second Third Third Order First First Second Second Third Class I 11 I 11 Class I 11 I 11 (-\._ ✓ Minimum number of complete Line length betweennetwork runs perline ...... 2 '--- �j') control pointsnot more Maximum deviation from a than (km) ...... 300 100 50 50 25 ( uniformrate of travel ( double-run) (including ZUPT)...... 15% 20% 25% 30% 25 10 Maximum ZUPTinterval (ZUPT (single-run) to ZUPT)(sec) ...... 200 240 300 300

New surveys are required to tie to existing network A complete ISS measurement consists of measurement of the line while traveling in one direction, followed by bench marksat the beginning and end of the leveling line. measurement of the same line while traveling in the re­ These network bench marks must have an order (and verse direction (double-run). A coordinate update should class) equivalent to or better than the intended order (and not be performed at the far point or at midpoints of a line, class) of the new survey. First-order surveys are required even though those coordinatesmay be known. to perform check connections to a minimum of six bench The mark offset should be measured to the nearest 5 marks, three at each end. All other surveys require a mm. minimum of four check connections, two at each end. "Check connection" means that the observed elevation OfficeProcedures difference agrees with the adjusted elevation difference within the tolerance limit of the new survey. Checking the Order Second Second Third Third elevation difference.between two bench marks located on Class I 11 I 11 the same structure, or so close together that both may Maximum differenceof smoothed-... have been affected by the same localized disturbance, is coordinatesbetween forward not considered a proper check. In addition, the survey is and reverserun ( cm) ...... 60 60 70 80 required to connect to any network control points within 3 km of its path. However, if the survey is run parallel to A minimally constrained least squares adjustment of existing control, then the following table specifies th� the raw or filtered survey data will be checked for blunders maximum spacing of extra connections between the survey by examining the normalized residuals. The observation and the control. At least one extra connection should ( weights will be checked by inspecting the postadjustment always be made. estimate of the variance of unit weight. Distance standard errors computed by error propagation in this correctly weighted least squares adjustment will indicate the provi­ Distance, survey Maximum spacing of sional accuracy classification. A survey variance factor to network extra connections (km) ratio will be computed to check for systematic error. The 0.5 km or less...... 5 least squares adjustment will use the best availa61e model 0.5 km to 2.0 km...... 10 for the particular inertial system. Weighted averages of 20 kmto 3.0 km...... 20 individually smoothed lines are not considered substitutes for a combine

Order First First Second Second Third 3.5 Geodetic Leveling Class I 11 I 11 Geodetic leveling is a measurement system comprised Levelinginstrument of elevation differences observed between nearby rods. Minimum repeatability of Leveling is used to extend vertical control. line of sight ...... 0.25" 0.25" 0.50" 0.50" 1.00" Leveling rod construction...... IDS IDS IDSt ISS Wood or or Metal NetworkGeometry ISS Instrumentrod and resolution Order First First Second Second Third (combined) Class I 11 I II Least count(mm) ...... 0.1 0.1 0.5-1.0* 1.0 1.0

Bench mark spacing not (IDS-Invar,double scale) more than (km) ...... _,. .. r . ·) 3 3 3 3 3 (ISS-Invar, singlescale) Average benchmark spacing t if optional micrometeris used. LJ�--' not more than (km) ...... 1.6 1.6 1.6 �.o 3.0 • 1.0 mm ·if 3-wire method,0.5 mmif optical micrometer. 3-6

I __ Only a compensator or tilting leveling instrument with Field Procedures-Continued an optical micrometer should be used for first-order leveling. Leveling rods should be one piece. Wooden or metal rods Order First First Second Second Third Class II I II may be employed only for third-order work. A turning I point consisting of a steel turning pin with a driving cap Difference of forwardand · should be utilized. If a steel pin cannot be driven, then a backward sight lengths turning plate ("turtle") weighing at least 7 kg should be never to exceed 2 5 substituted. In situations allowing neither turning pins per setup (m) ...... 5 10 10 per section (m) ...... 4 10 10 10 10 nor turning plates (sandy or marshy soils), a long wooden Maximum sight length (m) .. 50 60 60 70 90 stake with a double-headed nail should be driven to a firm Minimum ground clearance depth. of line of sight (m) ..... ,.... 0.5 0.5 0.5 0.5 0.5 Even number of setups when not using leveling CalibrationProcedures rods with detailed calibration ...... yes yes yes yes Order First First Second Second Third Determinetemperature Class I II I II gradient forthe vertical range of the line of sight Levelinginstrument at each setup ...... yes yes yes Maximum collimation error, Maximum section single line of sight (mm/m) .... 0.05 0.05 0.05 0.05 0.10 Maximum collimationerror, misclosure· (mm) ...... 3 yD 4yD 6yD 8yD 12yD reversible compensator type Maximum loop 5y 6yE 8yE 12yE instruments, mean of two misclosure (mm) ...... 4yE E lines of sight (mm/m) ...... 0.02 0.02 . 0.02 0.02 0.04 Single-runmethods Time intervalbetween collimation Reverse direction of single error determinations not runsevery half day...... yes yes yes longer than (days) Reversible compensator ...... 7 7 . 7 7 7 Nonreversible compensator Other types ...... 1 1 1 1 7 levelinginstruments · Maximum angular difference Off-level/relevel between two lines of sight, instrument between reversible compensator ...... 40" 40" 40" 40" 60" observing the high and low rodscales...... yes yes yes Leveling rod Minimum scale calibration 3-wiremethod standard...... N N N M M Reading check (difference Time intervalbetween between top and bottom scale calibrations (yr)...... intervals) for one setup not to exceed (tenths of Leveling rodbubble verticality rodunits) ...... 2 2 3 maintained to within ...... 10' 10' 10' 10' 10' Read rod1 firstin alternate setup method... yes yes yes (N-National standard)

(M--;-Manufacturer'sstand ard) Doublescale rods Low-high scale elevatiqn Compensator-type instruments should be checked for differencefor one setup proper operation at least every 2 weeks of use. Rod not to exceed (mm) With reversible calibration should berepeated whenever the rodis droppedor compensator...... 0.40 1.00 1.00 2.00 2.00 damaged in any way. Rod levels should· be checked for Otherimtrument types: proper alignment once a week. The manufacturer's Half-centimeterrods .... 0.25 0.30 0.60 0.70 1.30 calibration standard should, as a minimum, describe scale Full-centimeterrods ... 0.30 0.30 0.60 0.70 1.30 behavior with respect to temperature. (SRDS-Singlo-Run,Double Simultaneousprocedure) (DR-Doublo-Run) Field Procedures (SP-SPur,less than 2� km,doublo-run) D-shortestlength of section (ono-way)in km £-perimeter

3-7 (alternate setup method). The date, beginning and ending 3.6 Photogrammetry times, cloud coverage, air temperature (to· the nearest degree), temperature scale, and average wind speed should PhotograD;1metry is a measurement system comprised of photographs taken by a precise metric camera and be. recorded for. each section plus any changes in the date ' mstrumentation, observer or time zone. The instrument measured by a comparator. Photogrammetry is used for densification of horizontal control. The following specifi­ (_ n�d not be off-leveled/releveled between observing the high and low scales when using an instrument with a cations apply only to analytic methods. reversible compensator. The low-high scale difference tolerance for a reversible compensator is used only for the Network Geometry · . . control of blunders. Order Second Second Third Third With double scale. rods, the following observing sequence Class I II I II should be used: Forwardoverlap not lessthan ...... 66% 66% 60% 60% backsight, low-scale Side overlap not Jess than ...... 66% 66% 20% 20% backsight, stadia Intersecting rays per pointnot foresight,low-scale lessthan ( design criteria) ...... 9 . 8 3 3 foresight, stadia off-leveJ/relevelor reverse compensator foresight,high-scale The photogrammetric survey should be areal:- single backsight, high-scale strips of photography are not acceptable. The survey should en�ompass, ideally, a minimum of eight horizontal con: OfficeProcedures trol points and four vertical points spaced about the perimeter of the survey. In addition, the horizontal con­ Order First . First Second Second Third Class I II I Ii trol points should be spaced no farther apart than seven air bases. The horizontal control points should have an Sectionmisclosures order (and class) .better than the intended order (and class) (backwardand forward) of the survey. The vertical points need not meet geodetic Algebraic sum of all correctedsection misclosures con�ol standards. If the required control points are not of� leveling line available, then they must be established by some other not to exceed (mm) ...... 3yD 4yD 6yD SyD 12yD measurement system. Section misclosurenot to exceed (mm) ...... 3yE 4yE 6yE SyE 12yE ( c:J . Instrumentation Loopmisclosures Algebraic sum of all Order Second Second Third Third correctedmisclosures Class I II I II not to exceed (mm)...... 4yF 5yF 6yF SyF 12yF Loopmisclosure not MetricCamera to exceed(mm) ...... 4yF 5yF 6yF SyF 12yF Maximum warp of platen not more than (µm)...... ,...... 1� 10 10 10 Dimensional control not (O-hortestlength of leveling line (on(}-way)in km) Jess than...... reseau 8 8 8 (8-horteston(}-way length of sectionin km) with fiducials fiducials fiducials (F-lengthof loopin km) maximum spacing The normalized residuals from a minimally constrained of2 cm least squares adjustment will be checked for blunders. Comparator The observation weights will be checked by inspecting the Least count(µm) ...... postadjustment estimate of the variance of unit weight. Elevation difference standard errors computed by error The camera should be of at least the quality of those P1:°P8:ga�on in a correctly weighted least squares adjustment will mdicate the provisional accuracy classification. A employed for large-scale mapping. A platen should be survey variance factor ratio will be computed to check for included onto which the film must be satisfactorily flat­ tened during exposure. Note that a reseau should be used systematic error. The least ;quares adjustment will use forsecond-order, classI surveys. modelsthat account for: gravity effector orthometric correction CalibrationProcedures rodscale errors rod(Invar) temperature Order Second Second Third Third refraction-need latitude and longitude to 6" or vertical tempera­ Class I II I II ture difference. observations between 0.5 and 2.5 m above the ground Metriccamera earthtides and magnetic field Rootmean square of calibrated collimationerror radial distortion not more crustal motion than(µm) ...... - 3 3 5 3-8 Calibration Procedures-Continued A least squares adjustment of the photocoordinates, constrained by the coordinates of the horizontal and ver­ Order Second Second Third Third tical control points, will bechecked for blunders by examin­ -� Class I 11 I II ing the normalized residuals. The observation weights () Root mean square of calibrated will be checked by inspecting the postadjustment esti­ (L decentering distortion not more mate of the variance of unit weight. Distance standard than (!Lm) ...... st st st errors computed by error propagation in this correctly Root mean square of reseau weighted least squares adjustment will indicate the provi­ coordinates not more than (!Lm) .... 3 3 sional accuracy classification. A survey variance factor Root mean square of fiducial coordinatesnot more than (!Lm).... 3 3 ratio will be computed to check for systematic error. The least squares adjustment will use models that incorporate t not usually treated separately in camera calibration facilities; manufacturer's the quantities determined by calibration. certificationis satisfactory. The metric camera should be calibrated every 2 years, and the comparator should be calibrated every 6 months. 3. 7 Satellite Doppler Positioning These instruments should also be calibrated after repair Satellite Doppler positioning is a three-dimensional or modifications. measurement system based on the radio signals of the Characteristics of the camera's internal geometry (radial U.S. Navy Navigational Satellite System (NNSS), symmetric distortion, decen�ered lens distortion, princi­ commonly referred to as the TRANSIT system. Satellite pal point and point of symmetry coordinates, arid reseau Doppler positioning is used primarily to establish hori­ coordinates) should be determined using recognized cali­ zontal control. bration techniques, like those described in the. current The Doppler observations are processed to determine edition of the Manual of Photogrammetry. These charac­ station positions in Cartesian coordinates, which can be teristics will be applied as corrections to the measured transformed to geodetic coordinates (geodetic latitude · image coordinates. and longitude and height above reference ellipsoid). There are two methods by which station positions can be derived: FieldProcedures point positioningand relative positioning. Photogrammetry invoives hybrid measurements: a metric Point positioning, for geodetic applications, requires camera photographs targets and features in the field, and that the processing of the Doppler data be performed with a comparator measures these photographs in an office the precise ephemerides that are supplied by the Defense environment. Although this section is entitled "Field Pro­ Mapping Agency. In this method, data from a single cedures," it deals with the actual measurement proce�s and thus includes comparator specifications.· station is processedto yield the station coordinates. Relative positioning is possible when two or more receivers are operated together in the survey area. The processing of the Doppler data can be performed in four modes: Order Second Second Third Third simultaneous point positioning, translocation, semishort Class I 11 I II arc, and short arc. The specifications for relative positioning Targets are valid only for data reduced by the semishort or short Control points targeted ...... yes yes yes yes arc methods. The semishort arc mode allows up to 5 Pass points targeted ...... yes yes optional optional degrees of freedomin the ephemerides; the short arc mode Comparator allows 6 or more degrees of freedom. These modes allow Pointings per target not less than ...... 4 3 2 2 the use of the broadcast ephemerides in place of the Pointings per reseau (or fiducial) precise ephemerides. not less than ...... 4 3 2 2 Number of differentreseau The specifications quoted in the following sections are intersections per target not based on the experience gained from the analysis of Doppler Jess than ...... 4 surveys performed by agencies of the Federal gov�rn­ Rejection limit from mean of ment. Since the data are primarily from surveys performed paintings per target (!Lm)...... 3 3 3 3 within the continental United States, the precisions and related specifications may not be appropriate for other OfficeProcedures areas of the world.

Order Second Second Third Third NetworkGeometry Class I II I 11 The order of a Doppler survey is determined by: the j spacing between primary Doppler stations, the order of Rootme1rn square of ad usted base network stations from which the primaries are photocoordinates not more the f-~C) than (!Lm) ...... 4 6 8 12 established, and the method of data reduction that is �-,/ used. The order and class of a survey cannot exceed the

3-9 lowest order (and class) of the base stations used to estab­ lish the survey. Order First Second Second Third Third 1 II 1 11 The primary stations should be spaced at regular inter­ Class (cm) vals which meet or exceed the spacing required for the sp D(km) desired accuracy of the survey. The primary stations will 200...... 566 242 114 56 28 carry the same order as the survey. 100...... 283 141 57 28 14 ( Supplemental stations may be established in the same 70 ...... 200 100 40 20 10 50 ...... 141 71 26 14 7 survey as the primary stations. The lowest order (and class) of a supplemental station is determined either by its spacing with, or by the order of, the neares� Doppler or Relative Positioning other horizontal control station. The processing mode determines the allowable station spacing. D = 2 sr3- In carrying out a Doppler survey, one should occupy, where using the same Doppler equipment and procedures, at a = denominator of distance accuracy classification least two existing horizontal network (base) stations of standard (e.g., a= 100,000for first-order stand ard). order (and class) equivalent to, or better than, theintended order (and class) of the Doppler survey. If the Doppler survey is to be first-order, at least three base stations Order First Second Second Third Third ,.; must be occupied. If relative positioning is to be used, all Class I 11 I II base station base lines must be directly observed during sr (cm) D(km) the survey. Base stations should be selected near the 50 ...... 100 50 20 10 5 perimeter of the survey, so as to encompass the entire 35 ...... 70 35 14 7 4 survey. 20 ...... ,,...... 40 20 8 4 2 Stations which have a precise elevation referenced by geodetic leveling to the National Geodetic Vertical Datum However, the spacing for relative positioning should (NGVD) are preferred. This will allow geoidal heights to not exceed 500 km. be determined. As mariy base stations as p<:>ssible should Instrumentation If is be tied to the NGVD. a selection to be made, those The receivers should receive the two carrier frequen­ stations should be chosen which span· the largest portion cies transmitted by the NNSS. The receivers should record of the survey. the Doppler count of the satellite, the receiver clock ( If none of the selected base stations is tied to the times, and the signal strength. The integration interval NGVD, at least two, preferably more, bench marks of the should be approximately 4.6 sec. Typically six or seven of NGVD should be occupied. An attempt should be made these intervals are accumulated to form a 30-second to span the entire surveyarea. Doppler count observation. The reference frequency should 11 Datum shifts for transformation of point position solu­ be stable to within 5.0(10- ) per 100 sec. The maximum tions should be derived from the observations made on the difference from the average receiver delay should not base stations. exceed 50 µsec. The best estimate of the mean electrical The minimum spacing, D, of the Doppler stations may center of the antenna should be marked. This mark will be be computed by a formula determined by the processing the reference pointfor all height-of-antennameasurements. mode to be employed. This spacing is also used in con­ Calibration Procedures junction with established control, and other Doppler Receivers should be calibrated at least once a year, or control, to determine the order and class cif the supple­ whenever a modification to the equipment is made. It is mental stations. desirable to perform a calibration before every vroject to By using the appropriate formula, tables .can be con­ verify that the equipment is operational. The two-receiver structed showing station spacing as a function of point or method explained next is preferred and should be used whenever possible. relative one-sigma position precision (sp or sr) and desired survey (or station) order. Two-ReceiverMethod Point Positioning The observations are made on a vector base line, of internal accuracy sufficient to serve as a comparison standard, 10 to 50 m in length. The base line should be locatedin an area free of radio interference in the 150 and where 400 MHz frequencies. The procedures found in the tal;,le a == denominator of distance accuracy classification on relative positioning in "Field Procedures" under the 20 standard (e.g., a = 100,000 for first-order stand­ cm column heading will be used. The data are reduced by ard). either shortarc or semishort arc methods. The receivers \... 3-10 will be considered operational if the differences between The antenna should be located where radio interference the Doppler and the terrestrial base line components do is minimal for the 150 and 400 MHz frequencies. Medium not exceed 40 cm (along any coordinateaxis). frequency radar, high voltage power lines, transformers, excessive noise from automotive ignition systems, and Single-ReceiverMethod high power radio and television transmission antennas Observations are made on a first-order station using should be avoided. The horizon should not be obstructed the procedures found in the table on relative positioning above 7.5 ° . in "Field Procedures" under the 50 cm column heading. The antenna should not be located near metal struc­ The dat� are reduced with the precise ephemerides. The tures, or, when on the roof of a building, less than 2 m resultant position must agree within 1 m of the network from the edge. The antenna must be stably located within position. 1 mm over the station mark for the duration of the observations. The height difference between the mark Field Procedures and the reference point for the antenna phase center The following tables of field proceµures are valid only should be measuredto the nearestmillimeter. If an antenna is for measurements made with the Navy Navigational Sa­ moved while a pass is in progress,· that pass is not accept­ tellite System (TRANSIT). able. If moved, the antenna should be relocated within 5 mm of the original antenna height; otherwise the data Point Positioning may have to be processed as if two separate stations were established. In the case of a reoccupation of an existing s (precise ephemerides) 50 cm 70 cm JOOcm 200 cm P Doppler station, the antenna should be relocated within 5 Max. standard deviation of mean mm of the originalobserving height. of counts/pass (cm), bfoadcast Long-term reference frequency drift should be moni­ ephemerides...... 25 25 25 25 tored to ensure it does not exceed the manufacturer's Period of observationnot less specifications. than (hr) ...... 48 36 24 12 Number of observed passes not Observations- of temperature and relative humidity should less thant ...... ·" 40 30 15 8 be collected, if possible, at or near the height of the phase Number of acceptable passes center of the antenna. Observations of wet-bulb and dry­ ( evaluated by on-site point bulb temperature readings should be recorded to the nearest processing)not less than...... 30 20 9 4 Minimum number of acceptable 0.5 • C. Barometric readings at the station site should be passes within each quadrant*...... 6 4 2 recorded to the nearest millibar and corrected for differ­ Frequency standard warm-up ence in height between the antenna and barometer. time (hr) crystal...... 48 48 24 24 atomic...... :...... 1.5 1.5 1.0 1.0 Office Procedures Maximum interval between The processing constants and criteria for determining meteorological observations (hr).... 6 § § § the quality of point and relative positioning results are as follows: t Number of passes refers to those for which the precise ephemerides are available forreduction. 1. For all passes for a given station occupation, the • There should be a nearly equal numberof northwardand southward passes. average number of Doppler counts per pass should § each setup, visit and takedown. be at least 20 (beforeprocessing). Relative positioning 2. The cutoff angle for both data points and passes should be 7 .5 • . 3. For a given pass, the maximum allowable rejection s, 20 cm 35 cm 50 cm of counts, 3 sigma postprocessing, will be 10. Maximum standard deviation of mean of 4. Counts rejected (excluding cutoff angle) for a solu­ counts/pass (cm), broadcast ephemerides ... 25 25 25 Period of observationnot less than (hr) ...... 48 36 24 tion should be less thap. 10 percent. Number of observed passesnot less thant...... 40 30 15 5. Depending on number of passes and quality of data, Number of acceptable passes (evaluated the standard deviation of the range residuals for all by on-site point positionprocessing) not less than ...... 30 20 9 passes of a solution should range between: Minimum number of acceptable passes Point positioning-IO to 20 cm within each quadrant* ...... 6 4 2· Relative positioning-5 to 20 cm Frequency standard warm-up time (hr) crystal...... 48 48 48 A minimally constrained least squares adjustment will atomic...... 1.5 1.5 1.5 be checked for blunders by examining the normalized Maximum interval between meteorological residuals. The observation weights will be checked by observations (hr) _...... 6 6 § inspecting the postadjustment estimate of the variance of t Number of observed passes refers to all satellites available for tracking and unit weight. Distance standard errors computed by error reduction with the broadcast or preciseephemerides. propagation between points in this correctly weighted • Numberof northward and southwardpasses should benearly equal. § Each setup, visit and takedown. least squares adjustment will indicate the maximum. achiev-

3-11 able accuracy classification. The formula presented in gy considered sufficiently accurate for absolute gravity "Standards" will be used to arrive at the actual classification. measurements. An absolute instrument measures gravity . (--1 The least squares adjustment will use models which ·account at a specific elevation above the surface, usually about 1 "/C1ror: m. For this reason, the gravity value is referenced to that level. A measurement of the vertical gravity gradient, tropospheric scale bias, 10 percentuncertainty receiver time delay using a relative gravity meter and a tripod, must be made satellite/receiver frequency offset to transfer the gravity value to ground level. Theaccuracy c· precise ephemeris of the relative gravimeter must satisfy the gravity gradi­ troposphericrefraction ent specificationsfound in "Field Procedures." ionospheric refraction long-term ephemeris variations crustal motion CalibrationProcedures Ballistic-laser instruments are extremely delicate and each one represents a unique entity with its own charac­ 3.8 Absolute Gravimetry teristics. It is impossible to identify common systematic errors for all instruments. Therefore, the manufacturer's Absolute gravimetry is a measurement system which recommendations for individual instrument calibration determines the magnitude of gravity at a station at a should be followedrigorously. specific time. Absolute gravity measurements are used to · To identify any possible bias associated with a particular establish and extend gravity control. Within the context instrument, comparisons with other absolute devices are of a geodeticgravity network, as discussed in "Standards," a strongly recommended whenever possible. Comparisons series of absolute measurements at a control point is in with previously established first-order, class I network itself sufficient to establish an absolute gravity value for points, as well as first-order, class II network points tied that location. to the class I points, are also useful. The value of gravity at a point is time dependent, being subject to dynamic effects in the Earth. The extent of gravimetric stability can be determined only by repeated FieldProcedures __. . observations over many years. The following specifications were determined from results of a prototype device built by J. Faller and M. Zumberge NetworkGeometry (Zumberge, M, "A Portable Apparatus for Absolute Mea­ Q Network geometry cannot by systematized since abso­ surements of the Earth's Gravity," Department of Physics, C; ' lute observations at a specific location ar� discrete and University of Colorado, 1981) and are given merely as a ( . uncorrelated with other points. In absolute gravimetry, a guideline. It is possible that some of these. values may be network may consist of a single point. inappropriate for other instruments or models. Therefore, A first-order, class l station must possess gravimetric exceptions to these specifications are allowed on a case­ stability, which only repeated measurements can deter­ by-case basis upon the recommendation of the manufac­ mine. This gravimetric stability should not be confused turer. Deviations from the specifications should be poted with the accuracy determined at a specific time. It is upon submissionof data forclassification. possible for a value to be determined very precisely at two different dates and for the values at each of these respec­ tive dates to differ. Although the ultimate stability of a Order First First Second Third point cannot be determined by a single observation ses­ Class I II sion, an attempt should be made to select sites which are believed to be tectonically stable, and sufficiently distant Absolutemeasurement ·from large bodies of water to minimize ocean tide coastal Standard deviation of each loading. accepted measurementset The classification of first-order, class I is reserved for not to exceed(µGal) ...... 20 20 50 100 network points which have demonstrated long-term sta­ Minimum number of sets/ bility.To ensure this stability, the point shou1dbe reobserved observation...... 5 s 5 5 Maximum differenceof a at least twice during the year of establishment and there­ measurementset from meanof after at sufficient intervals to ensure the continuing sta­ all measurements(µGal) ...... 12 12 37 48 bility of the point. The long-term drift should indicate Baroinetricpressure standard that the value will not change by more than 20 µGal for at error(mbar) ...... 4 4 least 5 years. A point intended as first-order, class I will initially be classified as first-order, class II until stability Gradientmeasurement Standard deviation of measurement duringthe firstyear is demonstrated. of verticalgravity gradient at time of observation(µGal/m) ...... 5 5 5 5 , _J ! Instrumentation Standard deviation of height of ( )�/ The system currently being used is a ballistic-laser instrumentabove point(mm) ...... 5 10 _ device and is the only one at the current state of technolo-

3-12 OfficeProcedures minimum connecting requirement if the intended order of The manufacturer of an absolute gravity instrument the new surveyis lessthan first-order. usually provides- a reduction process. which identifies and accounts for error sources and identifiable parameters. Instrumentation This procedure may be sufficient, making further office Regardless of the type of a relative gravimeter, the adjustments unnecessary. internal error is of primaryconcern. A least squares adjustment will be checked for blun­ ders by examining the normalized residuals. The observation weights will be checked by inspecting the postadjustment Order First First Second Third estimate of the variance of unit weight. Gravity value Class I II standard deviations compu�ed by error propagation in a Minimum instrument internal correctly weighted, least squares adjustment will indicate ( ) (µ ) the provisional accuracy classification. The least squares error one-sigma , Gal ...... 10 10 20 30 adjustment, as well as digital filtering techniques and/or sampling, should use modelswhich account for: The instrument's internal accuracy may be determined by performing a r�lative survey over a calibration line (see atmospheric massattraction microseismicactivit y below) and examining the standard deviation of a single instrumentalcharacteristics · reading. This determination should be performed after lunisolar attraction the instrument is calibrated using the latest calibration elastic and plastic response of the Earth( tidal loading) information. Thus the internal error is the measure of instrument' uncertainty after all possible systematic error sources have been eliminatedby calibration. 3.9 Relative_Gravimetry Relative gravimetry is a measurement system which CalibrationProcedures determines the difference in magnitude of gravitybetween An instrument should be properly calibrated before a two stations. Relative gravity measur�ments · are used to geodetic survey is performed. The most important cali­ extend and densify gravity control. bration item is the determination of the mathematical model that relates dial units, voltage, or some other NetworkGeometry observable to milligals. This may consist only of a scale A first-order, class I station must possess gravimetric factor. In other cases the model may demonstrate nonlin­ stability, which only repeated measurements can deter­ . earity or periodicity. Most manufacturers provide tables mine. This gravimetric stability should not be confused or scale factors with each instrument. Care must be taken with the accuracy determined at a specific time. It is to ensure the validity of thesedata over time. possible for a value to be determined veryprecisely at two When performing first-order work, this calibration model · different dates, and for the values at each of these respec­ should be determinedby a combination of bench tests and tive dates to differ. Although the ultimate stability of a field measurements. The bench tests are specified by the point cannot be determined by a single observation ses­ manufacturer. A field calibration should be performed sion, an attempt should be made to select sites which are over existing control points of first-order, class I or II. believed to be tectonicallystable. The entire usable gravimeter range interval should be The classification of first-order, class I is reserved for sampled to ensure an uncertainty of lessthan 5 µGal. FGCC network points that have demonstrated long-term sta­ member agencies have established calibration lines for bility. To ensure this stability,the point should be reobserved this specificpurpose. at least twice during the year of establishment and there­ The response of an instrument to air pressure and tem­ after at sufficient intervals. The long-term drift should · peratureshould be determined. Themeter shouldbe adjusted indicate that the value will not change by· more ·than the (?r calibrated for various pressures and temperatures so 20 µGal for at least 5 years. A point intendedas first-order, that the allowable uncertainty from these sources does not class I will initially be classified as first-order, class II exceed the valuesin the table below. until stability during the firstyear is demonstrated. The manufacturer's recommendations should be fol­ The new survey is required to tie at least two network lowed to ensure that all internal criteria, such as galva­ poip.ts, which should have an order (and class) equivalent nometer sensitivity, long and cross level or tilt sensitivity, to or better than the intended order (and class) of the new and reading line, are within the manufacturer's allowable survey. This is required to check the validity of existing tolerances. network points as well as to ensure instrument calibration. The response of an instrument due to local orientation Users are encouraged to exceed this minimal require­ should also be determined. Systematic differences may be ment. However, if one of the network stations is a first­ due to an instrument's sensitivity to local magnetic varia­ order, class I mark, then that station alone can satisfy the tions. Manufacturers attempt to limit or negate such a response. However, if a meter displays a variation with respect to orientation, then one must either have the The modified ladder sequence also begins and ends at instrument repaired by the manufacturer, or minimize the same network, point. However, not all the survey points the effect by fixing the orientation of the instrument are observed twice during the sequence. Again, more than (�;·· · (l throughout a survey. one network point may be observed in the sequence. The line sequence begins at a network point and ends at a different network point A surveypoint in a line sequence is Order First First Second Third usually observed only once. Class I II One should always monitor the internal temperature of Necessaryfor user to determine the instrument to ensure it does not fluctuate beyond the calibration model...... Yes Yes Yes No manufacturer's recommended limits. The time of each Allowable uncertainty of reading should be recorded to the nearest minute. calibration model(µGal) ...... s s 10 15 Allowable uncertainty due to externalair temperature OfficeProcedures changes (µGal) ...... 3 Maximum uncertainty due to First First Second Third external airpressure Order I II changes (µGal) ...... 2 Allowable uncertainty due to Rejectionlimits .,.. Maximum standard errorof a other factors(µGal) ...... 3 3 5 gravity value (µGal) ...... 20 20 so 100 • Total allowable instrument uncertainty (µGal) ...... 10 10 FieldProcedures 20 30 'A relative gravity survey is performed.. using a sequence ModelUncertainties of measurements known as a loop sequence. There are Uncertainty of atmosphericmass model (µGal) ...... 0.5 0.5 three common types: ladder, modifiedladder, and line. Uncertainty of lunisolar The ladder sequence begins and ends at the same net­ attraction (µGal) ...... : ...... s s work point, with the survey points being observed twice Uncertainty of Earthelastic and during the sequence: once in forward running and �mce in plastic responseto tidal backward running. Of course, more than one network loading (µGal) ...... 2 2 s �-- /'\ point may be present in a ladder sequence. . . L�--) . . A least squares adjustment, constrained by the network configuration and precision of established gravity con­ (. Order First First Second Third trol, will be checked for blunders by examining the nor­ Class I II malized residuals. The observation weights will be checked Minimum number of instruments by inspecting the postadjustment estimate of the variance used in survey...... 2 2 2 Recommended number of of unit weight. Gravity standard errors computed by error propagation in a correctly weighted least squares adjust­ instruments used in survey ...... 3 3 2 1 Allowable loopsequence ...... a a a,b a,b,c ment will· indicate the provisional accuracy classification.

Minimum number of readings at / A survey variance factor ratio will be computed to check each observation/instrument...... V s s 2t for systrmatic error. The least squares adjustment will Standard deviation of consecutive use models which account for: readings (undamped) from mean* not to exceed (µGal) ...... s instrumentcalibrations Monitor externaltemperature and 2 2 1) conversion factors (linear and higher order) air pressure ...... • Yes Yes No No 2) thermal response (if necessary) Standard deviation of temperature 3) atmospheric pressure response (if necessary) measurements (" C) ...... Standard deviation of air pressure 0.1 0.1 instrument dnft static measurement (mbar) ...... 1 1) Standard deviation of height of 2) dynamic instrumentabove point (mm) ...... s 10 atmospheric mass attraction (if necessary)

(a-ladder) (b-modified ladder) (c--line) Earth tides t Although two readingsare required,only one readingneed be recorded. 1) lunisolar attraction • correctedfor lunisolar attraction. 2) Earthelastic and plastic response (if necessary)

..-- r) ( ,--' (_ '"-...,...,..:

3-14

--��------4. Information

Geodetic control data and cartographic information Federal, State, and local governments, and private that pertain to the National Geodetic Control Networks organizations contribute survey data from their field are widely distributed by a component of the National operations. These are incorporated into the NGS data Geodetic Survey, theNational Geodetic Information Branch base. NOAA has entered into formal agreements with (NGIB). Users of this information include Federal, State, several Federal and State Government agencies whereby and local agencies, universities, private companies, and NGIB publishes, maintains, and distributes geodetic data individuals. Data are furnished in response to individual received from these organizations. Guidelines and for­ orders, or by an automatic mailing service (the mecha­ mats have been established to standardize the data for nism whereby users who maintain active geodetic files processing and inclusion into the NGS data base. These automatically receive newly published data for specified formats are available to organizations interested in areas). Electronic retrieval of data can be carried out participatingin thetransfer of their filesto NOAA (appendix directly fromthe NGS data base by a user. C). Geodetic control data for the national networks are Upon completion of the geodetic data base manage­ primarily published as standard quadrangles of 30' in ment system, · inform!l,tion generated from the data base latitude by 30' in longitude. However, in congested areas, will be automatically revised. A new data output formatis the standard .quadrangles are 15' in latitude by 15' in being designed for both horizontal and vertical published longitude. In most areas of Alaska, because·of the sparse­ control information. These formats, which were necessi­ ness of control, quadrangle units are 1 • in latitude by 1 • tated by the requirements of the new adjustments of the in longitude. Data are now available in these formats for horizontal and vertical geodetic networks, will be more all horizontal control and approximately 65 percent of the comprehensive than the present versions. vertical control. The remaining 35 percent are presented New micropublishing techniques are being introduced in the old formats; i.e., State leveling lines and description in the form of computer-generated microforms. Some booklets. Until the old format data have been converted to geodetic data are available on magnetic tape, microfilm, the standard. quadrangle formats, the vertical control and microfiche. These services will be expanded as the data in the unconverted areas will be available only by automation system is fully implemented. Charges for digital complete county coverage. Field data and recently adjusted data are determined on the basis of the individual requests, projects with data in manuscript form are available from and reflect processing time, materials, and postage. The NGS upon special request. The National Geodetic Con­ booklets Publications of the National Geodetic Survey trol Networks are cartographically depicted on approxi­ and Products and Services of the National Geodetic Sur-. mately 850 different control diagrams. NGS provides vey are available fromNGIB. other related geodetic information: e.g., geoid heights, For additional information, write: deflections of the vertical, calibration base lines, gravity Chief, National GeodeticInformation values, astronomic positions, horizontal and vertical data Branch, N/CG17 for crustal movement studies, satellite-derived. positions, National Oceanic and AtmosphericAdministration UTM coordinates, computer programs, geodetic calcula­ Rockville, MD 20852 tor programs, and reference materials from the NGS data To order by telephone: bases. data: ...... 301-443-8631 The NGIB receives data from all NOAA geodetic field publications: ...... 301-443-8316 operations and mark-recovery programs. In addition, other computer programsor digital data: ...... 301-443-8623

4-1 5. References

(Specialreference lists� foil ow appendixesA andB)

Basic GeodeticInformation lication 4, U.S. Coast and Geodetic Survey, Rock.ville, Bomford, G., 1980: Geodesy (4th ed.). Clarendon Press, Md., 14 pp. (revision of Special Publication 247, by Oxford, England, 855 pp. Gossett, F., 1959, pp. 84-94). Defense Mapping Agency, 1981: Glossary of Mapping, Defense Mapping Agency, 1975: Field Operations Man­ Charting, and Geodetic Terms ( 4th edition), Defense ual-Doppler Point Positioning. Defense Mapping Agen­ Mapping Agency Hydrographic/Topographic Center, cy Tech. Manual TM-T-2-52220, Department of Washington, D.C., 203 pp. Defense, 76 pp. Mitchell, H., 1948: Definitions of terms used in geodetic Dewhurst, w.; 1983: Input Formats and Specifications of and other surveys, Special Publication 242, U.S.. Coast the NationalGeodetic Survey Data Base, vol III: Gravity and Geodetic Survey, Washington, D.C., 87 pp. control data, Federal Geodetic Control Committee, Torge, W., 1980: Geodesy. Walter de Gruyter & Co., New Rock.ville,163 Md., pp. Yorlc, N.Y., 254 pp. Floyd, R., 1978: Geodetic bench ma{ks, NOAA Manual Vanicek, P., and Krakiwsky, E., 1982: Geodesy: The Con­ NOS NGS 1, National Oceanic and Atmospheric cepts. North-Holland Publishing Co., New York, N.Y., Administration, Rock.ville,Md., 50 pp. 691 pp. Gos�ett, F., }950, rev. 1959: Manual of geodetic triangu­ lation, Special Publication 247, U.S. Coast and Geo­ Standards and Specifications detic Survey,Washington, D.C., 205 pp. CC) Director of National Mapping, 1981: Standard Specifi­ Hoskinson, A, and Duerksen, J., 1952: Manual of geodetic cations and Recommended Practices for Horizontal as_tronomy: determination of longitude, latitude, and and Vertical· Control Surveys (3rd edition), Director azimuth, Special Publication 237, U.S. Coast and Geo­ of National Mapping, Canberra, Australia, 51 pp. detic Survey,Washington, D.C., 205 pp. Federal Geodetic Control Committee, 1974: Classifica­ Mussetter, W., 1941, rev. 1959: Manual of reconnais­ tion, Standards of Accuracy, and General Specifica­ sance for triangulation, Special Publication 225, U.S. tions of Geodetic Control Surveys, National Oceanic Coast and Geodetic Survey,Washington, D.C. 100 pp. and Atmospheric Administration, Rock.ville, Md., 12 Pfeifer, L., 1980: Input Formats and Specifications of the pp. National Geodetic Survey Data Base, vol I: Horizontal Federal Geodetic Control Committee, -1975, rev. 1980: Specifications to Support Classification, Standards control data, Federal Geodetic Control Committee, of Accuracy, and General Specifications of 'Geodetic Rock.ville,Md., 205 pp. Control Surveys, National Oceanic and Atmospheric Pfeifer, L., and Morrison, N., 1980: Input Formats and Administration, Rock.ville,Md., 46 pp. Specifications of the National Geodetic Survey Data Surveys and Mapping Branch, 1978 : Specifications and Base, vol. II: Vertical control data, Federal Geodetic Recommendations for Control Surveys and Survey ControlCommittee, Rock.ville, Md. 136 pp. Markers, Surveys and Mapping Branch, Ottawa, Schomaker, M., and Berry, R., 1981: Geodetic lev�ling, Canada. NOAA Manual NOS NGS 3. National Oceanic and AtmosphericAdministration, Rock.ville, Md. 209 pp. Manuals on FieldProcedures Slama, C. (editor), 1980: Manual of Photogrammetry Baker, L., 1968: Specifications for horizontal control marks, ( 4th edition), American Soi;:iety of Photogrammetry, ESSA Tech. Memo. Coast and "Geodetic Survey Pub- Falls Church, Va., 1056 pp.

5-1 APPENDIXA GovernmentalAuthority

A.1 Authority for Geodetic Control and Related Surveys was appointed April 4, 1969. The FGCC Circular No. 1, "�xchange of The U.S. Department of Commerce's National Qceanic Information," dated October 16, 1972, prescnbes report­ and Atmospheric Administration (NOAA) is responsible ing procedures for the committee (vice Exhibit C of Cir­ for establishing and maintaining the basic national hori­ cularA-16) (FederalGeodetic Control Committee 1972). zontal, vertical, and gravity geodetic control networks to The Federal Coordinator for Geodetic Control and Relat­ meet the needs of the Nation. Within NOAA this task is ed Surveys, Department of Commer�, is responsible for assigned to the National Geodetic Survey, a Division of coordinating, planning, and executing national geodetic the Office of Charting and Geodetic Services within the control surveys and related survey activities of Federal National Ocean Service. This responsibility has evolved agencies, financed in whole or in part by Federal funds. from iegislation dating back to the Act of February 10, The Executive Directive (Bureau of the Budget 1967: p. 1807 (2 Stat. 4131 which created the first scientific Fed­ 2) states: eral agency, known as the "Survey of the Coast." Current . (1) The geodetic control needs of Government agen­ authority is contained in United States Code, Title 33, cies and the public at large are met in the most USC 883a, as amended, and specifically defined by Execu­ · expeditious and economical manner possible with tive Directive, Bureau of the Budget (now the Office of available resources; and Management and Budget) Circular No. A-16, Revised (2) all surveying activities financed in whole or in part (Bureau of theBudget 1967). Federal funds contribute to the National Net­ To coordinate national mapping, charting, and survey­ by ing activities, the Board of Surveys and Maps of the works of Geodetic Control when it is practicable Federal Government was formed December 30, 1919, by and economical to do so. Executive Order No. 3206. "Specifications for Horizon­ The Federal Geodetic Control Committee assists �nd tal and Vertical Control" were agreed upon by Federal advises the Federal Coordinator for Geodetic Control and surveying and mapping agencies and approved by the Related Surveys. Board on May 9, 1933. When the Board was abolished March 10, 1942, its functions were transferred to the Bureau of the Budget, now the Office of Management and A.2 References Budget, by Executive Order No. 9094. The basic survey Bureau of the Budget, 1967: Coordination of surveying specifications continued in effect. Bureau of the Budget and mapping activities. Circular No. A-16, Revised, Circular No. ,A.-16, published January 16, 1953, and revised May 6, 1967 (Bureau of the Budget 1967), pro­ May 6, 3 pp. Executive Office of thePresident, Bureau vides for the coordination of Federal surveying and map­ of the Budget (now Office of Management and Bud­ ping activities. "Classification and Standards of Accura­ get), Washington, D.C. 20503. Bureau of the Budget, 1958: Programing and coordina­ cy of Geodetic Control Surveys," published March 1, Transmittal Memo­ 1957, replaced the 193� specifications. Exhibit C to Cir­ tion of geodetic control surveys. randum Circular cular A-16, dated October 10, 1958 (Bureau of the Bud­ No. 2, 1 p., and Exhibit C of No. get 1958), established procedures for the required coordi­ A-16, 4 pp. Executive Office of the President, Bureau nation of Federal geodetic and control, surveys performed of the Budget (now Office of Management and Bud­ in accordance with the Bureau of the Budget classifica­ get), Washington, D.C. 20503. tions and standards. Federal Geodetic Control Committee, 1972: Exchange of The Federal Ge'odetic Control Committee (FGCC) was Information. Circular No. 1, Federal Geodetic Control chartered December 11, 1968, and a Federal Coordinator Committee, October 16, 6 pp.

A-1 APPENDIXB Variance Factor Estimation

B.1 Introduction The classification accuracies for the National Geodetic where ½ is the vector of actual observations and La is the Control Networks measure how well a survey can provide vector described above. position, elevation, and gravity. (More specifically, a dis­ tance accuracy is used for horizontal networks, and an Associated with the observation vector ½ is a symmet­ elevation difference accuracy is used for vertical networks.) ric variance-covariance matrix l":11,, which contains infor- The interpretation of what is meant by "how well" con­ mation on observationprecision and correlation. tains two parts. A survey must be precise, i.e., fairly free The observation equation may now be written in linear­ of random error; it must also be accurate, i.e., relatively ized form free of systematic error. This leads to a natural question of how to test forrandom and systematic error. AX=L+V Testing forrandom error is an extremely broad subject, and is not examined here. It is assumed that the standard where V is a vector of residual errors and X is a vector of deviation of distance, elevation difference, or gravity pro­ corrections to the parameter vector �- The least squares videsan adequate basis to describe the amount of random estimate of X is error in a survey. Furth�r, it is assumed that the· selection 1 1 X = (N(l": YA)· A1(l":L L of the worst instance of the classification accuracy com- 11, / . puted at all points (or between all pairs of points) provides a satisfactory means of classifying a new survey. This where the superscripts 1 and ·1 denote transpose and inverse procedure may seem harsh, but it allows the user of (of a matrix) respectively. geodetic control to rely better upon a minimum· quality of The estimate provides a new set of values for the survey work. The nominal quality of a survey could be parameters by much higher. Consider the method of observation equations (see Mikhail(1976) fora general discussion):

If the observation model F(Xa) is nonlinear (that is, A is not constant for any set of Xa), then the entire process, starting with the first equation, must be iterated until the where vector X reaches a stationary point. La is a vector of computed values for the observations of Once convergence is achieved, La, computed from the dimension n, first equation, is the vector of adjusted observations. The Xa is a vector of coordinate and model parameters of vector of observationresidual errors,V, is dimension u, and F is a vector of functions that describes the observations in terms of the parameters. The designmatrix, A, is defined as Estimates of parameter precision and correlations are given by the adjusted parameter variance-covariance matrix, l":x computed by a

l":x = (A1(l":L/1A)·l. where A is a matrix of differentialchanges in theobservation a model F with respect to the parameters, �. evaluated at a The precision of any other quantity that can be derived particular set of parameter values, X0• A vector of from the parameters may also be computed. Suppose one observation misclosures is wishesto compute a vector of quantities,S,

B-1 B.2 GlobalVariance Factor Estimation(k = 1) The global variance factor, f, is simply the a posteriori from the adjusted parameters, Xa. A geometry matrix, G, tr/, is definedas variance of unit weight, when given an a priori vari­ ance of unit weight, rr-02. equal to 1. ( It can be shown that

E(Vt(�L,)"1V) = n - u. . (Mikhail 1976: p. 287) where G is a matrix of differential changes in the func­ For a single variance factor tions, S, with respect to the parameters, Xa, evaluated at a particular set of parameter values, X0• By the principle of linear error propagation,

t so that �s=G �xGa = or I }:(yt(}:�)-1v) n - u

or forf to be unbiased (Hamilton 1964, p. 130)

where �s is the variance-covariance matrix of the com­ = E(Vt(}:�)-lV) = yt(}:v-1y f puted quantities. n-u n-u t This last equation is important since its terms are vari­ . . . ,.2 y py . Th1s 1s 1"d entlca 1 hto t e C1orm cr0 = -- , w here p 1s ances and covariances such as those for distance or height 1 n -. u difference. Use of this equation assumes that the model is defined as cr5(}:�)- 1 · not too nonlinear, that the parameter vector � has been Since we are given that u/ = 1, then P = (� )· • Then f adequately estimated by the method of least squares, that · = tr/,as we wished to prove. the design matrix A, the geometry matrix 0-, a,p.d the The derivation assumes that there is no bias in the variance-covariance matrix of the observations �L are residuals (Mikhail 1976), i.e., known. This last assumption is the focal point fo¥ the remainder of this appendix. E(V) = 0. ( We must somehow estimate the n (n + 1)/2 elements of };L· Usually, we know �L subject to some global vari­ However, outliers, as well as systematic errors, can ance factor,f. We would then assume that produce a biased global variance factor. We must be satisfied that the observations contain no blunders, and that our mathematical model is satisfactory in order to use the global variance factor. where = Particular types of systematic errors-global scale or };L the "true" variance-covariance matrix of the ob­ orientation errors-are not detectable in a survey adjust­ servations };f ment. They will not bias the residuals and will not influ­ = initial estimate of variance-covariance matrix of ence the global variance factor. For example, to detect .a the observations global scale error, it must be transformed into a local Our assumption aqout the the structure of � · relative scale error by addition of more data or measurements that to a single factor usually suffices. But this assumption can can discriminate between global and local. be improved if we generalize theidea. Consider a partition 'of the observations into k homogeneous groups. We now (k estimate k different local variance factors B.3 LocalFactor Variance Esfunation = 2,3,... ) Let us separate our observations into k homogeneous groups, and assume that we know the variance-covariance

matrices of all k groups, �-1 , subject to k local variance factors, fi. Then

-r \ As will be discussed later, we may also detect systematic C�-) error if one of the variance components is based on certi­ fiednetwork observations.

B-2 A variety of methods has been proposed that can be used work can be discovered by local variance factor esti­ to estimate local variance factors. Among them are Min­ mation. Of course a systematic error, such as a scale imum Norm Quadratic Unbiased Estimation (MINQUE) factor influencing both thenetwork and the survey, would (Rao 1971), IteratedMlnimum Norm Quadratic Estimation continue to remain hidden. o(� ( \.../) (IMINQE) (Rao 1972), Almost Unbiased Estimation (AUE) (Horn et al. 1975), and Iterated Almost Unbiased Estimation (IAUE) (Lucas 1984). Underlying these methods B.4 Iterated Almost Unbiased Estimation is the assumption that there is no bias in any group of (IAUE) residuals; that is The IAUE method (Lucas 1984) can be used to esti­ mate covariance elements as well as the variance ele­ ments of i1. However, in testing for systematic error we are concerned only with thesurvey and the network vari­ This assumption can be turned to our advantage in the ance factors(k = 2). detection of localsystematic error. A:s suggested by the title, the method is iterative. We Consider the . partition of observations into a network start with the initial values group, subscript N, and a survey group, subscript s (k === 2). Then � and L�, with � set to 1

Let

For an adjustment of the network only, we may estimate

L� =f�L� and for�n adjustment of the survey only, we may estimate

L� = f�L� We now iterate fromi = 0 to convergence where �•s is the global variance factor of the survey observations computed by a least squares adjustment free 1) Perform leastsquares adjustment for of outliers and knownsystematic errors. 1 With perfect information and an unbiased model we :X = (A'P[�)- A'PLL compute fN = f'N and fs = f's· On the·other band, if our model is biased, this may not be the case. In other 1 1 words, we have a linkage between systematic error and 2) L\is' = (Pk)- - A8(A'PLA)- A� consistent estimation of localvariance factors. 3) i+l _ (Vk)1PkVk Now assume that our network observations are certi­ fs fied as having no systematic error, and that we have - tr(��5 Pk) perfe�� �owledge of their weights. Then f'N = 1 and� = i �- In the absence of residual bias in the survey, we should compute fN = 1 and fs = f's· In fact, we could where tr is the trace function. impose a constraint on the computation, fN = 1, to ensure this result. A survey systematic error could. then manifest itself as an increase in fs over f's· There is no guarantee that systematic error in a survey We test forconvergence by will increase fs over f's· For exan;iple, a survey may be connected to the network at only one control point. A scale error local to the survey would remain undetectable with combined variance factor estimation. With a second con­ nection to the network, the survey scale error will begin to where E is a presetquantity > 0. The local surveyvariance be detectable. A:s the survey is more closely connected to factoris the network, the· capability to detect a survey scale error In" becomes much better. We see that systematic error in a fs = ITf k survey that is well-connected to a certified geodetic net- i=O B-3 where m is the number of iterations to convergence. We of the normal equations. Thus, the usual apparatus of can then compute a survey variancefactor ratio, sparse least squares adjustmentscan beretained.

fs/f's B.5 References Computer simulations have shown that when the sur­ ( vey variance factor ratio exceeds 1.5, then the survey Hamilton, Walter Clark, 1964: Statistics in Physical contains systematic error. This rule becomes less reliable Science, The Ronald Press Company, New York. when a surveyis minimally connected to a network. Horn, S.D., Horn, RA, and Duncan, D.B.,1975: Estimat­ We note that for k = 1, the third step of the method ing heteroscedastic variances in linear models, Journal yields of the American Statistical Association, 70, 380-385. Lucas, James R., 1984: A variance component estimation (vipv)i method for sparse matrix applications, unpublished n-u manuscript, NOS, NOAA, Rockville,Md. Mikhail,Edward M., 1976: Observations and Least Squares, It is immediately recognized as the a posteriori esti­ IBP-A Dun-Donnelley publisher,New York. mate of the variance of unit weight. In this special case, Rao, C.R., 1972: Estimation of variance and covariance IAUE convergence is correct,immediate, and unbiased. components in linear models,Journal of the American The IAUE method is particularly attractive from a Statistical Association, 67, 112-115. computational point of view. If liL is diagonal, or nearly Rao, C.R.,· �9?1: Estimation of variance and covariance so, then the requisite elements of liL may · be computed components-MINQUE theory, Journal of Multivan"ate fromelements of lixthi�.t lie completely within the profile Analysis, 1, 257-275.

(

B-4 I

I ��----�------APPENDIXC Procedures for Submitting Data to the National Geodetic Survey

The National Geodetic Survey (NGS) has detennined cal Network. Gravity control surveys must be accom­ that the value to the national network of geodetic obser­ plished to at least second-order standards and tied to the vations performed by other Federal, State, and local National Geodetic Gravity Network. Third-order gravi­ organizations compensates forthe costs of analyzing, adjust­ ty surveys ("detail" surveys) willbe accepted by NGS for ing, and publishing the associated data. Consequently, a inclusion into the NGS Gravity Working Files only in procedure has been established for data from horizontal, accordance with the above mentioned FGCC publication. vertical, and gravity control surveys to be submitted to A clear and accurate station description should be pro­ NGS. Persons submitting data'-mtist adhere· to the require­ vided for all controlpoints. ments stated herein, but in any event, the filial decision of The original field records (or acceptable copies),.including acceptance on data will be the responsibility of the Chief, sketches, record books, and project reports, are required. NGs.· NGS will retain these records in the National Archives. The survey data must be submitted in the format speci­ This is necessary if questions arise concerning the surveys fied in the Federal Geodetic Control Committee {FGCC) on which the adjusted data are based. In lieu of the publication, Input Formats and Specifications of the original notes, high quality photo copies and microfilm are National Geodetic Survey Data Base, which describes acceptable. The material in the original field books or �he procedures for submission of data for adjustment and sheets are needed, not the abstracts or intermediate assimilation into the National Geodetic Survey .data base. computations. Volume I (Horizontal control data), volume II (Vertical Reconnaissance reports should be submitted before begin­ control data) or volume III (Gravity control data) may be ning the field measurements, describing proposed con­ purchased from: nections to the national network, the instrumentation, NationalGeodetic Information Branch (N/CG17x2) and the field proceduresto be used. This will enable NGS National Oceanic and AtmosphericAdministration to comment on the proposed survey, drawing on the informa­ Rockville, MD 20852 tion available in the NGS data base concerning the accu­ Horizontal control surveys must be accomplished to at racy and condition of these points, and to detennine if the least third-order, class I standards and tied to the National proposed survey can meet its anticipated accuracy. This Geodetic Horizontal Network. Vertical control surveys project review saves the submitting agency the expense of must be accomplished in accordance with third-order or placing data that would fail to meet accuracy criteria into higher standards and tied to the National Geodetic Verti- computer-readable form.

* U.S. Government Printing Office : 1985 - 465-281/20664 I ( ' (: �·'--- C-1