US006373396B2 (12> Ulllted States Patent (16) Patent N63 US 6,373,396 B2 Zamfes (45) Date of Patent: Apr. 16, 2002

(54) METHOD FOR PREDICTING SEISMIC (56) References Cited EVE TS N U.S. PATENT DOCUMENTS (76) Inventor? Konstalldinos 5- Zamfes, 1830-10TH 4,359,766 A * 11/1982 Waters et al...... 367/38 Avenue, Ca1gary,A1b9rta (CA), T3C 4,964,087 A * 10/1990 Widrow ...... 367/45

018 5,555,220 A * 9/1996 Minto ...... 340/853.9 5,784,334 A * 7/1998 Sena et al...... 367/47 ( * ) Notice: Subject to any disclaimer, the term of this * _ d b _ patent is extended or adjusted under 35 Cue y exammer U-S-C- 154(k)) by 0 days- Primary Examiner—Van T. Trieu (74) Attorney, Agent, or Firm—Sean W. Goodwin (21) Appl. No.: 09/736,313 (57) ABSTRACT (22) Filed: Dec. 15, 2000 A method for predicting seismic events Wherein measurable (30) FOI‘EigIl APPIiCHtiOII PI‘iOI‘itY Data and calculable parameters relating to alterations in the shape of the , such as centripetal and tidal gravitational Dec. 17, 1999 (CA) ...... 2292803 effects, and gravitational anomalies related to a buildup of (51) Int. Cl.7 ...... G08B 21/00 energy at any given point in the are incorporated With (52) US. Cl...... 340/690; 340/601; 340/853.9; Observations from at least tWO previous, subsequent seismic 367/45 events, to calculate the energy buildup required to result in (58) Field Of Search ...... 340/601, 690, a future Seismic event 340/853.9, 853.1, 854.1; 367/38, 45, 47, 86; 324/344, 347, 348 2 Claims, 6 Drawing Sheets U.S. Patent Apr. 16, 2002 Sheet 1 6f 6 US 6,373,396 B2 U.S. Patent Apr. 16, 2002 Sheet 2 6f 6 US 6,373,396 B2

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KSAg US 6,373,396 B2 1 2 METHOD FOR PREDICTING SEISMIC BRIEF DESCRIPTION OF THE DRAWINGS EVENTS FIG. 1 is a section through the center of the earth Which FIELD OF THE INVENTION illustrates the effect of polar shift on the corresponding section through the geoid surface; The present invention relates to methods of predicting the FIG. 2 is a section through the center of the earth Which occurrence of seismic events from changes in the earth’s illustrates the effect of polar shift on the forces at a geo equipotential gravitational surface due to polar motion. graphical location on the earth; More particularly, accumulated gravitation shift in FIG. 3 is a side vieW of a truncated ellipsoid earth betWeen successive polar motions is associated With the 10 illustrating rotational planes and rotation vectors of a single accumulation in energy in the earth’s crust Which can be mass on the surface of a geoid; correlated to seismic events. FIG. 4 is a fanciful vieW to illustrate the tidal gravitational BACKGROUND OF THE INVENTION effects of the sun and the moon; FIG. 5 is a plot of the polar motion of the earth over a The majority and most destructive of earthquakes or 15 seismic events are the tectonic quakes Which are a result of selected time period of 1964—1968; a sudden release of energy accompanying a shift or dislo FIG. 6a illustrates tWo geoids spaced in time With partial cation of the earth’s crust (shalloW) and in the upper mantle indications of the many intermediate incremental geoids (deep). Which could be calculated therebetWeen and the magnitude of the change in gravitational effect; Shifts in the earth’s crust create a potential energy, Which 20 is occasionally released in a seismic event. Due to the FIG. 6b is a pair of charts Which respectively illustrate; a devastating results of earthquakes, particularly those occur plot of the Ag over each time increment betWeen tWo seismic ring in populated areas, there have been concerted efforts to events at t1 and tn and accumulates over time future event at predict such events. tm, and a plot of the accumulation of energy betWeen events. There are knoWn areas of frequent seismic activity such as 25 DETAILED DESCRIPTION OF THE geological locations having faults. Monitoring stations are PREFERRED EMBODIMENT provided at these locations Which, at best, provide Warning of an immediately impending event. Monitoring primarily It is not neW that gravitational anomalies affect the shape consists of recording geophysical precursors such as P-Wave of the equipotential surface of the earth. This undulating velocity, ground uplift, radon emission, rock electrical resis 30 surface is also knoWn as a geoid. Effects Which alter the tivity and Water level ?uctuations. These precursors can shape of the geoid include the centripetal effect of the earth’s have lead times of one day through to several years depend rotation (an equatorial bulge) and tidal gravitational effects. ing upon the magnitude of the upcoming event. The surface undulates due to local gravitational anomalies. Some approaches to obtaining more advance notice or While the surface of the ocean provides a good approxima prediction of future events includes statistical analysis of the 35 tion of the geoid, the shape of the geoid can also be history of earthquakes in a given location so as to determine calculated over a land mass. These undulations are conven Whether there is a recurrent, or cyclical pattern to the events. tionally determined as departures from the theoretical ellip These methods can provide a statistical value, for eXample, soid. a 70% probability of an event happening every 100 years, The geoid is associated With the earth’s orientation Which 40 but still leave an uncertainty of tens of years. varies according to an annual elliptical component and a Generally hoWever, there is a need for an earlier Warning Chandler circular component With a period of about 435 system and one Which can be tied to knoWn and independent days. The variation is due in part to annual spring melt factors. cycles and tidal effects Which eXert a torque on the earth. This torque results in of the earth’s rotational 45 SUMMARY OF THE INVENTION aXis. The precession is not a steady process hoWever, there Using the motion of the earth’s poles, a series of succes being discontinuities or a lull in the precession each time the sive geoids can be determined. The shift betWeen incremen tidal mass crosses the equatorial plane. Further, beyond the tal geoids provides information necessary to determine tidal precession, the earth itself undergoes a free, Eulerian precession, some times called a “free ” or the changes in gravitational anomalies and ultimately the accu 50 mulation in energy at a given geological location. Knowing . the energy Which Was released in a previous seismic event, The earth’s orientation or polar motion is monitored. One the geoidal shift method of the present invention can be used such monitoring service is the International Earth Rotation to monitor and predict a subsequent seismic event. Service (IERS) located at the US. Naval Observatory. It has In a broad form of the invention, a method is provided for 55 been determined that the earth’s aXis has scribed a conical predicting seismic events comprising: determining a ?rst path of about 235° in about 26,000 years. geoid surface at ?rst instance in time; determining succes The major sources of energy for seismic events are the sive geoid surfaces for successive and incremental instances gravitational anomalies. Gravitational anomalies are gener in time; determining an incremental energy associated With ated by differences betWeen the gravity equipotential sur each incremental shift betWeen the successive geoid sur 60 faces and the centripetal force of the earth’s rotation (r002). faces; accumulating energy associated With the incremental This value, of course, varies With latitude from Zero at a pole shifts; and comparing the accumulated energy With a pre to a maXimum at the (r=R cos (1)). A shift in aXis of determined energy Which has resulted in a seismic event as the earth’s rotation changes the radius of rotation (a vector being indicative of the likelihood of a future seismic event. of rotation force is a component of the gravitation vector). Preferably, the pre-determined energy for a seismic event is 65 Variation of sea-level gravity from a theoretical ellipsoid determined by establishing measures of the energy released Was ?rst set forth, by mid-18th century scientist Alexis in a previous seismic event. Clairaut, as a function of latitude. Adoption of internation US 6,373,396 B2 3 4 ally agreed upon constants improved the accuracy of the energy required to cause the earthquake. This energy rep gravity calculations. Using the expression for gravity, relat resents energy accumulated from factors including those ing mass and distance, increased distance from the earth’s caused by the shift of axis of the earth betWeen said events. center can be added to the calculation. At sea level, the From the knoWn energy level, one can predict a similar gradient is about —0.3086 milligal per meter of elevation energy Which Will trigger or initiate a subsequent seismic increase. Calculations for such uniform changes in elevation event at that same location. are also knoWn as the Free-Air Anomaly. Pierre Bouguer, The energy due to polar motion can be estimated by again in the mid-18th century, made corrections for actual summation of the incremental shift Ag at that location. variations in topography. The resulting correction, about Accordingly, by extrapolating polar motion and resulting +0.20 milligal per meter of elevation increase, Was termed 10 shifts in geoid, one can predict the time of the next seismic the Bouguer Anomaly. Further, there are Well described event and its magnitude. variations in the crust of the earth, knoWn as the Mohorov icic discontinuities (Moho). Warping of these density inter The theoretical determination of locations and forces faces also produce gravity at the earth’s surface. involved in earthquakes can be obtained through mathemati Suf?ce it to say that the geophysics for determining the 15 cal modeling. Depending upon the data available and the geoid surface are knoWn and the detailed mathematics are variables involved, the method varies in complexity. not reproduced herein. In one embodiment, a simpli?ed general formula is devel The equipotential surfaces, or geoids, change continu oped Which considers the energy sources, medium proper ously over time and certainly as a function of the polar ties and geoid con?gurations. A mathematical formula is motion. While this is a continuous process, a series of derived With its end use applicable for computer-generated incremental geoid surfaces can be determined from the modeling. empirical polar motion and tidal data. Of all the possible energy sources, gravity and gravitation The equipotential surfaces of the gravitation of successive is considered to be dominant. Other secondary sources are geoids intersect. A gravitational difference or shift Ag is divided betWeen independent sources such as the gravita 25 represented by the difference betWeen successive geoids. tional effects of the sun and the moon, solar radiant heat, and Maximum shifts Ag are along the meridian of shift. Mini dependent sources involving the transformation of energy mums or Zero Ag are found at intersection points of the tWo such as pressure to heat, and others. equipotential gravitational surfaces. The earth’s rotation, is considered to be the major variable Adjustments can be made to correct for delay in change source and is subject to rapid change. Rotational energy is of the hard body of the earth to compensate for the already handled as an equation of the shape of the geoid and the changed rotation vectors. present drift of the geoid’s axis of rotation. BetWeen time t1 The shift Ag can be expressed as a neW surface over the and time t2, there Will be incremental geoid surfaces g1 and earth. The Ag shift represents forces applied to the earth at g2. The shift Ag is the difference therebetWeen, or that point. The surface of the Ag shift is calculated in 35 incremental steps. Integration of the Ag over time represents Ag=g1—g2 (1) the accumulation of energy for the earth at that point. Having reference to FIG. 4, one can see that the geoid Further, secondary energy sources include, listed accord rotational surface is de?ned by equal vectors of rotation. The ing to magnitude, the moon’s tidal Wave and the sun’s tidal motion of a material point is the dynamic earth’s surface. Wave. Another source of unbalancing of the polar motion is the movements of the masses on the earth’s surface by rivers The knoWn phenomena of drift of axis of rotation is de?ned as a change in position of an imaginary axis of and oceans. symmetry of rotation of the material points Where the radius The movements of the earth surface itself, such as moun is equal to Zero. tain groWth, can be a reaction to the gravitational anomalies and have the same sign as the anomaly. The plastic During an earthquake, rapid movement of the earth’s Mohorovicic discontinuity moves to compensate gravity to matter is generated. This displacement or movement Ah is a stable position or to minimiZe the anomaly. Additionally, Working against the plastic properties of the earth at this thermal effects of the Earth are as a result of Pressure point—the earthquake epicenter. As a result of a rapid strain Temperature-Melting point drop function as described by release, the geological medium breaks, and the energy Boyle-Mariotte’s laW. released is in a shock-Wave form. The major horiZontal earth movement energy in the earth The value of the function representing the energy gener is generated by coriolis force and a gravitational sliding or ated is the seismic energy. doWnWard motion.

The movement of the earth’s masses obeys the laW of 55 mechanics of continuum Where every material point has its oWn force ?eld application and is not simply a hard, non compressible body of ?at form. These material point forces Where: are integrated by the volume to obtain a large scale mass E q is referred to as the energy generated, movement estimation. Earthquakes or seismic events are knoWn to be caused by Fk is the force, the sudden release of energy Within some limited region of K is the coef?cient of the medium property, re?ecting the the Earth. The energy is largely a result of an accumulation change of potential energy of tension to the dynamic of elastic strain. The release of the elastic strain energy can energy of rotation), produce major earthquakes. 65 Ah—is the displacement or throW of the fault, and By observing the point or region of the earth having tWo At—is the time of duration of the movement or accumu consecutive earthquakes in time, one can determine the lated time in the case of multiple shock events. US 6,373,396 B2 5 From the laW of the preservation of energy, the energy accumulated Ea equals the energy released E q. (6) Va : 2 AV; [:1 11 q (3) This condition is satis?ed When in the same geographical area, We have repeated earthquakes after knoWn time inter The limit of this value is val T, Where T is greater than Zero. (T>>0). Historically, one earthquake occurs at a ?rst instance in time t1 and a successive earthquake occurs at a second instance in time t2. The total potential energy Ep is that energy accumulated 10 in elapsed time T. After elapsed time T, folloWing the seismic event, the potential energy Ep is substantially Zero The physical limit is reached When the potential (stress) due to the release during the earthquake. Smaller or minor earthquakes having energy Eqo, may be a result of residual energy is transformed into the dynamic (strain) energy and accumulated energy of Ea—EqO. As is later shoWn, the 15 results in the earthquake. Therefore these tWo values are potential energy is a measurable and calculable element. equaliZed at this time by equation. From the knoWn potential energy, We can ?nd the total stress-force that is required to produce the earthquake. Geological media properties A, Which can be termed media property parameters, can be calculated using conven tional methods of determination such as drilling, seismic, gravity, etc. This gives one the ability to adjust the solutions Where fk is a speci?c function Which can be estimated. of systems of equations regarding one of the parameters. One plots the equipotential surfaces of the AV on a geoid One ?rst models the earth’s surface as a geoid surface and surface. Overlaps indicate multiplication of Ag in this point the geoid as an ellipsoid of revolution. NoW, assume that it 25 and signal a concentration of energy. As stated, using is a plastically deformable body Whose equipotential sur historical data for the energy and the incident of the last faces are substantially parallel to the geoid’s surface. A earthquake event, the next may be predicted. graph of the model can be simpli?ed to that shoWn in FIGS. Accordingly, by monitoring the accumulation of potential 2 and 3. gravitational energy Ea betWeen tWo successive earthquakes When, due to a shift in the axis of rotation, the equipo tential surface of the gravitation V0, shifts to a position at a geographical location and betWeen times t1 and tn, and relative to the gravitated body of earth surface-geoid, the by extrapolating the ongoing accumulation of potential estimate of the value of gravitation changes as AV. energy to some future polar motion at tm, We can predict the moment When the conditions are satis?ed for a similar 35 seismic event. Where Having reference to FIG. 5, the polar motion for the Vi is the equipotential gravitation surface of the geoid period of time betWeen 1964 and 1968 are illustrated. It is before the shift of axis, hypothesiZed that a beat betWeen the annual and the 14 V‘i is the equipotential surface of the geoid after the shift month cycles results in the occasional collapse or approach of axis, of the generally circular polar motion. V is the potential energy accumulated at this point on the Turning to FIG. 6a, an exaggerated shift of the geoids geoid, and over time due to polar motion (P1— n) illustrates hoW the net AV is the difference betWeen the neW and the old equi gravitational effects are increased in some areas and potential levels. 45 decreased in others. As shoWn at point Z, the effect is Where the geoidal surfaces at t1 and t2 coincide, there is minimal at the intersection of the geoids. In FIG. 6b, the a minimal change in the trajectory of the earth’s crust. incremental changes in Ag for incremental instances in time Where the geoidal surfaces vary, there is a gravitational t1—tn are plotted. At time tn, an earthquake event is indicated. anomaly and a shift in the velocity vector or trajectory of the earth. This results in signi?cant forces in the earth’s crust. By integrating Ag over time betWeen t1—tn, and applying the appropriate constants for determining energy, the energy Eq At each point, there are tWo forces applied: F) due to Which Was necessary to cause the earthquake at that par a a a a gravity and K due to the centripetal force for g = F + K. The ticular locale can be determined. centripetal force is applied in the plane of rotation and Having Vm as an anomaly produced from periodic func perpendicular to the axis of rotation. Centripetal force can be 55 tions such as moon gravity and sun gravity Waves Agm, the represented as K=uu2p Where p is the radius of the plane of V, of Eqn. 8 can be adjusted. rotation and u) is the angular velocity. Theoretical calculated values of Moon and Sun tidal In an ideal situation: gravity change are: AV=kAg (5) for the moon, Where Ag—is the gravitation anomaly generated. But in practice the solutions are more complicated. The IERS and others have precisely documented the polar motion for more than 100 years. From this, We can obtain the 65 accumulated value of the total number of events, A, in a given area US 6,373,396 B2 8 and for the sun, experiments have shoWn good correlation betWeen seismic events and moon peaks. There is a geological part of the methodology that is similarly determinable applying similar techniques. The vector calculus equations that actually de?ne the gravity, gravitation and the elastic properties of the Earthquake, Where vector movements of a solid point of the geoid and centrip Ag,Ag—?rst differentials on the of tidal gravity potential. etal potential belong to the ?eld of vector calculus and the theory of the earth topography Which are knoWn to those of f—Gravity constant, 10 MC—mass of Moon, ordinary skill in the art. M€B—mass of Sun, The embodiments of the invention for Which and eXclu p=ot(1—e sin2 1p)—the distance from centre of earth to sive property or privilege are claimed are de?ned as folloWs: point of measurement, 1. A method for predicting seismic events comprising: cC—Average distance from centre of the earth to centre 15 (a) determining a ?rst geoid surface at ?rst instance in of the moon, RC the distance from centre of the earth to centre of the time; Moon on the moment of measurement, (b) determining successive geoid surfaces for successive r®—-the radius-vector of the sun. and incremental instances in time; sin rue, sin 75$ the equatorial horiZontal parallaXes of (c) determining an incremental energy associated With moon and sun, each incremental shift betWeen the successive geoid Z—momentary geocentric distance of moon and sun surfaces; and (d) accumulating energy associated With the incremental shifts; and cos Z=sin 6 sin 1p+cos 6 cos 14; cos 1: (11) 25 (e) comparing the accumulated energy With a pre Where determined energy Which has resulted in a seismic 6—Latitude of the Moon or Sun, event as being indicative of the likelihood of a future "c—Hourly angle of the Sun and Moon seismic event. 1p—Geocentric latitude of the point of measurement. 2. The method of claim 1 Wherein the pre-determined The value of Ag is in range of hundreds of mgal compared energy for a seismic event is determined by: to the average of the earth’s gravity being 980 gal (1 gal=1 cm/s2). (a) identifying a ?rst instance in time When a seismic The tidal correction can be made as follows: event occurred at the geographical location; (b) identifying a second instance in time When a second 35 A (9) successive seismic event occurred at the geographical v, 5 2 AV; + vm location; and [:1 (c) establishing measures of the energy released in the second successive seismic event. Through satisfying this condition, one is able to determine or predict an earthquake event in time and place. Past