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On Different Techniques for the Calculation of Bouguer Gravity University of Texas at El Paso DigitalCommons@UTEP Open Access Theses & Dissertations 2013-01-01 On Different Techniques For The alcC ulation Of Bouguer Gravity Anomalies For Joint Inversion And Model Fusion Of Geophysical Data In The Rio Grande Rift Azucena Zamora University of Texas at El Paso, [email protected] Follow this and additional works at: https://digitalcommons.utep.edu/open_etd Part of the Applied Mathematics Commons, and the Geophysics and Seismology Commons Recommended Citation Zamora, Azucena, "On Different Techniques For The alcC ulation Of Bouguer Gravity Anomalies For Joint Inversion And Model Fusion Of Geophysical Data In The Rio Grande Rift" (2013). Open Access Theses & Dissertations. 1965. https://digitalcommons.utep.edu/open_etd/1965 This is brought to you for free and open access by DigitalCommons@UTEP. It has been accepted for inclusion in Open Access Theses & Dissertations by an authorized administrator of DigitalCommons@UTEP. For more information, please contact [email protected]. ON DIFFERENT TECHNIQUES FOR THE CALCULATION OF BOUGUER GRAVITY ANOMALIES FOR JOINT INVERSION AND MODEL FUSION OF GEOPHYSICAL DATA IN THE RIO GRANDE RIFT AZUCENA ZAMORA Program in Computational Science APPROVED: Aaron Velasco, Chair, Ph.D. Rodrigo Romero, Ph.D. Vladik Kreinovich, Ph.D. Benjamin C. Flores, Ph.D. Dean of the Graduate School Para mi familia con amor Sin ustedes nada de esto seria posible ON DIFFERENT TECHNIQUES FOR THE CALCULATION OF BOUGUER GRAVITY ANOMALIES FOR JOINT INVERSION AND MODEL FUSION OF GEOPHYSICAL DATA IN THE RIO GRANDE RIFT by AZUCENA ZAMORA THESIS Presented to the Faculty of the Graduate School of The University of Texas at El Paso in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE Program in Computational Science THE UNIVERSITY OF TEXAS AT EL PASO May 2013 Acknowledgements Throughout the years as a student at the University of Texas at El Paso, I've had the oppor- tunity of working with professors with different backgrounds and areas of expertise that have impacted my career choices and have helped me to reach my academic goals. Special thanks to my advisor Dr. Aaron Velasco of the Geological Science Department, who, with his con- stant support, advice, and encouragement, has been a key in the achievement of this degree. To Dr. Rodrigo Romero for his dedication and support and to Dr. Vladik Kreinovich for his guidance and help in the completion of this work. Thanks to the Program in Computational Science, the Cyber-ShARE Center of Excellence, and the Graduate STEM Fellows in K-12 Education Program at UTEP for all their support. Special thanks to the Cyber-ShARE Geological Science team for all their collaboration, help, and support for the completion of this work. This work was funded by the National Science Foundation grants of Crest Cyber-ShARE HRD-0734825 and HRD-1242122, and the Graduate STEM Fellows in K-12 Education Grant DGE-0947992. iv Abstract Density variations in the Earth result from different material properties, which reflect the tectonic processes attributed to a region. Density variations can be identified through measur- able material properties, such as seismic velocities, gravity field, magnetic field, etc. Gravity anomaly inversions are particularly sensitive to density variations but suffer from significant non-uniqueness. However, using inverse models with gravity Bouguer anomalies and other geo- physical data, we can determine three dimensional structural and geological properties of the given area. We explore different techniques for the calculation of Bouguer gravity anomalies for their use in joint inversion of multiple geophysical data sets and a model fusion scheme to integrate complementary geophysical models. Various 2- and 3- dimensional gravity profile forward modeling programs have been developed as variations of existing algorithms in the last decades. The purpose of this study is to determine the most effective gravity forward modeling method that can be used to combine the information provided by complementary datasets, such as gravity and seismic information, to improve the accuracy and resolution of Earth models obtained for the underlying structure of the Rio Grande Rift. In an effort to de- termine the most appropriate method to use in a joint inversion algorithm and a model fusion approach currently in development, we test each approach by using a model of the Rio Grande Rift obtained from seismic surface wave dispersion and receiver functions. We find that there are different uncertainties associated with each methodology that affect the accuracy achieved by including gravity profile forward modeling. Moreover, there exists an important amount of assumptions about the regions under study that must be taken into account in order to obtain an accurate model of the gravitational acceleration caused by changes in the density of the material in the substructure of the Earth. v Table of Contents Page Acknowledgements . iv Abstract . .v Table of Contents . vi List of Figures . viii Chapter 1 Introduction . .1 1.1 Background . .3 1.2 Motivation . .8 1.3 Potential Fields . 10 1.3.1 Gravity Data . 11 1.3.2 Corrections to Gravity Data . 13 1.3.3 Free-Air and Bouguer Anomalies . 17 1.3.4 Interpretation of Gravity Anomalies . 20 2 Problem Formulation . 22 2.1 Forward Modeling . 23 2.2 Inverse Modeling . 23 3 Methodology . 26 3.1 Forward Model of Gravitational Acceleration . 26 3.2 Simple Bodies . 28 3.3 Rectangular Prisms . 30 3.4 Polygonal Prisms . 32 4 Gravity Dataset . 35 5 Numerical Experimentation . 41 5.1 Synthetic Problems . 41 5.1.1 Rectangular Prisms . 41 vi 5.1.2 Horizontal Cylinder . 43 5.2 Rio Grande Rift Dataset . 45 6 Discussion . 49 6.1 Advantages and Disadvantages of Techniques . 49 6.1.1 Simple Bodies . 49 6.1.2 Rectangular Prisms . 51 6.1.3 Polygonal Prisms . 52 6.1.4 Comments on Implementation Results . 54 6.2 Recommendation on Technique . 55 6.3 Significance of the Result . 57 6.4 Future Work . 59 7 Conclusions . 61 References . 63 Appendix A Gravity Corrections . 68 Curriculum Vitae . 75 vii List of Figures 1.1 Geometries for the gravitational attraction of (a) 2 point masses, (b) a point mass outside a sphere, and (c) a point mass on the surface of the sphere. 12 1.2 Free-air and Bouguer anomalies across a mountain range (as taken from Lowrie, 1997). 18 2.1 Definition of forward and inverse problems. 22 3.1 Non-uniqueness in the calculation of Bouguer gravity anomalies using simple bodies. 29 3.2 Rectangular prisms scheme proposed by Plouff (Maceira et al. 2009). 30 3.3 Rectangular prisms used to model layers of different density material (modified from Maceira et al. 2009). 31 3.4 Rectangular prisms code used with a prism of three different density contrast values. 32 3.5 Polygonal prisms scheme proposed by Talwani et al. (1959). 33 3.6 Polygonal prisms scheme using an horizontal rectangular prism with three dif- ferent density contrasts . 34 4.1 Bouguer gravity anomaly map for SRGR. Inset map contains locations of gravity readings (black dots) (Averill, 2007). 36 4.2 Bouguer gravity anomaly map for RGR with location of all 45,945 gravity stations 37 4.3 Modified Bouguer gravity anomaly map for RGR (Thompson et al. 2013) . 38 4.4 Preliminary gravity anomaly cross-section from West-East of the RGR . 38 4.5 Gravity anomaly cross-section at latitude 32◦ (Thompson et al. 2013) . 39 4.6 Gravity anomaly cross-section at latitude 34◦ (Thompson et al. 2013) . 39 4.7 Gravity anomaly at Northwest-Southeast cross-section (Thompson et al. 2013) 40 viii 5.1 Gravity anomaly results using rectangular (Plouff) and polygonal (Talwani) modeling in the given prism. 42 5.2 Gravity anomaly results using polygonal prisms algorithm for two bodies . 42 5.3 Gravity anomaly results using rectangular prisms algorithm for two bodies . 43 5.4 2-D modeling of the cross-section of a horizontal cylinder using polygonal prisms 44 5.5 3-D modeling of a horizontal cylinder using rectangular prisms algorithm . 44 5.6 Gravity anomaly results obtained using the polygonal prisms for the density profile of the RGR and a tie-point of 40 km. 46 5.7 Gravity anomaly results obtained using the polygonal prisms for the density profile of the RGR and a tie-point of 100 km. 46 5.8 3-D modeling of a cross section of the RGR using rectangular prisms . 47 5.9 Gravity anomaly results using the rectangular prisms algorithm for the initial density profile of the RGR. 47 6.1 Seismic stations used for the joint inversion scheme proposed by Sosa et al. (2013a, 2013b). 56 A.1 Linear Fit in Least Squares Sense of Instrument Drift (data from Wolf, 1940). 69 A.2 The terrain correction takes into consideration the effects caused by topographic rises(1 and 3) and depressions (2 and 4) (Sharma, 1997). 71 A.3 (a) Topography is divided into vertical segments, (b) correction is computed for each cylindrical element according to its heigth above or below the gravity station, and (c) the contributions from all elements around the station are added with the aid of aa transparent overlay on a topographic map. (Lowrie, 1997). 72 A.4 (a) Terrain corrections, (b) Bouguer plate correction, and (c) free-air correc- tion where P and Q are gravity stations and the Rs represent their theoretical position on the reference ellipsoid (Lowrie, 1997). 73 ix Chapter 1 Introduction Geophysical problems dealing with imaging of the Earth structure and determining its processes and evolution have seen a growing interest in the scientific community throughout the last decades. This endless need to accurately determine the physical and geological properties of the Earth has made the quest for novel methodology for the solution of applied inverse problems in the area a relevant topic in geophysics.
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