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PhD Thesis_Prakash

Chandra Prakash Dubey
Chandra Prakash Dubey

This document is a thesis submitted by Chandra Prakash Dubey to Andhra University for a Doctor of Philosophy degree in geophysics. The thesis investigates joint modeling of gravity and gravity gradients and their application in geological interpretation. It develops computational algorithms to calculate the gravity and gravity gradient tensor for regular geometric bodies like slabs, sheets, spheres, cylinders and prisms. It applies these algorithms over two case study regions, the Wichita Uplift and Vredeforte Dome, to analyze subsurface structures using rectangular prism models. The thesis was conducted under the guidance of Dr. Virendra Mani Tiwari at CSIR-National Geophysical Research Institute.

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JOINT MODELLING OF GRAVITY & GRAVITY GRADIENTS AND ITS APPLICATION IN GEOLOGICAL INTERPRETATION A Thesis Submitted to the Andhra University for the degree of DOCTOR OF PHILOSOPHY in GEOPHYSICS By CHANDRA PRAKASH DUBEY CSIR National Geophysical Research Institute Hyderabad 500 007, India Under the guidance of DEPARTMENT OF GEOPHYSICS COLLEGE OF SCIENCE & TECHNOLOGY ANDHRA UNIVERSITY April, 2015 Dr. Virendra Mani Tiwari, FNASc Internal Supervisor Gravity and Magnetic Studies Group CSIR-National Geophysical Research Institute Hyderabad, Telangana, India Prof. Paluri Rama Rao External Supervisor Department of Geophysics Andhra University, Vishakhapatnam Andhra Pradesh, India
Dedicated to my grandparent Lt. Shri Kamala Prasad Dubey, Smt. Kailashi Devi.................
PhD Thesis_Prakash
DECLARATION This is to certify that the thesis entitled JOINT MODELING OF GRAVITY & GRAVITY GRADIENTS AND ITS APPLICATION IN GEOLOGICAL INTERPRETATION, submitted by me to the Department of Geophysics, Andhra University, Vishakhapatnam for the award of the degree of PhD is a bonafide record of research work carried out by me. The contents of this thesis, in full or in parts, have not been submitted to any other Institute or University for the award of any degree. The literature related to the problem investigated has been cited. Due acknowledgements have been made wherever necessary. Date: Chandra Prakash Dubey, CSIR-SRF Place: Hyderabad Ph.D (Geophysics) CSIR-NGRI, Hyderabad & Department of Geophysics, Andhra University, Vishakhapatnam.
v ACKNOWLEDGEMENT I would like to express my heartfelt indebtedness to my supervisor Dr. Virendra Mani Tiwari, without whom the present research is not possible. Dr. Tiwari provided the best opportunity to work with him in NGRI and was supportive of my excursions into many different areas apart from my PhD work. His teachings and scientific temper greatly influenced me in my research work. My deepest thanks to Prof. P. Rama Rao who agreed to guide me as my co- supervisor from Andhra University whose continuous support made possible the fulfilment of my aspirations. Prof. Rao always encouraged me to pursue my ideas, and willingly offered suggestions for improvement. I acknowledge Prof. Dr. Hans J端rgen Gotze, IFG, CAU, Kiel, Germany for giving me an excellent exposure to overseas research problems during my visit as a DAAD Fellow to their Institute. I am also grateful to Dr. Sabine Schmidt for her continuous guidance and support for IGMAS+ and allowing me to access to the historical torsion balance measurements. I thank Mr. Ben, Mr. Peter, Mr. Nils and Ms. Christiana at IFG, CAU, Kiel for their contribution and support. My sincere thanks to Dr. D. C. Mishra, Dr. Bijendra Singh, Dr. M. R. K. Prabhakar Rao, Dr. A. P. Singh, Dr. Ch. V. Raju, and Dr. Niraj Kumar, scientists of Gravity working group at NGRI, Hyderabad who always encouraged me to do quality research and provided me with invaluable skills and tools by way of regular group interactions. Particularly, I would like to thank Dr. D. C. Mishra and Dr. Prabhakar Rao for the time and effort they made in reading my thesis and for constructive suggestions which greatly improved my thesis. Help rendered by my colleagues of gravity and magnetic studies group at different stages of this work is unforgettable. I am particularly thankful to my colleagues Mr. Narakula Srinivas Rao, Tehnical Assistant, Gravity Group for his restless help whenever needed, and Mrs. Jyothi, PhD Student, Gas Hydrate Group for the motivation and encouragement all the time. I thank my friend Ms. Alka, Assistant Manager, Syndicate Bank, Hyderabad for her cheerful support during last stages of the thesis. Last but not the least; I thank my grandparents and my family for their selfless cooperation, warmth and affection shown towards me during the course of my research. They have supported and encouraged me throughout my studies and I am extremely grateful for their patience and love. I also wish to thank my parents for their time to time support and encouragement. I also wish to thank my sweet nephew Shivansh and my brothers and sisters for their keen and constant encouragement. (Chandra Prakash Dubey)
vi TABLE OF CONTENTS Acknowledgements v Table of Contents vi Abstract ix Research Publications xii List of Figures xiv List of Tables xx 1. Introduction.............................................................................................................. 1 1.1. Problem definition and research aims.................................................................................... 2 1.2. Motivation.............................................................................................................................. 4 1.3. The conventional modeling of single geophysical field and its limitations.......................... 4 1.4. Joint Modeling of Different Potential Field Data.................................................................. 6 1.4.1. The Parameter/Structural Approach for Modeling..................................................... 7 1.5. Thesis outline............................................................................................. 8 2. Fundamentals of Gravity and Gravity Gradiometry........................................... 10 2.1. Introduction............................................................................................................................. 10 2.2. Newtonian Gravity.................................................................................................................. 11 2.2.1. Gravitational Force........................................................................................................ 11 2.2.2. Gravitational Field......................................................................................................... 12 2.2.3. Gravitational Potential.................................................................................................. 13 2.3. Gravity Gradient...................................................................................................................... 16 2.4. Historical Background of Gravity Measurements................................................................... 18 2.4.1. Types of Gravimeter......................................................................................................... 18 2.4.2. The Simple Pendulum....................................................................................................... 19 2.4.3. Comparison of Absolute and Relative Methods............................................................... 20 2.4.4. Gravity Measurements..................................................................................................... 20 2.5. Historical Background of Gravity Gradient Measurements................................................... 22 2.5.1. Construction and Design of an E旦tv旦s Torsion Balance................................................. 25 2.5.2. Early application of Torsion Balance Measurements...................................................... 26 2.5.3. Drawbacks of Torsion Balance Measurements................................................................ 28 2.6. Advantage Measurements of Gravity....................................................................................... 28 2.6.1. Gravity Gradiometry vs. Conventional Gravimetry......................................................... 30 2.7. Gravity and Gravity Gradiometry Modeling............................................................................ 31
vii 2.8. Application and Opportunities................................................................................................. 31 2.8.1. Geophysical Application.................................................................................................. 32 2.8.2. Geodetic Application........................................................................................................ 33 2.8.2. Opportunities.................................................................................................................... 33 3. Computational Algorithm of Gravity & Gravity gradient Tensor and their Applications.............................................................................................................. 34 3.1. Introduction.............................................................................................................................. 34 3.2. Forward Modeling.................................................................................................................... 35 3.3. Model Calculation of Regular Geometries............................................................................... 36 3.3.1. 2D Geometries: Semi Infinite Horizontal Slab and Vertical Sheet/Dike......................... 36 3.3.2. 3D Geometries.................................................................................................................. 38 3.3.2.1. Solid Sphere and Vertical Cylinder........................................................................ 38 3.3.2.2. Rectangular Lamina or prism................................................................................ 42 3.3.2.3. Invariants of prism................................................................................................. 47 3.3.3. Normal Fault Model......................................................................................................... 48 3.4. Application of Algorithm over Two Different Geographical Regions.................................... 49 3.4.1. Case Study 1. Structural Analysis of Wichita Uplift using Rectangular Prism: Horst Model................................................................................................................................ 49 3.4.2. Case Study 2. Analysis of Irregular 3D Geometries using Vertical Rectangular Prisms or Infinite Cell: Vredeforte Dome, South Arica................................................... 52 3.5. Strategy behind the Generation and Computation of Irregular Shaped Geometries................ 56 3.6. Summary................................................................................................................................ 58 4. Joint Modelling of Gravity and Gravity Gradient for Shallow Structures........ 59 4.1. Introduction.............................................................................................................................. 59 4.2. Torsion Balance Data over Saxony Basin, Germany........................................................... 61 4.2.1. Operational Details.......................................................................................................... 63 4.3. Geology of Study Area and Database Information.................................................................. 65 4.3.1. Salt Tectonics in the Lower Saxony Basin....................................................................... 65 4.3.2. Database Information of Wathlingen- H辰nigsen Area................................................... 67 4.4. 3D Forward Modelling of Gravity, Gravity Gradient and Curvature...................................... 70 4.4.1. Analytical Forward Modeling.......................................................................................... 72 4.4.2. 3D Density Modelling of the Wathlingen - H辰nigsen Salt Dome.................................... 74
viii 4.5. Summary.................................................................................................................................. 81 5. Modelling of Gravity Data for Deeper Lithosphere Structures: Bay of Bengal..................................................................................................................... 83 5.1. Introduction.............................................................................................................................. 83 5.2. Tectonics and Sedimentary Evolution of the Bay of Bengal................................................... 86 5.3. Utilized Data Sets..................................................................................................................... 89 5.3.1. Bathymetry and Gravity data........................................................................................... 89 5.3.2. Sediment Thickness Data................................................................................................. 89 5.3.2.1. Density-Depth Relationship for BOB Sediments................................................... 91 5.4. 3D Density Model of Bay of Bengal........................................................................................ 93 5.4.1. Gravity Effect of Bathymetry............................................................................................ 94 5.4.2. Gravity Effect of Sediments.............................................................................................. 96 5.4.3. Crustal Gravity Anomaly................................................................................................. 100 5.5. 3D Crustal and Lithospheric Structure.................................................................................... 102 5.5.1. Crust mantle interface (CMI)........................................................................................... 102 5.5.2. Lateral Density Variation (LDV) in Upper Mantle.......................................................... 104 5.5.2.1. Analysis of LDV in Terms of Mass Distribution.................................................. 105 5.5.3. 3D Lithospheric Thickness............................................................................................... 112 5.6. Structural Analysis of BoB from Computed Gravity Gradient................................................ 118 5.6.1. Integrated Analysis of Seismic and Gravity Gradient over the 850 East Ridge............... 126 5.7. Summary.................................................................................................................................. 128 6. Results and Discussion............................................................................................ 132 6.1. Local Structural settings........................................................................................................... 133 6.2. Regional Structural Settings..................................................................................................... 135 6.3. The Implications of Jointly Models for Subsurface Characterisation...................................... 136 6.3.1. The Gravity Gradient and Curvatures vs Gravity Field.................................................. 137 6.3.2. The Joint Modeling Algorithm and Their Application..................................................... 137 6.4. Suggestions for Further Research............................................................................................ 138 7. Appendix................................................................................................................... 140 8. References................................................................................................................. 159
ix ABSTRACT New measuring instruments of Earths gravity gradient tensors (GGT) have offered a fresh impetus to gravimetry and its application in the shallow and deep subsurface exploration. Several efforts are made to provide a thorough understanding of the complex properties of the gravity gradient tensor and mathematical formulations to compute GGT. However, there are not many open source softwares in this regard. The understanding of the tensor properties is imperative and provides fundamental guidelines in the development of a three dimensional geological model. From the last few decades, numerous attempts have been made on modelling and deciphering the three dimensional complex geometries like Salt domes and other complex tectonic environments using gravity and gravity gradiometry. Recent advancement of gravity gradiometry on different platforms like airborne and space using satellite opened up a path way for their use both in exploration and geodynamics so as to understand the complexity below the earths surface, even though the interpretation techniques of gravity gradiometer are still in developing mode. In the above said context, the author in the present thesis developed a MATLAB computational algorithm to calculate the gravity field and full gravity gradient tensor for undulated surface followed by regular geometries like, an infinite horizontal slab, vertical sheet, solid sphere, vertical cylinder, normal fault model, and rectangular lamina or conglomerations of such bodies and the results are compared with responses using professional software based on different computational schemes. Real subsurface geometries are approximated through infinite cell of vertical rectangular lamina to characterize the response due to complex geological structure of interest. Thus, these computational algorithms help to understand the complex behavior of gravity gradient responses even for simple geometries that produces complex pattern of anomalies like monopole, dipole, tripole, and quadrupole responses and further to correlate these responses with real geological data to infer simple as well as complex subsurface structures. The geological application of this algorithm is demonstrated over a horst-type structure of Oklahoma Aulacogen, USA and Vredefort Dome, South Africa, where measured GGT data are available. The thorough understanding of the behavior of gravity gradients through MATLAB computation of different geometries mentioned above was used in the second part of the thesis to
x derive a 3D density model of salt domes. For this, the real gravity and reprocessed gradient data of the Wathlingen salt dome situated in the southern part of the Northwest German basin was made use for joint modelling. Numerous attempts are made on modelling of salt tectonics and several models are developed to explain the ascent of salt diapirs using different geophysical parameters like gravity, magnetic, seismic etc. Since, salt diapirs are salt structures that pierce their overburden. Such diapirism occurs in variety of different tectonic settings including passive continental margins, intra cratonic basin or fold and thrust belts. The structures produced by salt tectonics can have a strong impact on the formation of hydrocarbon reservoirs. A 3D density model of the Wathlingen salt dome, situated in the southern part of the Northwest German basin is derived from the joint modelling of reprocessed torsion balance measurements. Gravity, gravity gradients (Wzx, Wzy), curvature (Wxy) derived from both horizontal gravity gradients, and Horizontal Directive Tendency (HDT) are jointly modeled to decipher the geometrical structure of the salt dome. The model is constrained by geological and borehole information. It is found that Wathlingen salt dome is a mushroom structured salt body, which is 14 km long, 4 km to 8 km wide extending up to ~ 4 km depth. The top mushroom structure of the salt is horizontally spread up to ~ 8 km. It would not have been possible to derive the complex 3D structure from modelling of gravity data alone. After the above successful effort in mapping salt dome features, which is of residual scale (few tens of km) the present study is extended to a regional scale (over hundreds of km) to address regional geodynamics. The regional scale study utilizes satellite gravity data derived from satellite altimetry over the region of Bay of Bengal, which is known for large sediment thickens to reveal hidden structures beneath sea floor. The basement depth and crustal thickness are important parameters when interpreting the tectonic or thermal evolution of a margin, however depth to basement, basement architecture and crustal structure remain poorly determined in the deep water parts of the Bay of Bengal. While regional-scale interpretation of the new and existing 2D seismic reflection data has provided important new insights into the structural framework of the basin, a number of outstanding issues remain which cannot be addressed using seismic data alone as they do not have information up to Moho or below it. The main goal of the study is an attempt to determine this sedimentary cover in oceanic crust and structural trends in a part of Bengal fan between the latitudes 0o 00 to 22o 00 N and the longitude of 80o 00 to 94o 00 E, through the integrated analysis and interpretation of gravity
xi observations and computed gravity gradients. Integrated interpretation leads to an improved representation of lithospheric structures in Bay of Bengal. For quantitative interpretation of the sources of the anomaly, a 3D density model of the oceanic lithosphere is designed by means of forward modelling and inversion constrained by prior information to investigate the crust mantle interface and detailed lithosphere properties. As a result of the current investigation, a regional structural map of the basement is constructed. In addition, two major ridges, 85o and 90o east ridges get easily identified using gradient components. This study also, reveals that, the depth to the basement surface ranges from 7 to more than 29 km, delineating promising deep sedimentary layer of around 22 km thick. Modelling results indicated that, the lateral density variation is so steep throughout the study area and also the thick sediment load changes the lateral property of deeper layer below crust. The last part of the thesis therefore demonstrates that satellite derived gravity data can be used to model regional gravity anomaly produced by lithospheric properties and structures evolve over the geological time period.
xii RESEARCH PUBLICATIONS Thesis Papers: Dubey, C. P., Gotze, H. J., Schmidt, S., Tiwari, V. M., 2014, A 3D model of the Wathlingen salt dome in the Northwest German Basin from joint modelling of gravity, gravity gradient, and curvature. Interpretation, Vol. 2, No. 4, p. 1-13, doi: 10.1190/INT-2014-0012.1. Dubey, C. P., and Tiwari, V. M., 2015, MATLAB Algorithm for Computation of gravity field and its gradient: some applications; Computer and Geosciences. (Submitted after minor revision). Dubey, C. P., and Tiwari, V. M., and Rao, P. R., Detailed lithosphere structure of Bay of Bengal and their tectonic implications. Lithosphere (To be Submitted) Dubey, C. P., Tiwari, V. M., and Rao, P. R., Mapping subsurface structures below Bay of Bengal Basin using full gravity gradient tensor. SEG-Interpretation (To be Submitted). Supplementary Paper: Gupta, H...Tiwari, V.M. Dubey, C. P... Nayak, S., 2014, Investigations related to scientific deep drilling to study reservoir-triggered earthquakes at Koyna, India, International Journal of Earth Sciences, DOI 10.1007/s00531-014-1128-0. Tiwari, V. M., Mishra, S., Dubey, C. P., and Raju, D. Ch. V., 2015, 3D Structural setting beneath Koyna Warna region from airborne gravity gradients and magnetic data; (In pipeline). International Conference Proceedings: Dubey, C. P., Gotze, H. J., Schmidt, S., and Tiwari, V. M., 2014, A 3D Model of the Wathlingen Salt Dome in the Northwest German Basin from joint modelling of Gravity, Gravity Gradient, and Curvature; Geophysical Research Abstracts, Vol. 16, EGU 2014- 13916, 2014, EGU General Assembly 2014. Dubey, C. P., 2014, Glimpses of SEG NGRI Student Chapter at CSIR-NGRI, Hyderabad, India and my personal research; 84th SEG Annual Meeting, Denver, Colorado, USA, 2014.
xiii Mishra, S., Dubey, C. P., and Tiwari, V. M., 2014, 3D Structural setting beneath Koyna Warna region from airborne gravity gradients and magnetic data, NGRI RC Meeting 2014, Hyderabad India. Dubey, C. P., and Tiwari, V. M., 2013 Imaging 3D complex geological structures from Gravity Gradiometry, NGRI RC Meeting 2013, Hyderabad, India. Dubey, C. P., and V. M. Tiwari, 2011, Computation of gravity potential and full gravity gradient tensor of arbitrary geometry and application, IGU 2011, Vishakhapatnam, India. Dubey, C. P., and V. M. Tiwari, 2010, A computational method to calculate the gravity potential and full gravity gradient tensor of arbitrary shape bodies and its applications, ICON- GSCESS 2010, BHU, Varanasi, India.

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PhD Thesis_Prakash

  • 1. JOINT MODELLING OF GRAVITY & GRAVITY GRADIENTS AND ITS APPLICATION IN GEOLOGICAL INTERPRETATION A Thesis Submitted to the Andhra University for the degree of DOCTOR OF PHILOSOPHY in GEOPHYSICS By CHANDRA PRAKASH DUBEY CSIR National Geophysical Research Institute Hyderabad 500 007, India Under the guidance of DEPARTMENT OF GEOPHYSICS COLLEGE OF SCIENCE & TECHNOLOGY ANDHRA UNIVERSITY April, 2015 Dr. Virendra Mani Tiwari, FNASc Internal Supervisor Gravity and Magnetic Studies Group CSIR-National Geophysical Research Institute Hyderabad, Telangana, India Prof. Paluri Rama Rao External Supervisor Department of Geophysics Andhra University, Vishakhapatnam Andhra Pradesh, India
  • 2. Dedicated to my grandparent Lt. Shri Kamala Prasad Dubey, Smt. Kailashi Devi.................
  • 4. DECLARATION This is to certify that the thesis entitled JOINT MODELING OF GRAVITY & GRAVITY GRADIENTS AND ITS APPLICATION IN GEOLOGICAL INTERPRETATION, submitted by me to the Department of Geophysics, Andhra University, Vishakhapatnam for the award of the degree of PhD is a bonafide record of research work carried out by me. The contents of this thesis, in full or in parts, have not been submitted to any other Institute or University for the award of any degree. The literature related to the problem investigated has been cited. Due acknowledgements have been made wherever necessary. Date: Chandra Prakash Dubey, CSIR-SRF Place: Hyderabad Ph.D (Geophysics) CSIR-NGRI, Hyderabad & Department of Geophysics, Andhra University, Vishakhapatnam.
  • 5. v ACKNOWLEDGEMENT I would like to express my heartfelt indebtedness to my supervisor Dr. Virendra Mani Tiwari, without whom the present research is not possible. Dr. Tiwari provided the best opportunity to work with him in NGRI and was supportive of my excursions into many different areas apart from my PhD work. His teachings and scientific temper greatly influenced me in my research work. My deepest thanks to Prof. P. Rama Rao who agreed to guide me as my co- supervisor from Andhra University whose continuous support made possible the fulfilment of my aspirations. Prof. Rao always encouraged me to pursue my ideas, and willingly offered suggestions for improvement. I acknowledge Prof. Dr. Hans J端rgen Gotze, IFG, CAU, Kiel, Germany for giving me an excellent exposure to overseas research problems during my visit as a DAAD Fellow to their Institute. I am also grateful to Dr. Sabine Schmidt for her continuous guidance and support for IGMAS+ and allowing me to access to the historical torsion balance measurements. I thank Mr. Ben, Mr. Peter, Mr. Nils and Ms. Christiana at IFG, CAU, Kiel for their contribution and support. My sincere thanks to Dr. D. C. Mishra, Dr. Bijendra Singh, Dr. M. R. K. Prabhakar Rao, Dr. A. P. Singh, Dr. Ch. V. Raju, and Dr. Niraj Kumar, scientists of Gravity working group at NGRI, Hyderabad who always encouraged me to do quality research and provided me with invaluable skills and tools by way of regular group interactions. Particularly, I would like to thank Dr. D. C. Mishra and Dr. Prabhakar Rao for the time and effort they made in reading my thesis and for constructive suggestions which greatly improved my thesis. Help rendered by my colleagues of gravity and magnetic studies group at different stages of this work is unforgettable. I am particularly thankful to my colleagues Mr. Narakula Srinivas Rao, Tehnical Assistant, Gravity Group for his restless help whenever needed, and Mrs. Jyothi, PhD Student, Gas Hydrate Group for the motivation and encouragement all the time. I thank my friend Ms. Alka, Assistant Manager, Syndicate Bank, Hyderabad for her cheerful support during last stages of the thesis. Last but not the least; I thank my grandparents and my family for their selfless cooperation, warmth and affection shown towards me during the course of my research. They have supported and encouraged me throughout my studies and I am extremely grateful for their patience and love. I also wish to thank my parents for their time to time support and encouragement. I also wish to thank my sweet nephew Shivansh and my brothers and sisters for their keen and constant encouragement. (Chandra Prakash Dubey)
  • 6. vi TABLE OF CONTENTS Acknowledgements v Table of Contents vi Abstract ix Research Publications xii List of Figures xiv List of Tables xx 1. Introduction.............................................................................................................. 1 1.1. Problem definition and research aims.................................................................................... 2 1.2. Motivation.............................................................................................................................. 4 1.3. The conventional modeling of single geophysical field and its limitations.......................... 4 1.4. Joint Modeling of Different Potential Field Data.................................................................. 6 1.4.1. The Parameter/Structural Approach for Modeling..................................................... 7 1.5. Thesis outline............................................................................................. 8 2. Fundamentals of Gravity and Gravity Gradiometry........................................... 10 2.1. Introduction............................................................................................................................. 10 2.2. Newtonian Gravity.................................................................................................................. 11 2.2.1. Gravitational Force........................................................................................................ 11 2.2.2. Gravitational Field......................................................................................................... 12 2.2.3. Gravitational Potential.................................................................................................. 13 2.3. Gravity Gradient...................................................................................................................... 16 2.4. Historical Background of Gravity Measurements................................................................... 18 2.4.1. Types of Gravimeter......................................................................................................... 18 2.4.2. The Simple Pendulum....................................................................................................... 19 2.4.3. Comparison of Absolute and Relative Methods............................................................... 20 2.4.4. Gravity Measurements..................................................................................................... 20 2.5. Historical Background of Gravity Gradient Measurements................................................... 22 2.5.1. Construction and Design of an E旦tv旦s Torsion Balance................................................. 25 2.5.2. Early application of Torsion Balance Measurements...................................................... 26 2.5.3. Drawbacks of Torsion Balance Measurements................................................................ 28 2.6. Advantage Measurements of Gravity....................................................................................... 28 2.6.1. Gravity Gradiometry vs. Conventional Gravimetry......................................................... 30 2.7. Gravity and Gravity Gradiometry Modeling............................................................................ 31
  • 7. vii 2.8. Application and Opportunities................................................................................................. 31 2.8.1. Geophysical Application.................................................................................................. 32 2.8.2. Geodetic Application........................................................................................................ 33 2.8.2. Opportunities.................................................................................................................... 33 3. Computational Algorithm of Gravity & Gravity gradient Tensor and their Applications.............................................................................................................. 34 3.1. Introduction.............................................................................................................................. 34 3.2. Forward Modeling.................................................................................................................... 35 3.3. Model Calculation of Regular Geometries............................................................................... 36 3.3.1. 2D Geometries: Semi Infinite Horizontal Slab and Vertical Sheet/Dike......................... 36 3.3.2. 3D Geometries.................................................................................................................. 38 3.3.2.1. Solid Sphere and Vertical Cylinder........................................................................ 38 3.3.2.2. Rectangular Lamina or prism................................................................................ 42 3.3.2.3. Invariants of prism................................................................................................. 47 3.3.3. Normal Fault Model......................................................................................................... 48 3.4. Application of Algorithm over Two Different Geographical Regions.................................... 49 3.4.1. Case Study 1. Structural Analysis of Wichita Uplift using Rectangular Prism: Horst Model................................................................................................................................ 49 3.4.2. Case Study 2. Analysis of Irregular 3D Geometries using Vertical Rectangular Prisms or Infinite Cell: Vredeforte Dome, South Arica................................................... 52 3.5. Strategy behind the Generation and Computation of Irregular Shaped Geometries................ 56 3.6. Summary................................................................................................................................ 58 4. Joint Modelling of Gravity and Gravity Gradient for Shallow Structures........ 59 4.1. Introduction.............................................................................................................................. 59 4.2. Torsion Balance Data over Saxony Basin, Germany........................................................... 61 4.2.1. Operational Details.......................................................................................................... 63 4.3. Geology of Study Area and Database Information.................................................................. 65 4.3.1. Salt Tectonics in the Lower Saxony Basin....................................................................... 65 4.3.2. Database Information of Wathlingen- H辰nigsen Area................................................... 67 4.4. 3D Forward Modelling of Gravity, Gravity Gradient and Curvature...................................... 70 4.4.1. Analytical Forward Modeling.......................................................................................... 72 4.4.2. 3D Density Modelling of the Wathlingen - H辰nigsen Salt Dome.................................... 74
  • 8. viii 4.5. Summary.................................................................................................................................. 81 5. Modelling of Gravity Data for Deeper Lithosphere Structures: Bay of Bengal..................................................................................................................... 83 5.1. Introduction.............................................................................................................................. 83 5.2. Tectonics and Sedimentary Evolution of the Bay of Bengal................................................... 86 5.3. Utilized Data Sets..................................................................................................................... 89 5.3.1. Bathymetry and Gravity data........................................................................................... 89 5.3.2. Sediment Thickness Data................................................................................................. 89 5.3.2.1. Density-Depth Relationship for BOB Sediments................................................... 91 5.4. 3D Density Model of Bay of Bengal........................................................................................ 93 5.4.1. Gravity Effect of Bathymetry............................................................................................ 94 5.4.2. Gravity Effect of Sediments.............................................................................................. 96 5.4.3. Crustal Gravity Anomaly................................................................................................. 100 5.5. 3D Crustal and Lithospheric Structure.................................................................................... 102 5.5.1. Crust mantle interface (CMI)........................................................................................... 102 5.5.2. Lateral Density Variation (LDV) in Upper Mantle.......................................................... 104 5.5.2.1. Analysis of LDV in Terms of Mass Distribution.................................................. 105 5.5.3. 3D Lithospheric Thickness............................................................................................... 112 5.6. Structural Analysis of BoB from Computed Gravity Gradient................................................ 118 5.6.1. Integrated Analysis of Seismic and Gravity Gradient over the 850 East Ridge............... 126 5.7. Summary.................................................................................................................................. 128 6. Results and Discussion............................................................................................ 132 6.1. Local Structural settings........................................................................................................... 133 6.2. Regional Structural Settings..................................................................................................... 135 6.3. The Implications of Jointly Models for Subsurface Characterisation...................................... 136 6.3.1. The Gravity Gradient and Curvatures vs Gravity Field.................................................. 137 6.3.2. The Joint Modeling Algorithm and Their Application..................................................... 137 6.4. Suggestions for Further Research............................................................................................ 138 7. Appendix................................................................................................................... 140 8. References................................................................................................................. 159
  • 9. ix ABSTRACT New measuring instruments of Earths gravity gradient tensors (GGT) have offered a fresh impetus to gravimetry and its application in the shallow and deep subsurface exploration. Several efforts are made to provide a thorough understanding of the complex properties of the gravity gradient tensor and mathematical formulations to compute GGT. However, there are not many open source softwares in this regard. The understanding of the tensor properties is imperative and provides fundamental guidelines in the development of a three dimensional geological model. From the last few decades, numerous attempts have been made on modelling and deciphering the three dimensional complex geometries like Salt domes and other complex tectonic environments using gravity and gravity gradiometry. Recent advancement of gravity gradiometry on different platforms like airborne and space using satellite opened up a path way for their use both in exploration and geodynamics so as to understand the complexity below the earths surface, even though the interpretation techniques of gravity gradiometer are still in developing mode. In the above said context, the author in the present thesis developed a MATLAB computational algorithm to calculate the gravity field and full gravity gradient tensor for undulated surface followed by regular geometries like, an infinite horizontal slab, vertical sheet, solid sphere, vertical cylinder, normal fault model, and rectangular lamina or conglomerations of such bodies and the results are compared with responses using professional software based on different computational schemes. Real subsurface geometries are approximated through infinite cell of vertical rectangular lamina to characterize the response due to complex geological structure of interest. Thus, these computational algorithms help to understand the complex behavior of gravity gradient responses even for simple geometries that produces complex pattern of anomalies like monopole, dipole, tripole, and quadrupole responses and further to correlate these responses with real geological data to infer simple as well as complex subsurface structures. The geological application of this algorithm is demonstrated over a horst-type structure of Oklahoma Aulacogen, USA and Vredefort Dome, South Africa, where measured GGT data are available. The thorough understanding of the behavior of gravity gradients through MATLAB computation of different geometries mentioned above was used in the second part of the thesis to
  • 10. x derive a 3D density model of salt domes. For this, the real gravity and reprocessed gradient data of the Wathlingen salt dome situated in the southern part of the Northwest German basin was made use for joint modelling. Numerous attempts are made on modelling of salt tectonics and several models are developed to explain the ascent of salt diapirs using different geophysical parameters like gravity, magnetic, seismic etc. Since, salt diapirs are salt structures that pierce their overburden. Such diapirism occurs in variety of different tectonic settings including passive continental margins, intra cratonic basin or fold and thrust belts. The structures produced by salt tectonics can have a strong impact on the formation of hydrocarbon reservoirs. A 3D density model of the Wathlingen salt dome, situated in the southern part of the Northwest German basin is derived from the joint modelling of reprocessed torsion balance measurements. Gravity, gravity gradients (Wzx, Wzy), curvature (Wxy) derived from both horizontal gravity gradients, and Horizontal Directive Tendency (HDT) are jointly modeled to decipher the geometrical structure of the salt dome. The model is constrained by geological and borehole information. It is found that Wathlingen salt dome is a mushroom structured salt body, which is 14 km long, 4 km to 8 km wide extending up to ~ 4 km depth. The top mushroom structure of the salt is horizontally spread up to ~ 8 km. It would not have been possible to derive the complex 3D structure from modelling of gravity data alone. After the above successful effort in mapping salt dome features, which is of residual scale (few tens of km) the present study is extended to a regional scale (over hundreds of km) to address regional geodynamics. The regional scale study utilizes satellite gravity data derived from satellite altimetry over the region of Bay of Bengal, which is known for large sediment thickens to reveal hidden structures beneath sea floor. The basement depth and crustal thickness are important parameters when interpreting the tectonic or thermal evolution of a margin, however depth to basement, basement architecture and crustal structure remain poorly determined in the deep water parts of the Bay of Bengal. While regional-scale interpretation of the new and existing 2D seismic reflection data has provided important new insights into the structural framework of the basin, a number of outstanding issues remain which cannot be addressed using seismic data alone as they do not have information up to Moho or below it. The main goal of the study is an attempt to determine this sedimentary cover in oceanic crust and structural trends in a part of Bengal fan between the latitudes 0o 00 to 22o 00 N and the longitude of 80o 00 to 94o 00 E, through the integrated analysis and interpretation of gravity
  • 11. xi observations and computed gravity gradients. Integrated interpretation leads to an improved representation of lithospheric structures in Bay of Bengal. For quantitative interpretation of the sources of the anomaly, a 3D density model of the oceanic lithosphere is designed by means of forward modelling and inversion constrained by prior information to investigate the crust mantle interface and detailed lithosphere properties. As a result of the current investigation, a regional structural map of the basement is constructed. In addition, two major ridges, 85o and 90o east ridges get easily identified using gradient components. This study also, reveals that, the depth to the basement surface ranges from 7 to more than 29 km, delineating promising deep sedimentary layer of around 22 km thick. Modelling results indicated that, the lateral density variation is so steep throughout the study area and also the thick sediment load changes the lateral property of deeper layer below crust. The last part of the thesis therefore demonstrates that satellite derived gravity data can be used to model regional gravity anomaly produced by lithospheric properties and structures evolve over the geological time period.
  • 12. xii RESEARCH PUBLICATIONS Thesis Papers: Dubey, C. P., Gotze, H. J., Schmidt, S., Tiwari, V. M., 2014, A 3D model of the Wathlingen salt dome in the Northwest German Basin from joint modelling of gravity, gravity gradient, and curvature. Interpretation, Vol. 2, No. 4, p. 1-13, doi: 10.1190/INT-2014-0012.1. Dubey, C. P., and Tiwari, V. M., 2015, MATLAB Algorithm for Computation of gravity field and its gradient: some applications; Computer and Geosciences. (Submitted after minor revision). Dubey, C. P., and Tiwari, V. M., and Rao, P. R., Detailed lithosphere structure of Bay of Bengal and their tectonic implications. Lithosphere (To be Submitted) Dubey, C. P., Tiwari, V. M., and Rao, P. R., Mapping subsurface structures below Bay of Bengal Basin using full gravity gradient tensor. SEG-Interpretation (To be Submitted). Supplementary Paper: Gupta, H...Tiwari, V.M. Dubey, C. P... Nayak, S., 2014, Investigations related to scientific deep drilling to study reservoir-triggered earthquakes at Koyna, India, International Journal of Earth Sciences, DOI 10.1007/s00531-014-1128-0. Tiwari, V. M., Mishra, S., Dubey, C. P., and Raju, D. Ch. V., 2015, 3D Structural setting beneath Koyna Warna region from airborne gravity gradients and magnetic data; (In pipeline). International Conference Proceedings: Dubey, C. P., Gotze, H. J., Schmidt, S., and Tiwari, V. M., 2014, A 3D Model of the Wathlingen Salt Dome in the Northwest German Basin from joint modelling of Gravity, Gravity Gradient, and Curvature; Geophysical Research Abstracts, Vol. 16, EGU 2014- 13916, 2014, EGU General Assembly 2014. Dubey, C. P., 2014, Glimpses of SEG NGRI Student Chapter at CSIR-NGRI, Hyderabad, India and my personal research; 84th SEG Annual Meeting, Denver, Colorado, USA, 2014.
  • 13. xiii Mishra, S., Dubey, C. P., and Tiwari, V. M., 2014, 3D Structural setting beneath Koyna Warna region from airborne gravity gradients and magnetic data, NGRI RC Meeting 2014, Hyderabad India. Dubey, C. P., and Tiwari, V. M., 2013 Imaging 3D complex geological structures from Gravity Gradiometry, NGRI RC Meeting 2013, Hyderabad, India. Dubey, C. P., and V. M. Tiwari, 2011, Computation of gravity potential and full gravity gradient tensor of arbitrary geometry and application, IGU 2011, Vishakhapatnam, India. Dubey, C. P., and V. M. Tiwari, 2010, A computational method to calculate the gravity potential and full gravity gradient tensor of arbitrary shape bodies and its applications, ICON- GSCESS 2010, BHU, Varanasi, India.