The seismoeletric method theory and application

Free ebooks ==> www.Ebook777.com www.Ebook777.com Free ebooks ==> www.Ebook777.com www.Ebook777.com The Seismoelectric Method Free ebooks ==> www.Ebook777.com The Seismoelectric Method Theory and applications André Revil Associate Professor, Colorado School of Mines, Golden, CO, USA Directeur de Recherche at the National Centre for Scientific Research (CNRS), ISTerre, Grenoble, France Abderrahim Jardani Associate Professor, Mtre de Conférence, Université de Rouen, Mont-Saint-Aignan, France Paul Sava Associate Professor, Colorado School of Mines, Golden, CO, USA Allan Haas Senior Engineering Geophysicist, hydroGEOPHYSICS, Inc., Tuscon, AZ, USA www.Ebook777.com This edition first published 2015 © 2015 by John Wiley & Sons, Ltd Registered Office John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK Editorial Offices 9600 Garsington Road, Oxford, OX4 2DQ, UK The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, UK 111 River Street, Hoboken, NJ 07030-5774, USA For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com/wiley-blackwell The right of the author to be identified as the author of this work has been asserted in accordance with the UK Copyright, Designs and Patents Act 1988 All rights reserved No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher Designations used by companies to distinguish their products are often claimed as trademarks All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners The publisher is not associated with any product or vendor mentioned in this book Limit of Liability/Disclaimer of Warranty: While the publisher and author(s) have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom If professional advice or other expert assistance is required, the services of a competent professional should be sought Library of Congress Cataloging-in-Publication Data Revil, André, 1970– The seismoelectric method : theory and applications / André Revil, associate professor, Colorado School of Mines, Golden CO, USA [and] Directeur de Recherche at the National Centre for Scientific Research (CNRS), ISTerre, Grenoble, France, Abderrahim Jardani, associate professor, Mtre de Conference, Université de Rouen, Mont-Saint-Aignan, France, Paul Sava, associate professor, Colorado School of Mines, Golden CO, USA, Allan Haas, senior engineering geophysicist, HydroGEOPHYSICS, Inc., Tuscon, AZ, USA pages cm Includes index ISBN 978-1-118-66026-3 (cloth) Seismic prospecting Prospecting–Geophysical methods I Jardani, Abderrahim II Sava, Paul III Haas, Allan IV Title TN269.8.R48 2015 622 1592–dc23 2015002784 A catalogue record for this book is available from the British Library Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Set in 8.5/12pt Meridien by SPi Publisher Services, Pondicherry, India 2015 This book is dedicated to two Russian scientists who developed the electrokinetic concepts attached to the seismoelectric effects Andrey Germogenovich Ivanov (1907–1972) Son of a teacher of geography, Andrey worked at the Institute of Earth Physics (SU Academia of Sciences) in 1930s and up to mid-1950s His work was mostly concerned with the seismoelectrical method, but he worked also on low-frequency electromagnetic methods Andrey wrote two handbooks The first book was concerned with geophysical methods applied to the detection of mineral deposits It was published in 1961 and in collaboration with Feofan Bubleinikov The second book was entitled Physics in Investigations of Earth Interior (1971) Andrey Germogenovich Ivanov is usually credited to have been the first scientist to record seismoelectric effects in field conditions Yakov Il’ich Frenkel (1894–1952) Frenkel was born on February 10, 1894, in the southern Russian city of Rostov-on-Don He was a very influential Russian scientist during the first half of the 20th century Geophysics was a field of Frenkel’s early interest In 1944, Frenkel visited the Institute of Theoretical Geophysics in Moscow There, he became interested in the work of Andrey Germogenovich Ivanov As mentioned above, Ivanov was the first to discover, in 1939, that the propagation of seismic waves in soils was accompanied by the appearance of an electrical field Ivanov recognized that this new phenomenon was caused by the pressure difference between two points in wet soil resulting from the propagation of longitudinal (P-)waves Frenkel modeled the wet soil as a two-phase material, and he formulated the first continuum hydromechanical theory for wave propagation in porous media Frenkel discovered the existence of the second compressional P-wave (usually named later the Biot slow P-wave), but he dismissed the electrical effects associated with this type of wave as unimportant because of the strong damping of this slow P-wave Frenkel was the first to understand that the seismoelectric effect recorded by Ivanov could be electrokinetic in nature Indeed, the presence of water in a porous material is responsible for the formation of an electric double layer on the mineral surface The relative movement of the excess charge of the electrical diffuse layer (the external part of the electrical double layer) due to the passage of a seismic wave is responsible for the generation of a source current density These currents are responsible in turn for the generation of electromagnetic disturbances Frenkel’s 1944 paper “On the theory of seismic and seismoelectric phenomena in moist soil” is the first to theoretically describe wave propagation in porous media A complete theory was however produced in 1956 by Maurice Biot The linear poroelasticity theory should generally be referred to as the Biot–Frenkel theory rather the Biot theory as done classically in the literature His life and contributions are described in the book Yakov Ilich Frenkel: His Work, Life and Letters by Frenkel, V Ya., and Birkhäuser Verlag (1996) Contents Foreword by Bernd Kulessa, xi Foreword by Niels Grobbe, xii Preface, xiv Acknowledgments, xvi Introduction to the basic concepts, 1.1 The electrical double layer, 1.1.1 The case of silica, 1.1.1.1 A simplified approach, 1.1.1.2 The general case, 1.1.2 The case of clays, 10 1.1.3 Implications, 14 1.2 The streaming current density, 15 1.3 The complex conductivity, 17 1.3.1 Effective conductivity, 18 1.3.2 Saturated clayey media, 19 1.4 Principles of the seismoelectric method, 22 1.4.1 Main ideas, 22 1.4.2 Simple modeling with the acoustic approximation, 25 1.4.2.1 The acoustic approximation in a fluid, 25 1.4.2.2 Extension to porous media, 26 1.4.3 Numerical example of the coseismic and seismoelectric conversions, 27 1.5 Elements of poroelasticity, 28 1.5.1 The effective stress law, 28 1.5.2 Hooke’s law in poroelastic media, 31 1.5.3 Drained versus undrained regimes, 31 1.5.4 Wave modes in the pure undrained regime, 33 1.6 Short history, 34 1.7 Conclusions, 36 Seismoelectric theory in saturated porous media, 42 2.1 Poroelastic medium filled with a viscoelastic fluid, 42 2.1.1 Properties of the two phases, 42 2.1.2 Properties of the porous material, 45 2.1.3 The mechanical equations, 49 2.1.3.1 Strain–stress relationships, 49 2.1.3.2 The field equations, 52 2.1.3.3 Note regarding the material properties, 53 2.1.3.4 Force balance equations, 53 2.1.4 The Maxwell equations, 53 vii Free ebooks ==> www.Ebook777.com viii Contents 2.1.5 Analysis of the wave modes, 54 2.1.6 Synthetic case studies, 56 2.1.7 Conclusions, 59 2.2 Poroelastic medium filled with a Newtonian fluid, 59 2.2.1 Classical Biot theory, 59 2.2.2 The u–p formulation, 60 2.2.3 Description of the electrokinetic coupling, 62 2.3 Experimental approach and data, 62 2.3.1 Measuring key properties, 62 2.3.1.1 Measuring the cation exchange capacity and the specific surface area, 62 2.3.1.2 Measuring the complex conductivity, 63 2.3.1.3 Measuring the streaming potential coupling coefficient, 63 2.3.2 Streaming potential dependence on salinity, 63 2.3.3 Streaming potential dependence on pH, 66 2.3.4 Influence of the inertial effect, 66 2.4 Conclusions, 69 Seismoelectric theory in partially saturated conditions, 73 3.1 Extension to the unsaturated case, 73 3.1.1 Generalized constitutive equations, 73 3.1.2 Description of the hydromechanical model, 77 3.1.3 Maxwell equations in unsaturated conditions, 81 3.2 Extension to two-phase flow, 81 3.2.1 Generalization of the Biot theory in two-phase flow conditions, 81 3.2.2 The u–p formulation for two-phase flow problems, 83 3.2.3 Seismoelectric conversion in two-phase flow, 85 3.2.4 The effect of water content on the coseismic waves, 86 3.2.5 Seismoelectric conversion, 90 3.3 Extension of the acoustic approximation, 91 3.4 Complex conductivity in partially saturated conditions, 92 3.5 Comparison with experimental data, 93 3.5.1 The effect of saturation, 93 3.5.2 Additional scaling relationships, 93 3.5.3 Relative coupling coefficient with the Brooks and Corey model, 95 3.5.4 Relative coupling coefficient with the Van Genuchten model, 96 3.6 Conclusions, 97 Forward and inverse modeling, 101 4.1 Finite-element implementation, 101 4.1.1 Finite-element modeling, 101 4.1.2 Perfectly matched layer boundary conditions, 102 4.1.3 Boundary conditions at an interface, 104 4.1.4 Description of the seismic source, 104 4.1.5 Lateral resolution of cross-hole seismoelectric data, 104 4.1.6 Benchmark test of the code, 105 4.2 Synthetic case study, 105 4.2.1 Simulation of waterflooding of a NAPL-contaminated aquifer, 105 www.Ebook777.com Misfit value (#) Plot of misfit − E3:1851 s Minimum misfit = 9.05 position = 47 of 360 elements 25 20 15 10 50 100 Figure 18 (a) 150 200 250 Modeled dipole position 300 350 Magnitude (mV) Real data versus GA synthetic data − E3:1851 s Norm of error = 9.05 Misfit parameter = L2 Norm Position = 47 of 360 elements Real Synthetic 20 10 −10 (b) 10 Magnitude (mAm) 1.4 15 20 Electrode Position (#) GA model vector − E3:1851 s 25 30 1.2 0.8 0.6 0.4 0.2 100 (c) 200 300 400 500 600 700 800 900 1000 Model vector location Figure 5.31 a) E3-related genetic algorithm localization misfit values for each position in the kernel matrix The red circle represents the minimum value and therefore the best fit for the measured data, given the inversion constraints b) Comparison of the real data and the genetic algorithm-based model vector forward computation c) The genetic algorithm-based best fit model vector Note that there are three points on the vector where there are values that are greater than zero These points are exactly 360 elements apart, representing a single dipole moment orthogonal components Plot of misfit − E3:1851 s Minimum misfit = 9.05 Position = 47 of 360 elements Misfit value (#) 10.5 10 9.5 X:17 Y: 9.193 8.5 10 20 X: 78 Y: 9.115 30 40 50 60 70 Modeled dipole position Figure 5.32 Zoom in the values of the misfit parameter obtained using the genetic algorithm-based inversion of Event E3 This figure shows that there are several dipole solutions that are close to the minimum of the data misfit function In this figure, there are several other possible solutions, and they are all close to the point found at position 47, the minimum These additional possible locations corresponds to dipole positions 17, 18, 48, 77, and 78 Full GA inverted model forward Spatial response (mV) – top array Full GA inverted model forward spatial response (mV) – back array 25 270 12 16 20 270 Time = 1851 s 24 28 32 20 Hole 10 11 15 E3 10 14 110 Y-position (mm) Y-position (mm) 15 190 19 190 23 27 31 10 CMS DRL 18 110 22 26 30 Hole 9 13 17 30 21 25 29 −5 30 −10 30 110 190 X-position (mm) (a) 270 20 (b) 0.25 0.2 0.2 (e) 0.1 0.05 0.05 0.05 0.1 0.15 0.2 0.25 X-position (m) Threshoulded dipole positions for top array (d) 0.12 0.11 0.11 0.1 0.1 0.08 (e) –0.05 –0.1 –0.15 –0.2 –0.25 0.09 0.08 0.07 0.07 0.06 0.2 Z-position (m) Threshoulded dipole positions for back array 0.12 0.09 (f) 0.15 0.1 (c) Y-position (m) Y-position (m) 0.25 260 Threshoulded dipole positions for back array 0.3 Y-position (m) Y-position (m) Threshoulded dipole positions for top array 0.3 0.15 100 180 Z-position (mm) 0.21 0.22 0.23 0.24 X-position (m) 0.25 0.06 0.26 (f) –0.08 –0.09 –0.1 –0.11 –0.12 –0.13 Z-position (m) Figure 5.33 Localization of the causative source of current a) and b) E3 forward modeled voltage distribution of the genetic algorithm located dipole c) and d) Spatial location of the dipole within the concrete block e) and f) Close-up of the dipole location showing the vertical orientation of the dipole moment Y-position (m) Thresholded dipole position for top array 0.12 E3 Time 1851 s 0.11 0.06 0.07 0.08 0.09 0.10 0.11 0.12 –0.08 E3 Time 1851 s Vertical progression notional section Well 0.09 0.08 –0.10 Cement 0.10 Z-position (m) Y-position (m) –0.09 –0.11 –0.12 0.07 Void Well –0.13 Epoxy 0.06 0.20 0.21 0.22 0.23 0.24 0.25 0.26 X-position (m) (a) (b) E3 Water Tubing Y-position (m) Thresholded dipole position for top array 0.12 E2 Time 1809.5 s 0.11 0.06 0.07 0.08 0.09 0.10 0.11 0.12 –0.08 E2 Time 1809.5 s Z-position (m) Y-position (m) –0.09 0.10 Well 0.09 0.08 –0.10 –0.11 E2 –0.12 0.07 Well –0.13 0.06 0.20 0.21 0.22 0.23 0.24 0.25 0.26 (c) X-position (m) (d) (e) Figure 5.34 Proposed explanation of the electrical disturbances observed in the experiment Events E2 and E3 are shown together with their spatial placement near Hole in panels a) through d) The blue x’s in panels a) through d) are the dipole point positions used in the genetic algorithm source inversion process The green circle in panels a) and c) represents the position of Hole as viewed from the top, and the vertical green lines in panels b) and d) represent the position of Hole as seen from the side The red circles in panels b) and d) are the position of one of the measurement electrodes It can be clearly seen in this figure that the first event, E2, occurs lower in the model representation (and by correlation, in the test specimen) than the later event, E3 The figure in panel e represents a conceptualization of the movement of the fluid through multiple epoxy barriers, filling voids in between each the barriers with water The voids represent points of open contact with the cement that allow the fracturing fluid to make direct contact, generating the observed pressure fluctuations and electrical impulses e) Sketch of the tubing showing the progression of the Events E2 and E3 along the well over time Thresholded dipole position for back array 0.12 0.11 0.11 0.10 0.10 Y-position (m) Y-position (m) Thresholded dipole position for top array 0.12 0.09 0.08 0.07 0.06 0.20 (a) 0.09 0.08 Initial Solution = 42 1% Noise = 5% Noise = 62 10% Noise = 61 0.21 0.22 0.23 0.07 0.24 X-position (m) 0.25 0.06 0.26 (b) –0.08 –0.09 –0.1 –0.11 –0.12 –0.13 Z-position (m) Figure 5.35 Localization of the causative source of current and noise analysis a) and b) These figures show the spatial positions of the dipoles found during the localization uncertainty test Note that the solutions cluster near the initial solution found during the inversion process The bias in the +y and −z directions may indicate that the true solution may be between the solutions with noisy data and the solution found initially Side view 0.3 0.25 0.25 0.2 0.2 Y-position (m) Y-position (m) View from above 0.3 0.15 Well #9 0.1 0.15 Well #9 0.1 0.05 0.05 Before voltage acquisition During voltage acquisition After voltage acquisition 0.05 0.1 0.15 0.2 0.25 0.3 –0.05 –0.1 –0.15 –0.2 –0.25 Z-position (m) X-position (m) Figure 5.36 Localization of the acoustic emissions with respect to the time window shown in Figure 5.20 The events localized far from Well #9 are probably associated with the reactivation of small cracks Note that only a tiny fraction of the AE hits shown in Figure 5.20 are localizable Resistivity tomogram prior the water pulse injection Well Iteration RMS error 4.7% 2.5 Depth (m) 2.4 2.3 0.8 2.2 1.2 2.1 1.6 Log (DC resistivity, Ohm m) 0.4 1.9 2 10 12 14 16 Distance (m) (a) Resistivity tomogram after the water pulse injection Well Iteration RMS error 4.7% 2.5 Depth (m) 2.4 2.3 0.8 2.2 1.2 2.1 1.6 Log (DC resistivity, Ohm m) 0.4 1.9 2 10 12 14 16 Distance (m) (b) Figure 5.44 Inverted DC resistivity section using the Gauss–Newton method The data are collected using 32 electrodes with 50 cm spacing a) Tomogram prior the pulse injection b) Tomogram after the pulse injection Raw electrograms 60 Amplitude (mV) 40 20 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 −20 −40 −60 140 141 142 143 144 145 146 147 148 147 148 Time (s) Channel number (a) Detrended and synchronized electrograms Amplitude (mV) 30 Injection t = 145.1 s 20 10 Preinjection −10 −20 Injection window −30 140 141 142 143 144 145 146 Time (s) (b) Electrograms from 144.5 s to 146 s 40 Amplitude (mV) 30 20 10 −10 −20 Snapshot t = 145.38 s −30 −40 144.5 146 145.5 145 Time (s) (c) Figure 5.45 Self-potential time series from the water injection experiment a) Raw electrograms b) Detrended and background corrected electrograms c) Magnification of the electrograms showing the preinjection and injection time windows Inverted volumetric current density × 10–4 Least square inversion result for 145.375 s Well −10 0.2 −11 −12 −2 Electric potential (mV) 0.6 0.8 Depth (m) Volumetric current density (A m–3) 0.4 1.2 −4 −14 −15 1.4 −16 −6 1.6 Measured −17 1.8 −8 7.0 7.5 8.0 8.5 9.0 9.5 −18 7.0 10 Distance (m) (a) −13 Predicted 7.5 8.0 8.5 9.0 9.5 10 Distance (m) (b) Figure 5.46 Source localization of a single snapshot at time 145.38 s the localization of the self-potential anomaly (positive pole associated with the pulse injection) is located very close to the end of the open well The electrical resistivity has been accounted for this inversion Results shown are at the third iteration 0 10 10 E29 Background 20 20 Background Anomaly 30 A 40 Depth (m) Depth (m) 40 50 60 50 Anomaly 60 70 70 80 80 90 A 30 B B 90 E46 E1 100 10 20 (a) 30 40 50 100 60 10 20 (b) Offset (m) 30 40 50 60 Offset (m) Figure 6.1 Geometry used for the beamforming problem The medium consists of a homogeneous background model (reference model, fully saturated) plus two anomalies termed Anomaly and Anomaly These anomalies correspond to areas that are unsaturated (see Table 6.3) The survey area is surrounded by two vertical wells located on each side The triangles correspond to the location of the seismic sources/geophones/electrodes The spacing between two consecutive sensors is m The two boreholes have 19 dipoles of electrodes each, and sets of sensors are located close to the ground surface (5 m deep) The two red-filled circles correspond to the focusing points used for our numerical experiments Ei corresponds to the position of electrode i There are 46 set of sensors in total with E1 and E46 at the bottom of the two wells a) Reference model (without the two heterogeneities) b) Model used for the numerical simulation with the two heterogeneities Pressure field at t = 20 ms Pressure field at t = 16 ms 10 Pressure field at t = 23 ms Background Background Background 0.5 0.5 0.5 20 Anomaly1 A 0.4 Anomaly2 60 0.2 A 0.4 0.3 Anomaly2 0.2 0.4 0.3 Anomaly2 0.2 70 80 0.1 0.1 Amplitude (a.U.) 0.3 50 Anomaly1 A Amplitude (a.U.) 40 Amplitude (a.U.) Depth (m) 30 Anomaly1 0.1 90 100 10 20 30 40 50 60 0 Offset (m) (A) Pressure field at t = 25 ms 20 30 40 Offset (m) 50 60 Background 10 Background 0.5 20 30 40 Offset (m) 50 60 Electric potential distribution 0.25 0.2 Background 0.5 20 0.15 Anomaly1 30 Anomaly1 A 0.4 Anomaly2 60 0.2 0.4 0.3 Anomaly2 0.2 70 0.1 A 0.05 −0.05 Anomaly2 Amplitude (a.U.) 0.3 50 Anomaly1 A Amplitude (a.U.) 40 Amplitude (a.U.) Depth (m) (C) Pressure field at t = 27ms 10 10 (B) −0.1 80 0.1 0.1 −0.15 90 100 (D) 0 10 20 30 40 Offset (m) 50 60 (E) 10 20 30 40 Offset (m) 50 60 −0.2 0 (F) 10 20 30 40 50 −0.25 Figure 6.3 Seismic beamforming and resulting electrical potential distribution (a–e) Snapshots show the pressure field (coming from the 46 seismic sources shown in Figure 6.1) focusing at point A At t = 27 ms, the wave field interferes constructively at point A producing a strong seismoelectric response that is recorded at the receiver electrodes f) The distribution of the electrical potential corresponds to the case where the seismic energy is focused at point A The seismoelectric conversion at the time of focusing is characterized by a strong dipolar behavior Well A (injector) water Water saturation at snapshot T3 Well B (producer) oil PML 2340 Depth (m) 2360 2380 2400 0.6 PML Reservoir 0.55 0.5 0.45 0.4 2420 0.35 2440 Water saturation (—) Saturation front 0.65 0.3 50 100 150 Offset (m) 0.25 200 Seismic sources and receivers Figure 6.6 Sketch of the domain used for modeling The total modeling domain is a 410 m × 250 m rectangle Injector Well A, located at position x = m, is also used for the seismic source Production and recording Well B is located at x = 250 m The discretization of the domain comprises a finite-element mesh of 205 × 125 rectangular cells Twenty-eight receivers are located in Well B, approximately 30 m away from the nearest PML boundary (the PML boundary layers are shown in gray) P-wave velocity (m–1s) 4320 2340 4300 2360 Depth (m) 4280 2380 4260 4240 2400 4220 2420 4200 2440 4180 50 100 (a) 150 200 Offset (m) Permeability (m2) 2340 −14 2360 Depth (m) −14.5 2380 −15 2400 −15.5 2420 2440 (b) −16 50 100 150 200 Offset (m) Figure 6.7 Sketch of the distribution of the P-wave velocity and permeability of the pore water phase at snapshot Note that the saturation front is characterized by a sharp contrast in permeability a) Velocity distribution for the compressional wave b) Distribution of the permeability Conductivity (S m–1) 2340 0.05 2360 Depth (m) 0.04 2380 0.03 2400 2420 0.02 2440 0.01 50 100 (a) 150 200 Offset (m) Porosity(—) 2340 0.36 Depth (m) 2360 0.34 2380 0.32 2400 0.3 2420 0.28 2440 50 (b) 100 150 200 0.26 Offset (m) Figure 6.8 Sketch of the distribution of the electrical conductivity and porosity at snapshot Note that the saturation front is characterized by a sharp contrast in electrical conductivity a) Electrical conductivity distribution b) Porosity distribution Detection of the saturation front – Tranmission test 2340 Saturation front Depth (m) 2360 Seismic source 2380 E1 F1 2400 2340 2420 2360 2440 2380 50 100 150 200 Offset (m) (a) Electric potential at E1 (a.u.) Coseismic field Electric potential 0.5 −0.5 Seismoelectric conversion −1 −1.5 20 (b) 30 40 50 60 70 Time (ms) 80 90 100 110 120 100 110 120 Fluid pressure field at saturation front, point F1 (a.u.) 1.5 Pressure 0.5 −0.5 −1 −1.5 20 (c) 30 40 50 60 70 Time (ms) 80 90 Figure 6.9 Transmission experiment with the seismic source in Well A and the electrical receiver in Well B a) Geometry of the test b) Time series for the electrical potential showing the seismoelectric conversion occurring at the interface and the coseismic field c) Fluid pressure field at a point located at the saturation front at the center of the Fresnel zone Pressure field #1 Pressure field #4 2340 2340 0.8 Depth (m) Focus point 0.4 2400 0.2 2420 2360 50 100 (a) 150 Offset (m) Focus point 0.2 2440 −0.2 200 −0.2 50 100 (d) 200 2340 0.2 2420 Depth (m) 0.4 2400 2360 50 100 (b) 150 Offset (m) Focus point 0.2 2440 −0.2 −0.2 200 50 100 (e) Pressure field #3 0.8 Focus point 0.4 2400 0.2 2420 (c) 150 Offset (m) 2380 Focus point 2400 2420 2440 2440 100 2360 −0.2 200 Amplitude (a.u.) 0.6 0.5 Saturation front Amplitude (a.u.) 2360 50 200 Electric potential at focus time Saturation front 2380 150 Offset (m) 2340 Depth (m) 2340 0.4 2400 2420 2440 0.6 2380 Amplitude (a.u.) Focus point Amplitude (a.u.) 0.6 2380 0.8 Saturation front 0.8 Saturation front 2360 Depth (m) 150 Offset (m) Pressure field at focus time Pressure field #2 2340 Depth (m) 0.4 2400 2420 2440 0.6 2380 Amplitude (a.u.) 2380 0.8 Saturation front Amplitude (a.u.) 0.6 Depth (m) Saturation front 2360 −0.5 50 100 (f) 150 200 Offset (m) Figure 6.10 Seismic beamforming at the saturation front and resulting electrical potential distribution (a–e) Evolution of the confining pressure P(r, t) for snapshots The propagating wave fields interfere constructively at the focus point f) Electrical potential distribution corresponding to the seismic energy focused at the saturation front (snapshot e) 0 200 200 400 400 600 Mass density × (m) 200 400 Geometry Well A × (m) Well B 200 400 200 Depth (m) z (m) z (m) Electrical conductivity × (m) 200 400 600 400 Scanned 600 800 800 800 1000 area ℜ 1000 1000 (a) 0.5 1.0 Conductivity (S m–1) (b) 2000 2000 Bulk density (kg/m–3) Horizontal distance (c) Figure 6.12 Model used for the scanning simulations a), b) Heterogeneous distribution of the electrical conductivity and mass density of the formations c) Geometry of the acquisition array The porous material is bimodal with a larger correlation length in the horizontal direction The seismic receivers are located in two wells (A and B) The area scanned through focusing is indicated by the yellow rectangle (scanning region ℜ) Scanning points Seismoelectric image × (m) 200 × (m) 400 0 200 200 400 400 200 400 z (m) z (m) 600 600 800 800 1000 1000 (a) (b) Figure 6.20 Seismoelectric image of the electrical potential using a set of electrodes located in the two wells for the domain ℜ a) Position of the scanning (focusing) points The total number of scanning points is actually (Nx = 128) × (Nz = 320), that is, a total of more than 40,960 points Only a fraction of these points is shown here b) High-definition voltage map with the position of the electrodes used in the wells to scan the electrical potential We see that the voltage map contains a lot of structural information regarding the position of the heterogeneities between the wells in the scanning area The voltages are opposite in sign on each side of the heterogeneities 0.9 200 0.8 Depth (m) 0.7 0.6 600 ℜ 0.5 800 Electrical resistivity (Ohm m) 400 0.4 0.3 1000 100 200 300 Distance (m) 400 Figure 6.22 Position of the electrodes (black circles, 105 electrodes per well, spacing 10 m) for the cross-well resistivity tomography and discretization of the domain (the size of the cells is 10 × 10 m) The resistivity image denotes the true resistivity image used to simulate the acquisition of the apparent resistivity data We are interested in recovering the resistivity information in domain ℜ Free ebooks ==> www.Ebook777.com No structure information Resistivity (Ohm m) 0.2 0.8 0.6 0.4 200 Depth (m) 400 600 800 1000 100 200 300 Distance (m) 400 Figure 6.23 Result of a classical cross-well resistivity tomography in domain ℜ using the least-square method without structural information to constrain the model covariance matrix Classical cross-well resistivity tomography is unable to image the formations between the wells due to a lack of resolution far away from the electrodes In addition, the values of the resistivity are smoother than the true values, which mean that the application of a petrophysical model to the recovered resistivity would lead to a misinterpretation of the petrophysical parameters of interest www.Ebook777.com Light structure information Extreme structure information Hard structure information Medium structure information 200 Depth (m) 1.2 1.0 0.8 600 0.6 0.4 0.2 Electrical resistivity (Ohm m) 400 800 1000 100 (a) 200 300 400 100 (b) Distance (m) 200 300 100 400 (c) Distance (m) 200 300 100 400 Distance (m) (d) 200 300 400 Distance (m) Figure 6.25 Importance of structure information in recovering the cross-well resistivity model through cross-well resistivity tomography We consider the following value of the regularization parameter β: 0.1 (light), (medium), 10 (hard), and 100 (extreme) Seismic supergather Seismoelectric supergather Offset (m) Time (ms) –50 (a) –30 –10 10 Offset (m) 30 50 –50 20 20 40 40 60 60 80 80 100 100 120 120 140 140 160 160 180 180 200 200 –30 –10 10 30 50 Seismoelectric conversion (b) Figure 7.3 Seismic and seismoelectric supergathers (position 128 along the line, modified from Dupuis et al., 2007, reproduced with the authorization from the SEG and the authors) a) Seismic supergather offset records b) Seismoelectric supergather offset records Time (ns) 200 GPR 300 400 500 600 50 100 150 200 250 300 Seismoelectric Time (ms) 10 20 30 40 50 60 70 80 50 100 150 200 250 300 Distance (m) Figure 7.4 Comparison between a GPR profile and a seismoelectric 300 m profile (modified from Dupuis et al., 2007, reproduced with the authorization from the SEG and the authors) Variable elevation static delays were applied to the data to account for the effect of elevation Anomaly corresponds to the water table, while anomaly likely corresponds to a unit that might have a high water content Permeability (m2) m2 × 10−15 Log (resistivity, Ohm m) Water content (—) 0.32 0.3 Depth (m) 0.24 0.18 (a) Distance (m) 12.5 2.2 0.16 –12.5 2.3 0.2 20 2.4 0.22 15 2.5 0.26 10 2.6 0.28 –12.5 (b) Distance (m) 12.5 2.1 –12.5 Distance (m) 12.5 (c) Figure 7.11 Material properties distribution constructed for modeling a) Permeability b) Volumetric water content c) Electrical resistivity distribution In addition, we use a constant porosity for the domain of interest (Table 7.1) Free ebooks ==> www.Ebook777.com wiley end user license agreement Go to www.wiley.com/go/eula to access Wiley’s ebook EULA www.Ebook777.com ... Al3+) and can reverse the charge of the mineral surface (surface and Stern later together) and therefore can reverse the sign of the charge of the diffuse layer The sorption is described by the. .. referred to as the Biot–Frenkel theory rather the Biot theory as done classically in the literature His life and contributions are described in the book Yakov Ilich Frenkel: His Work, Life and Letters... relatively to the skeleton formed by the solid grains In the context of the seismoelectric theory, the propagation of seismic waves is responsible for such a relative flow of the pore water, and the associated