Seismoelectric Method

André Revil is Associate Professor at the Colorado School of Mines and Directeur de Recherche at the National Centre for Scientific Research (CNRS) in France. His research focuses on the development of new methods in petrophysics, and the development of electrical and electromagnetic geophysical methods applied to geothermal systems, water resources, and oil and gas reservoirs.Abderrahim Jardani is Associate Professor at the University of Rouen, where he also obtained his PhD in Geophysics 2007. His research interests centre on environmental geophysics, mathematical modeling of hydrologic systems and inverse problems.Paul Sava is an Associate Professor of Geophysics at Colorado School of Mines. He specializes in imaging and tomography using seismic and electromagnetic wavefields, stochastic imaging and inversion, computational methods for wave propagation, numeric optimization and high performance computing.Allan Haas is currently working at hydroGEOPHYSICS, Inc. as a Senior Engineering Geophysicist.  He graduated with a PhD in Geophysics at the Colorado School of Mines, on December 13, 2013.  During his PhD research, Allan investigated the measurable electrical signals associated with leakages in wells, hydraulic fracturing, and subsurface fracture flow.

• Foreword by Bernd Kulessa xiForeword by Niels Grobbe xiiPreface xiv1 Introduction to the basic concepts 11.1 The electrical double layer 11.1.1 The case of silica 21.1.1.1 A simplified approach 21.1.1.2 The general case 81.1.2 The case of clays 101.1.3 Implications 141.2 The streaming current density 151.3 The complex conductivity 171.3.1 Effective conductivity 181.3.2 Saturated clayey media 191.4 Principles of the seismoelectric method 221.4.1 Main ideas 221.4.2 Simple modeling with the acoustic approximation 251.4.2.1 The acoustic approximation in a fluid 251.4.2.2 Extension to porous media 261.4.3 Numerical example of the coseismic and seismoelectric conversions 271.5 Elements of poroelasticity 281.5.1 The effective stress law 281.5.2 Hooke’s law in poroelastic media 311.5.3 Drained versus undrained regimes 311.5.4 Wave modes in the pure undrained regime 331.6 Short history 341.7 Conclusions 362 Seismoelectric theory in saturated porous media 422.1 Poroelastic medium filled with a viscoelastic fluid 422.1.1 Properties of the two phases 422.1.2 Properties of the porous material 452.1.3 The mechanical equations 492.1.3.1 Strain–stress relationships 492.1.3.2 The field equations 512.1.3.3 Note regarding the material properties 522.1.3.4 Force balance equations 532.1.4 The Maxwell equations 532.1.5 Analysis of the wave modes 542.1.6 Synthetic case studies 562.1.7 Conclusions 592.2 Poroelastic medium filled with a Newtonian fluid 592.2.1 Classical Biot theory 592.2.2 The u–p formulation 602.2.3 Description of the electrokinetic coupling 612.3 Experimental approach and data 622.3.1 Measuring key properties 622.3.1.1 Measuring the cation exchange capacity and the specific surface area 622.3.1.2 Measuring the complex conductivity 632.3.1.3 Measuring the streaming potential coupling coefficient 632.3.2 Streaming potential dependence on salinity 632.3.3 Streaming potential dependence on pH 662.3.4 Influence of the inertial effect 662.4 Conclusions 693 Seismoelectric theory in partially saturated conditions 733.1 Extension to the unsaturated case 733.1.1 Generalized constitutive equations 733.1.2 Description of the hydromechanical model 773.1.3 Maxwell equations in unsaturated conditions 813.2 Extension to two-phase flow 813.2.1 Generalization of the Biot theory in two-phase flow conditions 813.2.2 The u–p formulation for two-phase flow problems 833.2.3 Seismoelectric conversion in two-phase flow 853.2.4 The effect of water content on the coseismic waves 863.2.5 Seismoelectric conversion 903.3 Extension of the acoustic approximation 913.4 Complex conductivity in partially saturated conditions 923.5 Comparison with experimental data 933.5.1 The effect of saturation 933.5.2 Additional scaling relationships 933.5.3 Relative coupling coefficient with the Brooks and Corey model 953.5.4 Relative coupling coefficient with the Van Genuchten model 963.6 Conclusions 974 Forward and inverse modeling 1014.1 Finite-element implementation 1014.1.1 Finite-element modeling 1014.1.2 Perfectly matched layer boundary conditions 1024.1.3 Boundary conditions at an interface 1044.1.4 Description of the seismic source 1044.1.5 Lateral resolution of cross-hole seismoelectric data 1044.1.6 Benchmark test of the code 1054.2 Synthetic case study 1054.2.1 Simulation of waterflooding of a NAPL-contaminated aquifer 1054.2.2 Simulation of the seismoelectric problem 1074.2.3 Results 1104.3 Stochastic inverse modeling 1124.3.1 Markov chain Monte Carlo solver 1124.3.2 Application 1154.3.3 Result of the joint inversion 1184.4 Deterministic inverse modeling 1184.4.1 A statement of the problem 1184.4.2 5D electric forward modeling 1214.4.3 The initial inverse solution 1254.4.4 Getting compact volumetric current source distributions 1264.4.5 Benchmark tests 1264.4.6 Numerical case studies 1274.4.7 Discussion 1334.5 Conclusions 1335 Electrical disturbances associated with seismic sources 1365.1 Theory 1365.1.1 Position of the problem 1365.1.2 Forward modeling 1375.1.3 Modeling noise-free and noisy synthetic data 1415.1.4 Results 1415.2 Joint inversion of seismic and seismoelectric data 1455.2.1 Problem statement 1455.2.2 Algorithm 1465.2.3 Results with noise-free data 1475.2.4 Results with noisy data 1485.2.5 Hybrid joint inversion 1505.2.6 Discussion 1545.3 Hydraulic fracturing laboratory experiment 1555.3.1 Background 1555.3.2 Material and method 1565.3.3 Observations 1595.3.4 Electrical potential evidence of seal failure 1645.3.5 Source localization algorithms 1655.3.5.1 Electrical and hydromechanical coupling 1665.3.5.2 Inversion phase 1: gradient-based deterministic approach 1675.3.5.3 Inversion phase 2: GA approach 1695.3.6 Results of the inversion 1705.3.6.1 Results of the gradient-based inversion 1705.3.6.2 Results of the GA 1755.3.6.3 Noise and position uncertainty analysis 1815.3.7 Discussion 1835.4 Haines jump laboratory experiment 1855.4.1 Position of the problem 1855.4.2 Material and methods 1865.4.3 Discussion 1875.5 Small-scale experiment in the field 1905.5.1 Material and methods 1915.5.2 Results 1915.5.3 Localization of the causative source of the self-potential anomaly 1925.6 Conclusions 1946 The seismoelectric beamforming approach 1996.1 Seismoelectric beamforming in the poroacoustic approximation 1996.1.1 Motivation 1996.1.2 Beamforming technique 2006.1.3 Results and interpretation 2026.2 Application to an enhanced oil recovery problem 2036.3 High-definition resistivity imaging 2086.3.1 Step 1: the seismoelectric focusing approach 2086.3.2 Step 2: application of image-guided inversion to ERT 2126.3.2.1 Edge detection 2126.3.2.2 Introduction of structural information into the objective function 2146.3.2.3 Results 2156.3.3 Discussion 2166.4 Spectral seismoelectric beamforming (SSB) 2176.5 Conclusions 2197 Application to the vadose zone 2207.1 Data acquisition 2207.2 Case study: Sherwood sandstone 2237.2.1 Experimental results 2237.2.2 Results 2247.2.3 Interpretation 2257.2.3.1 Seismoelectric signal preprocessing 2257.2.3.2 Seismoelectric–water content relationship 2267.2.4 Empirical modeling 2277.2.5 Discussion 2287.3 Numerical modeling 2297.3.1 Theory 2297.3.2 Description of the numerical experiment 2317.3.3 Model application and results 2317.4 Conclusions 2358 Conclusions and perspectives 237Glossary: the seismoelectric method 240Index 243