An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data
Esben Auken 1 8 Anders Vest Christiansen 1 Casper Kirkegaard 1 Gianluca Fiandaca 1 Cyril Schamper 2 Ahmad Ali Behroozmand 1 7 Andrew Binley 3 Emil Nielsen 4 Flemming Effersø 5 Niels Bøie Christensen 1 Kurt Sørensen 1 5 Nikolaj Foged 1 Giulio Vignoli 1 6
+ Author Affiliations
- Author Affiliations
1 Department of Earth Sciences, Aarhus University, C.F. Møllers Allé 4, DK-8000 Aarhus C, Denmark.
2 Sorbonne Universités, UPMC Univ Paris 06, 4 Place Jussieu, 75005 Paris, France.
3 Lancaster University, Bailrigg, Lancaster LA1 4YW, UK.
4 Danish Technical University, Anker Engelunds Vej 1, Bygning 101A 2800 Kgs. Lyngby, Denmark.
5 SkyTEM Surveys, Dyssen 2, DK-8200 Aarhus N, Denmark.
6 Geological Survey of Denmark and Greenland (GEUS), Lyseng Allé 1, 8270 Højbjer, Denmark.
7 School of Earth Sciences, Stanford University, 397 Panama Mall, Mitchell Building, Suite 101, Stanford, CA 94305-2210, USA.
8 Corresponding author. Email: esben.auken@geo.au.dk
Exploration Geophysics 46(3) 223-235 https://doi.org/10.1071/EG13097
Submitted: 28 November 2013 Accepted: 26 May 2014 Published: 29 July 2014
Abstract
We present an overview of a mature, robust and general algorithm providing a single framework for the inversion of most electromagnetic and electrical data types and instrument geometries. The implementation mainly uses a 1D earth formulation for electromagnetics and magnetic resonance sounding (MRS) responses, while the geoelectric responses are both 1D and 2D and the sheet’s response models a 3D conductive sheet in a conductive host with an overburden of varying thickness and resistivity. In all cases, the focus is placed on delivering full system forward modelling across all supported types of data. Our implementation is modular, meaning that the bulk of the algorithm is independent of data type, making it easy to add support for new types. Having implemented forward response routines and file I/O for a given data type provides access to a robust and general inversion engine. This engine includes support for mixed data types, arbitrary model parameter constraints, integration of prior information and calculation of both model parameter sensitivity analysis and depth of investigation. We present a review of our implementation and methodology and show four different examples illustrating the versatility of the algorithm. The first example is a laterally constrained joint inversion (LCI) of surface time domain induced polarisation (TDIP) data and borehole TDIP data. The second example shows a spatially constrained inversion (SCI) of airborne transient electromagnetic (AEM) data. The third example is an inversion and sensitivity analysis of MRS data, where the electrical structure is constrained with AEM data. The fourth example is an inversion of AEM data, where the model is described by a 3D sheet in a layered conductive host.
Key words: airborne electromagnetic, frequency domain electromagnetic, geoelectric, inversion, magnetic resonance sounding, transient electromagnetic.
References
Auken, E., and Christiansen, A. V., 2004, Layered and laterally constrained 2D inversion of resistivity data: Geophysics, 69, 752–761| Layered and laterally constrained 2D inversion of resistivity data:Crossref | GoogleScholarGoogle Scholar |
Auken, E., Nebel, L., Sørensen, K. I., Breiner, M., Pellerin, L., and Christensen, N. B., 2002, EMMA – a geophysical training and education tool for electromagnetic modeling and analysis: Journal of Environmental & Engineering Geophysics, 7, 57–68
| EMMA – a geophysical training and education tool for electromagnetic modeling and analysis:Crossref | GoogleScholarGoogle Scholar |
Auken, E., Christiansen, A. V., Jacobsen, B. H., Foged, N., and Sørensen, K. I., 2005, Piecewise 1D laterally constrained inversion of resistivity data: Geophysical Prospecting, 53, 497–506
| Piecewise 1D laterally constrained inversion of resistivity data:Crossref | GoogleScholarGoogle Scholar |
Auken, E., Christiansen, A. V., Jacobsen, L., and Sørensen, K. I., 2008, A resolution study of buried valleys using laterally constrained inversion of TEM data: Journal of Applied Geophysics, 65, 10–20
| A resolution study of buried valleys using laterally constrained inversion of TEM data:Crossref | GoogleScholarGoogle Scholar |
Auken, E., Christiansen, A. V., Viezzoli, A., Fitzpatrick, A., Cahill, K., Munday, T., and Berens, V., 2009a, Investigation on the groundwater resources of the South Eyre Peninsula, South Australia, determined from laterally constrained inversion of TEMPEST data: ASEG Extended Abstracts 2009, 1–5.
Auken, E., Christiansen, A. V., Viezzoli, A., Fitzpatrick, A., and Munday, T., 2009b, Laterally constrained inversion of TEMPEST data from Eyre Peninsula area, South Australia: 15th European Meeting of Environmental and Engineering Geophysics, 2009.
Auken, E., Christiansen, A. V., Westergaard, J. A., Kirkegaard, C., Foged, N., and Viezzoli, A., 2009c, An integrated processing scheme for high-resolution airborne electromagnetic surveys, the SkyTEM system: Exploration Geophysics, 40, 184–192
| An integrated processing scheme for high-resolution airborne electromagnetic surveys, the SkyTEM system:Crossref | GoogleScholarGoogle Scholar |
Balch, S. J., Boyko, W. P., and Paterson, N. R., 2003, The AeroTEM airborne electromagnetic system: The Leading Edge, 22, 562–566
| The AeroTEM airborne electromagnetic system:Crossref | GoogleScholarGoogle Scholar |
Behroozmand, A. A., Auken, E., Fiandaca, G., and Christiansen, A. V., 2012a, Improvement in MRS parameter estimation by joint and laterally constrained inversion of MRS and TEM data: Geophysics, 74, WB191–WB200
Behroozmand, A. A., Auken, E., Fiandaca, G., Christiansen, A. V., and Christensen, N. B., 2012b, Efficient full decay inversion of MRS data with a stretched-exponential approximation of the T2* distribution: Geophysical Journal International, 190, 900–912
| Efficient full decay inversion of MRS data with a stretched-exponential approximation of the T2* distribution:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC38XhtFGhtrjM&md5=0f012f379eb03965d098eb8d870890c4CAS |
Bracewell, R. N., 1986, The Fourier transform and its applications (2nd edition): McGraw-Hill, Inc.
Brodie, R., and Sambridge, M., 2006a, A holistic approach to inversion of frequency-domain airborne EM data: Geophysics, 71, G301–G312
| A holistic approach to inversion of frequency-domain airborne EM data:Crossref | GoogleScholarGoogle Scholar |
Brodie, R., and Sambridge, M., 2006b, A holistic approach to inversion of time-domain airborne EM: ASEG Extended Abstracts 2006, 1–4.
Christensen, N. B., 1990, Optimized fast Hankel transform filters: Geophysical Prospecting, 38, 545–568
| Optimized fast Hankel transform filters:Crossref | GoogleScholarGoogle Scholar |
Christensen, N. B., 2002, A generic 1-D imaging method for transient electromagnetic data: Geophysics, 67, 438–447
| A generic 1-D imaging method for transient electromagnetic data:Crossref | GoogleScholarGoogle Scholar |
Christensen, N. B., and Auken, E., 1992, Simultaneous electromagnetic layered model analysis: Proceedings of the Interdisciplinary Inversion Workshop 1, Geoskrifter, 49–56.
Christiansen, A. V., and Auken, E., 2012, A global measure for depth of investigation: Geophysics, 77, WB171–WB177
Christiansen, A. V., Auken, E., and Viezzoli, A., 2011, Quantification of modeling errors in airborne TEM caused by inaccurate system description: Geophysics, 76, F43–F52
| Quantification of modeling errors in airborne TEM caused by inaccurate system description:Crossref | GoogleScholarGoogle Scholar |
Cox, L. H., Wilson, G. A., and Zhdanov, M. S., 2010, 3D inversion of airborne electromagnetic data using a moving footprint: Exploration Geophysics, 41, 250–259
| 3D inversion of airborne electromagnetic data using a moving footprint:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BC3cXhsFyjt7jN&md5=189db35320cb17f04fecacc801e6f22bCAS |
d’Ozouville, N., Auken, E., Sørensen, K. I., Violette, S., Marsily, G. D., Deffontaines, B., and Merlen, G., 2008, Extensive perched aquifer and structural implications revealed by 3D resistivity mapping in a Galapagos volcano: Earth and Planetary Science Letters, 269, 518–522
| Extensive perched aquifer and structural implications revealed by 3D resistivity mapping in a Galapagos volcano:Crossref | GoogleScholarGoogle Scholar |
Danielsen, J. E., Auken, E., Jørgensen, F., Søndergaard, V. H., and Sørensen, K. I., 2003, The application of the transient electromagnetic method in hydrogeophysical surveys: Journal of Applied Geophysics, 53, 181–198
| The application of the transient electromagnetic method in hydrogeophysical surveys:Crossref | GoogleScholarGoogle Scholar |
Effersø, F., Auken, E., and Sørensen, K. I., 1999, Inversion of band-limited TEM responses: Geophysical Prospecting, 47, 551–564
| Inversion of band-limited TEM responses:Crossref | GoogleScholarGoogle Scholar |
Fiandaca, G., Auken, E., Gazoty, A., and Christiansen, A. V., 2012, Time-domain induced polarization: full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters: Geophysics, 77, E213–E225
| Time-domain induced polarization: full-decay forward modeling and 1D laterally constrained inversion of Cole-Cole parameters:Crossref | GoogleScholarGoogle Scholar |
Fiandaca, G., Ramm, J., Binley, A., Gazoty, A., Christiansen, A. V., and Auken, E., 2013, Resolving spectral information from time domain induced polarization data through 2-D inversion: Geophysical Journal International, 192, 631–646
| Resolving spectral information from time domain induced polarization data through 2-D inversion:Crossref | GoogleScholarGoogle Scholar |
Fitterman, D. V., and Anderson, W. L., 1987, Effect of transmitter turn-off time on transient soundings: Geoexploration, 24, 131–146
| Effect of transmitter turn-off time on transient soundings:Crossref | GoogleScholarGoogle Scholar |
Gazoty, A., Fiandaca, G., Pedersen, J., Auken, E., and Christiansen, A.V., 2012, Mapping of landfills using time-domain spectral induced polarization data: the Eskelund case study: Near Surface Geophysics, 10, 563–574
Gribenko, A., Wan, L., and Zhdanov, M. S., 2010, Three-dimensional inversion of magnetotelluric data for complex resistivity: Proceedings of the CEMI Annual Meeting, 269–294.
Günther, T., Rücker, C., and Spitzer, K., 2006, Three-dimensional modelling and inversion of dc resistivity data incorporating topography – II. Inversion: Geophysical Journal International, 166, 506–517
| Three-dimensional modelling and inversion of dc resistivity data incorporating topography – II. Inversion:Crossref | GoogleScholarGoogle Scholar |
Günther, T., Liebau, J., Akca, I., and Mueller-Petke, M., 2011, Block joint inversion (BJI) of MRS and DC resistivity soundings for aquifer imaging at the North Sea island, Borkum: Near Surface 2011 – The 17th European Meeting of Environmental and Engineering Geophysics, 2011.
Hertrich, M., Braun, M., and Yaramanci, U., 2005, Magnetic resonance soundings with separated transmitter and receiver loops: Near Surface Geophysics, 3, 141–154
Johansen, H. K., and Sørensen, K. I., 1979, Fast Hankel transforms: Geophysical Prospecting, 27, 876–901
| Fast Hankel transforms:Crossref | GoogleScholarGoogle Scholar |
Jørgensen, F., and Sandersen, P. B. E., 2006, Buried and open tunnel valleys in Denmark – erosion beneath multiple ice sheets: Quaternary Science Reviews, 25, 1339–1363
| Buried and open tunnel valleys in Denmark – erosion beneath multiple ice sheets:Crossref | GoogleScholarGoogle Scholar |
Jørgensen, F., Scheer, W., Thomsen, S., Sonnenborg, T. O., Hinsby, K., Wiederhold, H., Schamper, C., Roth, B., Kirsch, R., and Auken, E., 2012, Transboundary geophysical mapping of geological elements and salinity distribution critical for the assessment of future sea water intrusion in response to sea level rise: Hydrology and Earth System Sciences, 16, 1845–1862
| Transboundary geophysical mapping of geological elements and salinity distribution critical for the assessment of future sea water intrusion in response to sea level rise:Crossref | GoogleScholarGoogle Scholar |
Kemna, A., Binley, A., Ramirez, A., and Daily, W., 2000, Complex resistivity tomography for environmental applications: Chemical Engineering Journal, 77, 11–18
| Complex resistivity tomography for environmental applications:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3cXhsFKjtLk%3D&md5=2a2522f551ccc8ff84f4692228d73c92CAS |
Kirkegaard, C., and Auken, E., 2014, A parallel, scalable and memory efficient inversion code for very large scale airborne EM surveys: Geophysical Prospecting, ,
Knight, J. H., and Raiche, A. P., 1982, Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method: Geophysics, 47, 47–50
| Transient electromagnetic calculations using the Gaver-Stehfest inverse Laplace transform method:Crossref | GoogleScholarGoogle Scholar |
Lane, R., Green, A. G., Golding, C., Owers, M., Pik, P., Plunkett, C., Sattel, D., and Thorn, B., 2000, An example of 3D conductivity mapping using the TEMPEST airborne electromagnetic system: Exploration Geophysics, 31, 162–172
| An example of 3D conductivity mapping using the TEMPEST airborne electromagnetic system:Crossref | GoogleScholarGoogle Scholar |
Loke, M. H., 2011, RES3DINV: Geotomo software. Available at www.geoelectrical.com
Loke, M. H., and Barker, R. D., 1996, Rapid least squares inversion of apparent resistivity pseudosections by a quasi-Newton method: Geophysical Prospecting, 44, 131–152
| Rapid least squares inversion of apparent resistivity pseudosections by a quasi-Newton method:Crossref | GoogleScholarGoogle Scholar |
Loke, M. H., Chambers, J. E., and Ogilvy, R. D., 2006, Inversion of 2D spectral induced polarization imaging data: Geophysical Prospecting, 54, 287–301
| Inversion of 2D spectral induced polarization imaging data:Crossref | GoogleScholarGoogle Scholar |
Macnae, J. C., Smith, R., Polzer, B. D., Lamontagne, Y., and Klinkert, P. S., 1991, Conductivity-depth imaging of airborne electromagnetic step-response data: Geophysics, 56, 102–114
| Conductivity-depth imaging of airborne electromagnetic step-response data:Crossref | GoogleScholarGoogle Scholar |
Marquardt, D., 1963, An algorithm for least squares estimation of nonlinear parameters: SIAM Journal of the Society for Industrial and Applied Mathematics, 11, 431–441
| An algorithm for least squares estimation of nonlinear parameters:Crossref | GoogleScholarGoogle Scholar |
Menke, W., 1989, Geophysical data analysis discrete inverse theory: Academic Press.
Mohnke, O., and Yaramanci, U., 2002, Smooth and block inversion of surface NMR amplitudes and decay times using simulated annealing: Journal of Applied Geophysics, 50, 163–177
| Smooth and block inversion of surface NMR amplitudes and decay times using simulated annealing:Crossref | GoogleScholarGoogle Scholar |
Møller, I., Verner, H., Søndergaard, V. H., Flemming, J., Auken, E., and Christiansen, A. V., 2009, Integrated management and utilization of hydrogeophysical data on a national scale: Near Surface Geophysics, 7, 647–659
Mueller-Petke, M., and Yaramanci, U., 2010, QT inversion – comprehensive use of the complete surface NMR data set: Geophysics, 75, WA199–WA209
| QT inversion – comprehensive use of the complete surface NMR data set:Crossref | GoogleScholarGoogle Scholar |
Newman, G. A., and Alumbaugh, D. L., 1997, Three-dimensional massively parallel electromagnetic inversion – I. Theory: Geophysical Journal International, 128, 345–354
| Three-dimensional massively parallel electromagnetic inversion – I. Theory:Crossref | GoogleScholarGoogle Scholar |
Newman, G. A., Hohmann, G. W., and Anderson, W. L., 1986, Transient electromagnetic response of a three-dimensional body in a layered earth: Geophysics, 51, 1608–1627
| Transient electromagnetic response of a three-dimensional body in a layered earth:Crossref | GoogleScholarGoogle Scholar |
Oldenburg, D. W., and Jones, F. H. M., 2011a, DCIP3D (Inversion for Applied Geophysics): University of British Columbia Geophysical Inversion Facility. Available at www.eos.ubc.ca/ubcgif/iag/
Oldenburg, D. W., and Jones, F. H. M., 2011b, EM1DFM (Inversion for Applied Geophysics): University of British Columbia Geophysical Inversion Facility. Available at www.eos.ubc.ca/ubcgif/iag/
Oldenburg, D. W., and Jones, F. H. M., 2011c, EM1DTM (Inversion for Applied Geophysics): University of British Columbia Geophysical Inversion Facility. Available at www.eos.ubc.ca/ubcgif/iag/
Oldenburg, D. W., and Li, Y., 1994, Inversion of induced polarization data: Geophysics, 59, 1327–1341
| Inversion of induced polarization data:Crossref | GoogleScholarGoogle Scholar |
Oldenburg, D. W., Haber, E., and Shekhtman, R., 2013, Three dimensional inversion of multisource time domain electromagnetic data: Geophysics, 78, E47–E57
| Three dimensional inversion of multisource time domain electromagnetic data:Crossref | GoogleScholarGoogle Scholar |
Pelton, W. H., Ward, S. H., Hallof, P. G., Sill, W. R., and Nelson, P. H., 1978, Mineral discrimination and removal of inductive coupling with multifrequency induced-polarization: Geophysics, 43, 588–609
| Mineral discrimination and removal of inductive coupling with multifrequency induced-polarization:Crossref | GoogleScholarGoogle Scholar |
Podgorski, J. E., Auken, E., Schamper, C., Christiansen, A. V., Kalscheuer, T., and Green, A. G., 2013, Processing and inversion of commercial helicopter time-domain electromagnetic data for environmental assessments and geologic and hydrologic mapping: Geophysics, 78, E149–E159
| Processing and inversion of commercial helicopter time-domain electromagnetic data for environmental assessments and geologic and hydrologic mapping:Crossref | GoogleScholarGoogle Scholar |
Reid, J. E., Munday, T., and Fitzpatrick, A., 2007, High-resolution airborne electromagnetic surveying for dryland salinity management: the Toolibin Lake SkyTEM case study, W.A.: ASEG Extended Abstracts 2007, 1–5.
Rücker, C., Günther, T., and Spitzer, K., 2006, Three-dimensional modelling and inversion of dc resistivity data incorporating topography – I. Modelling: Geophysical Journal International, 166, 495–505
| Three-dimensional modelling and inversion of dc resistivity data incorporating topography – I. Modelling:Crossref | GoogleScholarGoogle Scholar |
Santos, F. A. M., 2004, 1-D laterally constrained inversion of EM34 profiling data: Journal of Applied Geophysics, 56, 123–134
| 1-D laterally constrained inversion of EM34 profiling data:Crossref | GoogleScholarGoogle Scholar |
Sato, H. K., 2000, Potential field from a dc current source arbitrarily located in a nonuniform layered medium: Geophysics, 65, 1726–1732
| Potential field from a dc current source arbitrarily located in a nonuniform layered medium:Crossref | GoogleScholarGoogle Scholar |
Schamper, C., Auken, E., and Kirkegaard, C., 2013, 3D sheets inversion with accurate modeling of AEM systems: SAGA AEM, South Africa, 1–2.
Schamper, C., Auken, E., and Sørensen, K. I., 2014, Coil response inversion for very early time modelling of helicopter-borne time-domain electromagnetic data and mapping of near-surface geological layers: Geophysical Prospecting, 62, 658–674
| Coil response inversion for very early time modelling of helicopter-borne time-domain electromagnetic data and mapping of near-surface geological layers:Crossref | GoogleScholarGoogle Scholar |
Sengpiel, K. P., and Siemon, B., 2000, Advanced inversion methods for airborne electromagnetic exploration: Geophysics, 65, 1983–1992
| Advanced inversion methods for airborne electromagnetic exploration:Crossref | GoogleScholarGoogle Scholar |
Siemon, B., Stuntebeck, C., Sengpiel, K. P., Röttger, B., Rehli, H., and Eberle, D. G., 2002, Investigation of hazardous waste sites and their environment using BGR helicopter-borne geophysical system: Journal of Environmental & Engineering Geophysics, 7, 169–181
| Investigation of hazardous waste sites and their environment using BGR helicopter-borne geophysical system:Crossref | GoogleScholarGoogle Scholar |
Sørensen, K. I., and Auken, E., 2004, SkyTEM – a new high-resolution helicopter transient electromagnetic system: Exploration Geophysics, 35, 191–199
Sørensen, K. I., and Larsen, F., 1999, Ellog auger drilling: 3-in-one method for hydrogeological data collection: Ground Water Monitoring and Remediation, 19, 97–101
| Ellog auger drilling: 3-in-one method for hydrogeological data collection:Crossref | GoogleScholarGoogle Scholar |
Sørensen, K. I., Auken, E., Christensen, N. B., and Pellerin, L., 2005, An integrated approach for hydrogeophysical investigations: new technologies and a case history, in D. K. Butler, ed., Near-surface geophysics, Part II: SEG, 585–603.
Tarantola, A., and Valette, B., 1982a, Generalized nonlinear inverse problems solved using a least squares criterion: Reviews of Geophysics and Space Physics, 20, 219–232
| Generalized nonlinear inverse problems solved using a least squares criterion:Crossref | GoogleScholarGoogle Scholar |
Tarantola, A., and Valette, B., 1982b, Inverse problems = quest for information: Journal of Geophysics, 50, 159–170
Tartaras, E., Zhdanov, M. S., Wada, K., Saito, A., and Hara, T., 2000, Fast imaging of TDEM data based on S-inversion: Journal of Applied Geophysics, 43, 15–32
| Fast imaging of TDEM data based on S-inversion:Crossref | GoogleScholarGoogle Scholar |
Thomsen, R., Søndergaard, V. H., and Sørensen, K. I., 2004, Hydrogeological mapping as a basis for establishing site-specific groundwater protection zones in Denmark: Hydrogeology Journal, 12, 550–562
| Hydrogeological mapping as a basis for establishing site-specific groundwater protection zones in Denmark:Crossref | GoogleScholarGoogle Scholar |
Viezzoli, A., Christiansen, A. V., Auken, E., and Sørensen, K. I., 2008, Quasi-3D modeling of airborne TEM data by spatially constrained inversion: Geophysics, 73, F105–F113
| Quasi-3D modeling of airborne TEM data by spatially constrained inversion:Crossref | GoogleScholarGoogle Scholar |
Viezzoli, A., Munday, T., Auken, E., and Christiansen, A. V., 2010, Accurate quasi 3D versus practical full 3D inversion of AEM data – the Bookpurnong case study: Preview, 149, 23–31
Vignoli, G., Fiandaca, G., Christiansen, A. V., Kirkegaard, C., and Auken, E., 2013, Sharp Spatially Constrained Inversion (sSCI) with applications to transient electromagnetic data: Geophysical Prospecting, ,
Wannamaker, P. E., Hohmann, G. W., and SanFilipo, W. A., 1984, Electromagnetic modeling of three-dimensional bodies in layered earths using integral equations: Geophysics, 49, 60–74
| Electromagnetic modeling of three-dimensional bodies in layered earths using integral equations:Crossref | GoogleScholarGoogle Scholar |
Ward, S. H., and Hohmann, G. W., 1988, Electromagnetic theory for geophysical applications, in M. N. Nabighian, ed., Electromagnetic methods in applied geophysics, Vol. 1: Society of Exploration Geophysicists, 131–311.
Weichman, P. B., Lavely, E. M., and Ritzwoller, M. H., 2000, Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 62, 1290–1312
| Theory of surface nuclear magnetic resonance with applications to geophysical imaging problems:Crossref | GoogleScholarGoogle Scholar | 1:CAS:528:DC%2BD3cXkvVegur8%3D&md5=13cf0abcc8d516f970ed6c5cf9c7f2cbCAS |
Weidelt, P., 1983, The harmonic and transient electromagnetic response of a thin dipping dike: Geophysics, 48, 934–952
| The harmonic and transient electromagnetic response of a thin dipping dike:Crossref | GoogleScholarGoogle Scholar |
Wisén, R., and Christiansen, A. V., 2005, Laterally and mutually constrained inversion of surface wave seismic data and resistivity data: Journal of Environmental & Engineering Geophysics, 10, 251–262
| Laterally and mutually constrained inversion of surface wave seismic data and resistivity data:Crossref | GoogleScholarGoogle Scholar |
Witherly, K. E., Irvine, R. J., and Morrison, E., 2004, The Geotech VTEM time domain helicopter EM system: ASEG Extended Abstracts 2004, 1–4.
Xiong, Z., 1989, Electromagnetic fields of electric dipoles embedded in a stratified anisotropic earth: Geophysics, 54, 1643–1646
| Electromagnetic fields of electric dipoles embedded in a stratified anisotropic earth:Crossref | GoogleScholarGoogle Scholar |
Yoshioka, K., and Zhdanov, M. S., 2005, Three-dimensional nonlinear regularized inversion of the induced polarization data based on the Cole-Cole model: Physics of the Earth and Planetary Interiors, 150, 29–43
| Three-dimensional nonlinear regularized inversion of the induced polarization data based on the Cole-Cole model:Crossref | GoogleScholarGoogle Scholar |
Zhdanov, M. S., and Keller, G. V., 1994, The geoelectrical methods in geophysical exploration: Elsevier.
Zhdanov, M. S., Fang, S., and Hursán, G., 2000, Electromagnetic inversion using quasi-linear approximation: Geophysics, 65, 1501–1513
| Electromagnetic inversion using quasi-linear approximation:Crossref | GoogleScholarGoogle Scholar |
Zhou, Q., 1989, Audio-frequency electromagnetic tomography for reservoir evaluation: Ph.D. dissertation, Lawrence Berkeley Laboratory, University of California.