scholarly journals 3-D inversion of induced polarization data

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1931-1945 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Wavelet Transforms ◽  
Joint Inversion ◽  
Linear Equations ◽  
Induced Polarization ◽  
Dc Resistivity ◽  
Data Sets ◽  
Bound Constraints ◽  
Borehole Data ◽  
Resistivity Data ◽  
Logarithmic Barrier

We present an algorithm for inverting induced polarization (IP) data acquired in a 3-D environment. The algorithm is based upon the linearized equation for the IP response, and the inverse problem is solved by minimizing an objective function of the chargeability model subject to data and bound constraints. The minimization is carried out using an interior‐point method in which the bounds are incorporated by using a logarithmic barrier and the solution of the linear equations is accelerated using wavelet transforms. Inversion of IP data requires knowledge of the background conductivity. We study the effect of different approximations to the background conductivity by comparing IP inversions performed using different conductivity models, including a uniform half‐space and conductivities recovered from one‐pass 3-D inversions, composite 2-D inversions, limited AIM updates, and full 3-D nonlinear inversions of the dc resistivity data. We demonstrate that, when the background conductivity is simple, reasonable IP results are obtainable without using the best conductivity estimate derived from full 3-D inversion of the dc resistivity data. As a final area of investigation, we study the joint use of surface and borehole data to improve the resolution of the recovered chargeability models. We demonstrate that the joint inversion of surface and crosshole data produces chargeability models superior to those obtained from inversions of individual data sets.

On: “Two‐dimensional joint inversion of magnetotelluric and dipole‐dipole resistivity data” by Y. Sasaki (GEOPHYSICS, 54, 254–262, February 1989)

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1212-1212
Author(s):  
D. J. Dodds
Keyword(s):  
Joint Inversion ◽  
Dc Resistivity ◽  
Two Dimensional ◽  
Resistivity Data

There appears to be an error in the formulation of the dc resistivity response in this paper. Equation (6) is valid only when the conductivity is constant, but the text and the notation imply that it is variable. Grant and West (1965) give the correct relation [their equation (14‐2)], which is restated here using Sasaki’s notation and accounting for source currents.

scholarly journals Efficient Probabilistic Joint Inversion of Direct Current Resistivity and Small-Loop Electromagnetic Data

Algorithms ◽  
2020 ◽  
Vol 13 (6) ◽  
pp. 144
Author(s):  
Christin Bobe ◽  
Daan Hanssens ◽  
Thomas Hermans ◽  
Ellen Van De Vijver
Keyword(s):  
Direct Current ◽  
Field Data ◽  
Joint Inversion ◽  
Dc Resistivity ◽  
Data Sets ◽  
Electrical Conductivities ◽  
Posterior Probability Density ◽  
Posterior Probability Density Function ◽  
Efficient Alternative ◽  
Synthetic Studies

Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

scholarly journals 3-D cross-gradient joint inversion of seismic refraction and DC resistivity data

2017 ◽  
Vol 141 ◽  
pp. 54-67 ◽  
Author(s):  
Zhanjie Shi ◽  
Richard W. Hobbs ◽  
Max Moorkamp ◽  
Gang Tian ◽  
Lu Jiang
Keyword(s):  
Joint Inversion ◽  
Seismic Refraction ◽  
Dc Resistivity ◽  
Resistivity Data

scholarly journals Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Huan Ma ◽  
Handong Tan ◽  
Yue Guo
Keyword(s):  
Message Passing ◽  
Message Passing Interface ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Induced Polarization ◽  
Conjugate Gradients ◽  
Processing Unit ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Surface Borehole

Four kinds of array of induced polarization (IP) methods (surface, borehole-surface, surface-borehole, and borehole-borehole) are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI) and graphics processing unit (GPU) to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG) solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG) iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.

Joint inversion of surface and three‐component borehole magnetic data

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 540-552 ◽  
Author(s):  
Yaoguo Li ◽  
Douglas W. Oldenburg
Keyword(s):  
Field Data ◽  
Joint Inversion ◽  
Magnetic Data ◽  
Data Sets ◽  
Source Depth ◽  
Inversion Algorithm ◽  
Borehole Data ◽  
Weighting Functions ◽  
Surface Data ◽  
Geometric Decay

The inversion of magnetic data is inherently nonunique with respect to the distance between the source and observation locations. This manifests itself as an ambiguity in the source depth when surface data are inverted and as an ambiguity in the distance between the source and boreholes if borehole data are inverted. Joint inversion of surface and borehole data can help to reduce this nonuniqueness. To achieve this, we develop an algorithm for inverting data sets that have arbitrary observation locations in boreholes and above the surface. The algorithm depends upon weighting functions that counteract the geometric decay of magnetic kernels with distance from the observer. We apply these weighting functions to the inversion of three‐component magnetic data collected in boreholes and then to the joint inversion of surface and borehole data. Both synthetic and field data sets are used to illustrate the new inversion algorithm. When borehole data are inverted directly, three‐component data are far more useful in constructing good susceptibility models than are single‐component data. However, either can be used effectively in a joint inversion with surface data to produce models that are superior to those obtained by inversion of surface data alone.

Improvement in MRS parameter estimation by joint and laterally constrained inversion of MRS and TEM data

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB191-WB200 ◽  
Author(s):  
Ahmad A. Behroozmand ◽  
Esben Auken ◽  
Gianluca Fiandaca ◽  
Anders Vest Christiansen
Keyword(s):  
Water Content ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Clear Correlation ◽  
Model Parameters ◽  
Dc Resistivity ◽  
Borehole Data ◽  
Simultaneous Inversion ◽  
Transient Electromagnetic ◽  
Magnetic Resonance Sounding

We developed a new scheme for joint and laterally constrained inversion (LCI) of magnetic resonance sounding (MRS) data and transient electromagnetic (TEM) data, which greatly improves the estimation of the MRS model parameters. During the last few decades, electrical and electromagnetic methods have been widely used for groundwater investigation, but they suffer from some inherent limitations; for example, equivalent layer sequences. Furthermore, the water content information is only empirically correlated to resistivity of the formation. MRS is a noninvasive geophysical technique that directly quantifies the water content distribution from surface measurements. The resistivity information of the subsurface is obtained from a complementary geophysical method such as TEM or DC resistivity methods. The conventional inversion of MRS data assumes the resulting resistivity structure to be correct and considers a constant MRS kernel through the inversion. We found that this assumption may introduce an error to the forward modeling and consequently could result in erroneous parameter estimations in the inversion process. We investigated the advantage of TEM for the joint inversion compared to DC resistivity. A fast and numerically efficient MRS forward routine made it possible to invert the MRS and TEM data sets simultaneously along profiles. Furthermore, by application of lateral constraints on the model parameters, lateral smooth 2D model sections could be be obtained. The simultaneous inversion for resistivity and MRS parameters led to a more reliable and robust estimation of all parameters, and the MRS data diminished the range of equivalent resistivity models. We examined the approach through synthetic data and a field example in Denmark where good agreement with borehole data was demonstrated with clear correlation between the relaxation time [Formula: see text] and the grain size distribution of a sandy aquifer.

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