Reconstruction of 1-D conductivity from dual‐loop EM data

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 492-501 ◽  
Author(s):  
Zhiyi Zhang ◽  
Partha S. Routh ◽  
Douglas W. Oldenburg ◽  
David L. Alumbaugh ◽  
Gregory A. Newman
Keyword(s):  
Inverse Problem ◽  
Joint Inversion ◽  
Synthetic Data ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Geological Structures ◽  
Electromagnetic Data ◽  
Independent Information ◽  
The Individual ◽  
Data Constraints

Inversions of electromagnetic data from different coil configurations provide independent information about geological structures. We develop a 1-D inversion algorithm that can invert data from the horizontal coplanar (HC), vertical coplanar, coaxial (CA), and perpendicular coil configurations separately or jointly. The inverse problem is solved by minimizing a model objective function subject to data constraints. Tests using synthetic data from 1-D models indicate that if data are collected at a sufficient number of frequencies, then the recovered models from individual inversions of different coil systems can be quite similar. However, if only a limited number of frequencies are available, then joint inversion of data from different coils produces a better model than the individual inversions. Tests on 3-D synthetic data sets indicate that 1-D inversions can be used as a fast and approximate tool to locate anomalies in the subsurface. Also for the test example presented here, the joint inversion of HC and CA data over a 3-D conductivity provided a better model than that produced by the individual inversion of the data sets.

Quasi-2D inversion of DCR and TDEM data for shallow investigations

Geophysics ◽  
2011 ◽  
Vol 76 (4) ◽  
pp. F239-F250 ◽  
Author(s):  
Fernando A. Monteiro Santos ◽  
Hesham M. El-Kaliouby
Keyword(s):  
Joint Inversion ◽  
Synthetic Data ◽  
Data Sets ◽  
Complex Environments ◽  
Inversion Algorithm ◽  
2D Inversion ◽  
New Approach ◽  
Earth Models ◽  
Time Domain Electromagnetic ◽  
Inversion Techniques

Joint or sequential inversion of direct current resistivity (DCR) and time-domain electromagnetic (TDEM) data commonly are performed for individual soundings assuming layered earth models. DCR and TDEM have different and complementary sensitivity to resistive and conductive structures, making them suitable methods for the application of joint inversion techniques. This potential joint inversion of DCR and TDEM methods has been used by several authors to reduce the ambiguities of the models calculated from each method separately. A new approach for joint inversion of these data sets, based on a laterally constrained algorithm, was found. The method was developed for the interpretation of soundings collected along a line over a 1D or 2D geology. The inversion algorithm was tested on two synthetic data sets, as well as on field data from Saudi Arabia. The results show that the algorithm is efficient and stable in producing quasi-2D models from DCR and TDEM data acquired in relatively complex environments.

scholarly journals Bayesian joint inversion of controlled source electromagnetic and magnetotelluric data to image freshwater aquifer offshore New Jersey

2019 ◽  
Vol 218 (3) ◽  
pp. 1822-1837 ◽  
Author(s):  
Daniel Blatter ◽  
Kerry Key ◽  
Anandaroop Ray ◽  
Chloe Gustafson ◽  
Rob Evans
Keyword(s):  
Parameter Uncertainty ◽  
Joint Inversion ◽  
Data Sets ◽  
Magnetotelluric Data ◽  
Model Parameter ◽  
Controlled Source ◽  
Low Salinity ◽  
Electromagnetic Data ◽  
Model Parameter Uncertainty ◽  
The Individual

SUMMARY Joint inversion of multiple electromagnetic data sets, such as controlled source electromagnetic and magnetotelluric data, has the potential to significantly reduce uncertainty in the inverted electrical resistivity when the two data sets contain complementary information about the subsurface. However, evaluating quantitatively the model uncertainty reduction is made difficult by the fact that conventional inversion methods—using gradients and model regularization—typically produce just one model, with no associated estimate of model parameter uncertainty. Bayesian inverse methods can provide quantitative estimates of inverted model parameter uncertainty by generating an ensemble of models, sampled proportional to data fit. The resulting posterior distribution represents a combination of a priori assumptions about the model parameters and information contained in field data. Bayesian inversion is therefore able to quantify the impact of jointly inverting multiple data sets by using the statistical information contained in the posterior distribution. We illustrate, for synthetic data generated from a simple 1-D model, the shape of parameter space compatible with controlled source electromagnetic and magnetotelluric data, separately and jointly. We also demonstrate that when data sets contain complementary information about the model, the region of parameter space compatible with the joint data set is less than or equal to the intersection of the regions compatible with the individual data sets. We adapt a trans-dimensional Markov chain Monte Carlo algorithm for jointly inverting multiple electromagnetic data sets for 1-D earth models and apply it to surface-towed controlled source electromagnetic and magnetotelluric data collected offshore New Jersey, USA, to evaluate the extent of a low salinity aquifer within the continental shelf. Our inversion results identify a region of high resistivity of varying depth and thickness in the upper 500 m of the continental shelf, corroborating results from a previous study that used regularized, gradient-based inversion methods. We evaluate the joint model parameter uncertainty in comparison to the uncertainty obtained from the individual data sets and demonstrate quantitatively that joint inversion offers reduced uncertainty. In addition, we show how the Bayesian model ensemble can subsequently be used to derive uncertainty estimates of pore water salinity within the low salinity aquifer.

Integration of diverse physical-property models: Subsurface zonation and petrophysical parameter estimation based on fuzzy c -means cluster analyses

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. H33-H44 ◽  
Author(s):  
Hendrik Paasche ◽  
Jens Tronicke ◽  
Klaus Holliger ◽  
Alan G. Green ◽  
Hansruedi Maurer
Keyword(s):  
Gamma Ray ◽  
Synthetic Data ◽  
Physical Property ◽  
Geophysical Data ◽  
Data Sets ◽  
Data Set ◽  
Petrophysical Parameters ◽  
Fcm Clustering ◽  
The Individual ◽  
Combine Information

Inversions of an individual geophysical data set can be highly nonunique, and it is generally difficult to determine petrophysical parameters from geophysical data. We show that both issues can be addressed by adopting a statistical multiparameter approach that requires the acquisition, processing, and separate inversion of two or more types of geophysical data. To combine information contained in the physical-property models that result from inverting the individual data sets and to estimate the spatial distribution of petrophysical parameters in regions where they are known at only a few locations, we demonstrate the potential of the fuzzy [Formula: see text]-means (FCM) clustering technique. After testing this new approach on synthetic data, we apply it to limited crosshole georadar, crosshole seismic, gamma-log, and slug-test data acquired within a shallow alluvial aquifer. The derived multiparameter model effectively outlines the major sedimentary units observed in numerous boreholes and provides plausible estimates for the spatial distributions of gamma-ray emitters and hydraulic conductivity.

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.

Structural joint inversion on irregular meshes

2019 ◽  
Vol 220 (3) ◽  
pp. 1995-2008 ◽  
Author(s):  
C Jordi ◽  
J Doetsch ◽  
T Günther ◽  
C Schmelzbach ◽  
H Maurer ◽  
...  
Keyword(s):  
Electrical Resistivity ◽  
Joint Inversion ◽  
A Priori ◽  
Structural Similarity ◽  
P Wave ◽  
Parameter Distribution ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Structural Joint ◽  
Irregular Meshes

SUMMARY Structural joint inversion of several data sets on an irregular mesh requires appropriate coupling operators. To date, joint inversion algorithms are primarily designed for the use on regular rectilinear grids and impose structural similarity in the direct neighbourhood of a cell only. We introduce a novel scheme for calculating cross-gradient operators based on a correlation model that allows to define the operator size by imposing physical length scales. We demonstrate that the proposed cross-gradient operators are largely decoupled from the discretization of the modelling domain, which is particularly important for irregular meshes where cell sizes vary. Our structural joint inversion algorithm is applied to a synthetic electrical resistivity tomography and ground penetrating radar 3-D cross-well experiment aiming at imaging two anomalous bodies and extracting the parameter distribution of the geostatistical background models. For both tasks, joint inversion produced superior results compared with individual inversions of the two data sets. Finally, we applied structural joint inversion to two field data sets recorded over a karstified limestone area. By including geological a priori information via the correlation-based operators into the joint inversion, we find P-wave velocity and electrical resistivity tomograms that are in accordance with the expected subsurface geology.

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.

Joint MT and CSEM data inversion using a multiplicative cost function approach

Geophysics ◽  
2011 ◽  
Vol 76 (3) ◽  
pp. F203-F214 ◽  
Author(s):  
A. Abubakar ◽  
M. Li ◽  
G. Pan ◽  
J. Liu ◽  
T. M. Habashy
Keyword(s):  
Cost Function ◽  
Large Scale ◽  
Joint Inversion ◽  
A Priori ◽  
Upper And Lower Bounds ◽  
Model Parameters ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Earth Resistivity ◽  
The Cost

We have developed an inversion algorithm for jointly inverting controlled-source electromagnetic (CSEM) data and magnetotelluric (MT) data. It is well known that CSEM and MT data provide complementary information about the subsurface resistivity distribution; hence, it is useful to derive earth resistivity models that simultaneously and consistently fit both data sets. Because we are dealing with a large-scale computational problem, one usually uses an iterative technique in which a predefined cost function is optimized. One of the issues of this simultaneous joint inversion approach is how to assign the relative weights on the CSEM and MT data in constructing the cost function. We propose a multiplicative cost function instead of the traditional additive one. This function does not require an a priori choice of the relative weights between these two data sets. It will adaptively put CSEM and MT data on equal footing in the inversion process. The inversion is accomplished with a regularized Gauss-Newton minimization scheme where the model parameters are forced to lie within their upper and lower bounds by a nonlinear transformation procedure. We use a line search scheme to enforce a reduction of the cost function at each iteration. We tested our joint inversion approach on synthetic and field data.

scholarly journals Joint inversion of crosshole radar and seismic traveltimes acquired at the South Oyster Bacterial Transport Site

Geophysics ◽  
2008 ◽  
Vol 73 (4) ◽  
pp. G29-G37 ◽  
Author(s):  
Niklas Linde ◽  
Ari Tryggvason ◽  
John E. Peterson ◽  
Susan S. Hubbard
Keyword(s):  
Joint Inversion ◽  
Synthetic Data ◽  
Physical Property ◽  
Shallow Aquifer ◽  
Model Parameters ◽  
Structural Constraints ◽  
Integral Scale ◽  
Point Spread Functions ◽  
Traveltime Tomography ◽  
The Individual

The structural approach to joint inversion, entailing common boundaries or gradients, offers a flexible and effective way to invert diverse types of surface-based and/or crosshole geophysical data. The cross-gradients function has been introduced as a means to construct models in which spatial changes in two distinct physical-property models are parallel or antiparallel. Inversion methods that use such structural constraints also provide estimates of nonlinear and nonunique field-scale relationships between model parameters. Here, we jointly invert crosshole radar and seismic traveltimes for structurally similar models using an iterative nonlinear traveltime tomography algorithm. Application of the inversion scheme to synthetic data demonstrates that it better resolves lithologic boundaries than the individual inversions alone. Tests of the scheme on GPR and seismic data acquired within a shallow aquifer illustrate that the resultant models have improved correlations with flowmeter data in comparison with models based on individual inversions. The highest correlation with the flowmeter data is obtained when the joint inversion is combined with a stochastic regularization operator and the vertical integral scale is estimated from the flowmeter data. Point-spread functions show that the most significant resolution improvements offered by the joint inversion are in the horizontal direction.

scholarly journals Pareto Joint Inversion of 2D magnetometric and gravity data- synthetic study

2019 ◽  
Vol 133 ◽  
pp. 01009
Author(s):  
Tomasz Danek ◽  
Andrzej Leśniak ◽  
Katarzyna Miernik ◽  
Elżbieta Śledź
Keyword(s):  
Pareto Front ◽  
Joint Inversion ◽  
Gravity Data ◽  
Group Analysis ◽  
Geophysical Methods ◽  
Model Parameters ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Promising Tool ◽  
Real Model

Pareto joint inversion for two or more data sets is an attractive and promising tool which eliminates target functions weighing and scaling, providing a set of acceptable solutions composing a Pareto front. In former author’s study MARIA (Modular Approach Robust Inversion Algorithm) was created as a flexible software based on global optimization engine (PSO) to obtain model parameters in process of Pareto joint inversion of two geophysical data sets. 2D magnetotelluric and gravity data were used for preliminary tests, but the software is ready to handle data from more than two geophysical methods. In this contribution, the authors’ magnetometric forward solver was implemented and integrated with MARIA. The gravity and magnetometry forward solver was verified on synthetic models. The tests were performed for different models of a dyke and showed, that even when the starting model is a homogeneous area without anomaly, it is possible to recover the shape of a small detail of the real model. Results showed that the group analysis of models on the Pareto front gives more information than the single best model. The final stage of interpretation is the raster map of Pareto front solutions analysis.

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