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.

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.

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.

From migration to inversion velocity analysis

Geophysics ◽  
2017 ◽  
Vol 82 (3) ◽  
pp. S207-S223 ◽  
Author(s):  
Hervé Chauris ◽  
Emmanuel Cocher
Keyword(s):  
Objective Function ◽  
Synthetic Data ◽  
Velocity Model ◽  
Specific Power ◽  
Model Parameters ◽  
Data Sets ◽  
Velocity Analysis ◽  
Low Velocity ◽  
Image Domain ◽  
New Approach

Migration velocity analysis (MVA) is a technique defined in the image domain to determine the background velocity model controlling the kinematics of wave propagation. In the presence of discontinuous interfaces, the velocity gradient used to iteratively update the velocity model exhibits spurious oscillations. For more stable results, we replace the migration part by an inversion scheme. By definition, migration is the adjoint of the Born modeling operator, whereas inversion is its asymptotic inverse. We have developed new expressions in 1D and 2D cases based on two-way wave-equation operators. The objective function measures the quality of the images obtained by inversion in the extended domain depending on the subsurface offset. In terms of implementation, the new approach is very similar to classic MVA. A 1D analysis found that oscillatory terms around the interface positions can be removed by multiplying the inversion result with the velocity at a specific power before evaluating the objective function. Several 2D synthetic data sets are discussed through the computation of the gradient needed to update the model parameters. Even for discontinuous reflectivity models, the new approach provides results without artificial oscillations. The model update corresponds to a gradient of an existing objective function, which was not the case for the horizontal contraction approach proposed as an alternative to deal with gradient artifacts. It also correctly handles low-velocity anomalies, contrary to the horizontal contraction approach. Inversion velocity analysis offers new perspectives for the applicability of image-domain velocity analysis.

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.

Two-dimensional inversion of magnetotelluric/radiomagnetotelluric data by using unstructured mesh

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. E197-E210 ◽  
Author(s):  
Özcan Özyıldırım ◽  
Mehmet Emin Candansayar ◽  
İsmail Demirci ◽  
Bülent Tezkan
Keyword(s):  
Surface Topography ◽  
Unstructured Grid ◽  
Unstructured Mesh ◽  
Synthetic Data ◽  
Solution Technique ◽  
Inversion Algorithm ◽  
2D Inversion ◽  
Two Samples ◽  
Speed And Accuracy ◽  
Grid Based

We have compared structured and unstructured grid-based 2D inversion algorithms for magnetotelluric (MT) and radiomagnetotelluric (RMT) data in terms of speed and accuracy. We have developed a new 2D inversion algorithm for MT and RMT data by using a finite-element (FE) method that uses unstructured triangle grids. We compare the inversion results of our unstructured grid-based algorithm with those of the conventional algorithm, which uses either a structured FE or structured finite-difference (FD) numerical solution technique. The imaging of the surface topography and the underground resistivity structures by the new algorithm requires fewer elements than those that use FE and FD structured grids. We also find that when unstructured grids are used, the quality of the mesh is increased and the numerical errors are significantly reduced. Thus, the program runs faster and can simulate the complex surface topography in a more stable setting than the classic inversion algorithms. Furthermore, we implement a new smoothing matrix format for the unstructured triangle grids for the inversion procedure. We use two samples of synthetic data for the MT and RMT frequencies as well as a sample of field RMT data collected across a fault zone for comparison. In our synthetic data experiment, we find that the resistivity values and the boundaries obtained from the inversion of the unstructured mesh are closer to those of the true a priori synthetic model. Results of the synthetic and field data verify the computational advantages (speed and accuracy) of our inversion algorithm with respect to the conventional structured grid-based inversion algorithms.

scholarly journals A new method for the in vivo identification of degenerated material property ranges of the human eye: feasibility analysis based on synthetic data

2021 ◽  
Author(s):  
Stefan Muench ◽  
Mike Roellig ◽  
Daniel Balzani
Keyword(s):  
Real Time ◽  
Test Data ◽  
Synthetic Data ◽  
New Method ◽  
Data Sets ◽  
New Approach ◽  
Full Field ◽  
Material Parameters ◽  
Virtual Test

AbstractThis paper proposes a new method for in vivo and almost real-time identification of biomechanical properties of the human cornea based on non-contact tonometer data. Further goal is to demonstrate the method’s functionality based on synthetic data serving as reference. For this purpose, a finite element model of the human eye is constructed to synthetically generate full-field displacements from different data sets with keratoconus-like degradations. Then, a new approach based on the equilibrium gap method combined with a mechanical morphing approach is proposed and used to identify the material parameters from virtual test data sets. In a further step, random absolute noise is added to the virtual test data to investigate the sensitivity of the new approach to noise. As a result, the proposed method shows a relevant accuracy in identifying material parameters based on full-field displacements. At the same time, the method turns out to work almost in real time (order of a few minutes on a regular workstation) and is thus much faster than inverse problems solved by typical forward approaches. On the other hand, the method shows a noticeable sensitivity to rather small noise amplitudes rendering the method not accurate enough for the precise identification of individual parameter values. However, analysis show that the accuracy is sufficient for the identification of property ranges which might be related to diseased tissues. Thereby, the proposed approach turns out promising with view to diagnostic purposes.

Inversion for magnetic anomalies of arbitrary three‐dimensional bodies

Geophysics ◽  
1990 ◽  
Vol 55 (10) ◽  
pp. 1321-1326 ◽  
Author(s):  
X. Wang ◽  
R. O. Hansen
Keyword(s):  
Three Dimensional ◽  
Large Data ◽  
Magnetic Anomalies ◽  
Large Data Sets ◽  
Data Sets ◽  
Inversion Algorithm ◽  
Geologic Model ◽  
Profile Inversion ◽  
Inversion Techniques ◽  
Medicine Lake

Two‐dimensional (profile) inversion techniques for magnetic anomalies are widely used in exploration geophysics: but, until now, the three‐dimensional (3-D) methods available have been restricted in their geologic applicability, dependent upon good initial values or limited by the capabilities of existing computers. We have developed a fully 3-D inversion algorithm intended for routine application to large data sets. The algorithm based on a Fourier transform expression for the magnetic field of homogeneous polyhedral bodies (Hansen and Wang, 1998), is a 3-D generalization of CompuDepth (O’Brien, 1972). Like CompuDepth, the new inversion algorithm employs thespatial equivalent of frequency‐domain autoregression to determine a series of coefficients from which the depths and locations of polyhedral vertices are calculated by solving complex polynomials. These vertices are used to build a 3-D geologic model. Application to the Medicine Lake Volcano aeromagnetic anomaly resulted in a geologically reasonable model of the source.

Handling gaps in acquisition geometries - improving Marchenko-based imaging using sparsity-promoting inversion and joint inversion of time-lapse data

Geophysics ◽  
2020 ◽  
pp. 1-49
Author(s):  
Claudia Haindl ◽  
Matteo Ravasi ◽  
Filippo Broggini
Keyword(s):  
Joint Inversion ◽  
Synthetic Data ◽  
Time Lapse ◽  
Velocity Model ◽  
Inversion Problem ◽  
Scattered Energy ◽  
Regular Sampling ◽  
Sparsity Constraint ◽  
Inversion Techniques ◽  
Source Geometry

Marchenko focusing and imaging are novel methods for correctly handling multiple scattered energy while processing seismic data. However, strict requirements in the acquisition geometry, specifically co-location of sources and receivers as well as dense and regular sampling, currently constrain their practical applicability. We reformulate the Marchenko equations to handle the case where there are gaps in the source geometry while receiver sampling remains regular (or the opposite, by means of reciprocity). Using synthetic data based on a velocity model that produces strong interbed multiples, we test different solvers for the newly formulated inversion problem and we compare these results to results obtained by applying standard Marchenko inversion to a previously reconstructed dataset. When using the unreconstructed dataset, the ability of the Marchenko equations to retrace multiple reflected energy deteriorates. Sparsity-promoting Marchenko inversion, while improving the appearance of focusing functions, barely decreases multiple leakage in gathers and does not visibly improve the final image when compared to standard least-squares inversion. On the other hand, reconstructing the wavefield in advance restores the proper functioning of the Marchenko methods. Further, we test a joint inversion technique designed for time-lapse data with non-repeated geometries and originally intended to be solved using sparsity-promoting inversion. Motivated by our previous results, we compare images produced by this method to images produced by solving the same joint inversion problem without sparsity constraint. We find that the joint inversion alone hardly improves the resulting images but, when combined with the sparsity constraint, it leads to better noise and multiple suppression and produces a clean time-lapse image. Overall, none of the results from sparsity-promoting inversion techniques match the results obtained when reconstructing the wavefield in advance. We show that this can be explained by the comparatively slow convergence rate of sparsity-promoting Marchenko inversion.

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