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.

scholarly journals An application of the NSGA-II algorithm in Pareto joint inversion of 2D magnetic and gravity data

2021 ◽  
Vol 47 (2) ◽  
pp. 59-70
Author(s):  
Katarzyna Miernik ◽  
Elżbieta Węglińska ◽  
Tomasz Danek ◽  
Andrzej Leśniak
Keyword(s):  
Pareto Front ◽  
Joint Inversion ◽  
Gravity Data ◽  
Model Parameters ◽  
Final Solution ◽  
Inversion Process ◽  
Nsga Ii ◽  
Heat Map ◽  
Real Model ◽  
All Solutions

Joint inversion is a widely used geophysical method that allows model parameters to be obtained from the observed data. Pareto inversion results are a set of solutions that include the Pareto front, which consists of non-dominated solutions. All solutions from the Pareto front are considered the most feasible models from which a particular one can be chosen as the final solution. In this paper, it is shown that models represented by points on the Pareto front do not reflect the shape of the real model. In this contribution, a collective approach is proposed to interpret the geometry of models retrieved in inversion. Instead of choosing single solutions from the Pareto front, all obtained solutions were combined in one “heat map”, which is a plot representing the frequency of points belonging to all returned objects from the solution set. The conducted experiment showed that this approach limits the problem of equivalence and is a promising way of representing the geometry of the model that was retrieved in the inversion process.

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.

Joint Gramian inversion of geophysical data with different resolution capabilities: case study in Yellowstone

2021 ◽  
Author(s):  
Xiaolei Tu ◽  
Michael S Zhdanov
Keyword(s):  
Joint Inversion ◽  
Gravity Data ◽  
Geophysical Methods ◽  
Structural Similarity ◽  
Geophysical Data ◽  
P Wave ◽  
Model Parameters ◽  
Magmatic System ◽  
Low Velocity ◽  
Velocity Anomaly

Summary Joint inversion of multiphysics data is a practical approach to the integration of geophysical data, which produces models of reduced uncertainty and improved resolution. The development of effective methods of joint inversion requires considering different resolutions of different geophysical methods. This paper presents a new framework of joint inversion of multiphysics data, which is based on a novel formulation of Gramian constraints and mitigates the difference in resolution capabilities of different geophysical methods. Our approach enforces structural similarity between different model parameters through minimizing a structural Gramian term, and it also balances the different resolutions of geophysical methods using a multiscale resampling strategy. The effectiveness of the proposed method is demonstrated by synthetic model study of joint inversion of the P-wave traveltime and gravity data. We apply a novel method based on Gramian constraints and multiscale resampling to jointly invert the gravity and seismic data collected in Yellowstone national Park to image the crustal magmatic system of the Yellowstone. Our results helped to produce a consistent image of the crustal magmatic system of the Yellowstone expressed both in low-density and low-velocity anomaly just beneath the Yellowstone caldera.

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.

Modeling the electrical conductivity of hydrogeological strata using joint-inversion of loop-loop electromagnetic data

Geophysics ◽  
2012 ◽  
Vol 77 (4) ◽  
pp. WB99-WB107 ◽  
Author(s):  
J. Triantafilis ◽  
V. Wong ◽  
F. A. Monteiro Santos ◽  
D. Page ◽  
R. Wege
Keyword(s):  
Electrical Conductivity ◽  
Water Table ◽  
Saline Water ◽  
Joint Inversion ◽  
Geophysical Methods ◽  
Agricultural Landscapes ◽  
Estuarine Sediments ◽  
North Coast ◽  
Inversion Algorithm ◽  
Text Data

In coastal-estuarine agricultural landscapes that are inherently rich in sulfidic sediments and saline water-tables, natural resource management data need to be collected to describe the heterogeneous nature of the soil, underlying regolith, and interactions with groundwater. Geophysical methods, such as electromagnetic (EM) induction instruments, are increasingly being used. This is because they measure apparent soil electrical conductivity [Formula: see text], which has previously been successfully used to map the areal distribution of soil (e.g., salinity) and hydrological (e.g., water-table depth) properties. We explored the potential of a next-generation DUALEM-421 and EM34 to be used independently and in conjunction with each other to provide information we can use to represent the pedological and hydrogeological setting of alluvial and estuarine sediments. A 1D laterally constrained joint-inversion algorithm can account for the nonlinearity of large [Formula: see text] (i.e., [Formula: see text]). We applied this algorithm to develop 2D cross sections of electrical conductivity ([Formula: see text]) from DUALEM-421 and EM34 [Formula: see text] data acquired across an estuarine landscape and situated within Quaternary fluvial sediments adjacent to Rocky Mouth Creek on the far north coast of New South Wales, Australia. We compared this joint-inversion model with inversions of the DUALEM-421 and EM34 [Formula: see text] data independently of each other. For the most part, the general patterns of the inverted models of [Formula: see text] compare favorably with existing pedological and hydrogeological interpretations, based on results achieved during a previous geoelectrical survey. However, the joint-inversion provides a more realistic model of the location and extent of a saline water-table and associated with the location of sulfidic sediments.

Decoupling strategy for large-scale multiphysics joint inversion

2020 ◽  
Author(s):  
Dmitry Molodtsov ◽  
Duygu Kiyan ◽  
Christopher Bean
Keyword(s):  
Large Scale ◽  
Joint Inversion ◽  
Gravity Data ◽  
Geophysical Methods ◽  
Quadratic Model ◽  
Reference Models ◽  
The Individual ◽  
Norm Penalty ◽  
Regional Problems ◽  
Cooperative Inversion

<p>We present a generalized 3-D multiphysics joint inversion scheme with a focus on large-scale regional problems. One of the key features of this scheme is the formulation of the structure coupling as a sparsity-promoting joint regularization. This approach makes it possible to simplify the structure of the objective function and to keep the number of hyperparameters relatively low, so that the inversion framework complexity scales well with respect to the number of geophysical methods and possible reference models used. To further simplify adding geophysical solvers to the framework and to optimize the discretization, we propose an alternating minimization scheme that decouples the inversion and the joint regularization steps. Decoupling is achieved by introducing an auxiliary multi-parameter model. This allows the individual subproblems to make use of problem-tailored grids and specialized optimization algorithms. As we will see, this is in particular important for the regularization subproblem. In contrast to straightforward 'cooperative inversion' formulation, decoupled inversion steps appear to be regularized by a standard quadratic model-norm penalty, and as a result existing separate inversion codes can be used with minimal, if any, modifications. The developed scheme is applied to magnetotelluric, seismic and gravity data and tested on synthetic model examples.</p>

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.

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 Advanced Methods of Joint Inversion of Multiphysics Data for Mineral Exploration

Geosciences ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 262
Author(s):  
Michael S. Zhdanov ◽  
Michael Jorgensen ◽  
Leif Cox
Keyword(s):  
Joint Inversion ◽  
Mineral Exploration ◽  
A Priori ◽  
Geophysical Methods ◽  
Physical Property ◽  
Model Parameters ◽  
Time Inversion ◽  
Structural Constraints ◽  
Considerable Uncertainty ◽  
Additional Information

Different geophysical methods provide information about various physical properties of rock formations and mineralization. In many cases, this information is mutually complementary. At the same time, inversion of the data for a particular survey is subject to considerable uncertainty and ambiguity as to causative body geometry and intrinsic physical property contrast. One productive approach to reducing uncertainty is to jointly invert several types of data. Non-uniqueness can also be reduced by incorporating additional information derived from available geological and/or geophysical data in the survey area to reduce the searching space for the solution. This additional information can be incorporated in the form of a joint inversion of multiphysics data. This paper presents an overview of the main ideas and principles of novel methods of joint inversion, developed over the last decade, which do not require a priori knowledge about specific empirical or statistical relationships between the different model parameters and/or their attributes. These approaches are designated as follows: (1) Gramian constraints; (2) Gramian-based structural constraints; (3) localized Gramian constraints; and (4) joint focusing constraints. We provide a short description of the mathematical foundations of each of these approaches and discuss the practical aspects of their applications in mineral exploration.

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