Joint inversion of multiple geophysical data using guided fuzzy c-means clustering

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. ID37-ID57 ◽  
Author(s):  
Jiajia Sun ◽  
Yaoguo Li
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Physical Property ◽  
Geophysical Data ◽  
Inversion Algorithm ◽  
Unified Framework ◽  
Parameter Domain ◽  
Fuzzy C Means ◽  
Fcm Clustering ◽  
Petrophysical Data

Joint inversion of multiple geophysical data has become an active area of research due to its potential to greatly enhance the fidelity of inverted models. Many open questions and challenges still remain. One of them is how to effectively incorporate into joint inversion multimodal petrophysical information that describes the statistical behavior of physical property values in the parameter domain (i.e., in a crossplot). We have regarded the multimodal petrophysical data as different clusters in the parameter domain and developed an approach that handles multimodal petrophysical information through guided fuzzy c-means (FCM) clustering in the parameter domain. We inverted the petrophysical data in the parameter domain in a similar manner to and simultaneously with the geophysical data in the spatial domain through minimizing one common objective function. Numerical examples have determined that the resulting models from this multidomain joint-inversion strategy are able to reproduce both the geophysical and the petrophysical data. In addition to incorporating a priori multimodal petrophysical information into inversion, guided FCM clustering also allows us to integrate geology differentiation and geophysical inversion into one unified framework that makes these two components positively affect each other. Geology differentiation results were obtained as a direct output from joint inversion. We have also developed a strategy for imposing different clustering constraints in different model regions, allowing region-specific a priori petrophysical information to be incorporated into inversion. We have applied our joint-inversion algorithm to the SEG/EAGE salt model in four different scenarios, and we found that the proposed algorithm produced much better geophysical models and geology differentiation results than separate inversions.

A study of fuzzy c-means coupling for joint inversion, using seismic tomography and gravity data test scenarios

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. W1-W15 ◽  
Author(s):  
Angela Carter-McAuslan ◽  
Peter G. Lelièvre ◽  
Colin G. Farquharson
Keyword(s):  
Seismic Velocity ◽  
Joint Inversion ◽  
Gravity Data ◽  
A Priori ◽  
Synthetic Data ◽  
Physical Property ◽  
Massive Sulfide ◽  
Realistic Model ◽  
Fuzzy C Means ◽  
Coupling Approach

Joint inversion, the inversion of multiple geophysical data sets containing complementary information about the subsurface, has the potential to significantly improve inversion results by reducing the nonuniqueness of the inverse problem. One of the challenges of joint inversion is deciding how to couple the multiple physical property models. If a coupling approach is used that is inconsistent with the physical truth, then inversion artifacts can occur and may lead to incorrect interpretations. In this paper, we investigated the fuzzy c-means (FCM) clustering approach to provide a lithological coupling of the seismic velocity and density models in joint 2D inversions of first-arrival traveltimes and gravity data. Even though this coupling approach has been used in previous works, recommendations for its effective use have not yet been developed. We conducted a suite of joint inversion tests on synthetic data generated from a geologically realistic model based on magmatic massive sulfide deposits. There is a known relationship between seismic velocity and density for the silicate rocks and sulfide minerals involved; this lithological relationship was used to design a clustered coupling strategy in the joint inversions. The tests we conducted clearly exhibited the benefits of joint inversion using FCM coupling. Our work revealed the effects of including inaccurate a priori physical property information. We also evaluated approaches to assess whether such inaccurate information may have been used.

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.

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 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 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.

Efficient inversion of 2.5D electrical resistivity data using the discrete adjoint method

Geophysics ◽  
2021 ◽  
pp. 1-54
Author(s):  
Diego Domenzain ◽  
John Bradford ◽  
Jodi Mead
Keyword(s):  
Electrical Resistivity ◽  
Gradient Descent ◽  
Adjoint Method ◽  
Sparse Matrices ◽  
Joint Inversion ◽  
Geophysical Data ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Model Parameters ◽  
Inversion Algorithm

We present a memory and operation-count efficient 2.5D inversion algorithm of electrical resistivity (ER) data that can handle fine discretization domains imposed by other geophysical (e.g, ground penetrating radar or seismic) data. Due to numerical stability criteria and available computational memory, joint inversion of different types of geophysical data can impose different grid discretization constraints on the model parameters. Our algorithm enables the ER data sensitivities to be directly joined with other geophysical data without the need of interpolating or coarsening the discretization. We employ the adjoint method directly in the discretized Maxwell's steady state equation in order to compute the data sensitivity to the conductivity. In doing so, we make no finite difference approximation on the Jacobian of the data and avoid the need to store large and dense matrices. Rather, we exploit matrix-vector multiplication of sparse matrices and find successful convergence using gradient descent for our inversion routine without having to resort to the Hessian of the objective function. By assuming a 2.5D subsurface, we are able to linearly reduce memory requirements when compared to a 3D gradient descent inversion, and by a power of two when compared to storing a 2D Hessian. Moreover, our method linearly outperforms operation counts when compared to 3D Gauss-Newton conjugate-gradient schemes, which scales cubically in our favor with respect to the thickness of the 3D domain. We physically appraise the domain of the recovered conductivity using a cut-off of the electric current density present in our survey. We present two case studies in order to assess the validity of our algorithm. First, on a 2.5D synthetic example, and then on field data acquired in a controlled alluvial aquifer, where we were able match the recovered conductivity to borehole observations.

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 Improved Fuzzy C-Means Clustering for Transformer Fault Diagnosis Using Dissolved Gas Analysis Data

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2344 ◽  
Author(s):  
Enwen Li ◽  
Linong Wang ◽  
Bin Song ◽  
Siliang Jian
Keyword(s):  
Fault Diagnosis ◽  
Membership Function ◽  
Data Clustering ◽  
Clustering Algorithm ◽  
Gas Analysis ◽  
Dissolved Gas ◽  
Fuzzy C Means ◽  
Dissolved Gas Analysis ◽  
Fcm Clustering ◽  
Transformer Fault

Dissolved gas analysis (DGA) of the oil allows transformer fault diagnosis and status monitoring. Fuzzy c-means (FCM) clustering is an effective pattern recognition method, but exhibits poor clustering accuracy for dissolved gas data and usually fails to subsequently correctly classify transformer faults. The existing feasible approach involves combination of the FCM clustering algorithm with other intelligent algorithms, such as neural networks and support vector machines. This method enables good classification; however, the algorithm complexity is greatly increased. In this paper, the FCM clustering algorithm itself is improved and clustering analysis of DGA data is realized. First, the non-monotonicity of the traditional clustering membership function with respect to the sample distance and its several local extrema are discussed, which mainly explain the poor classification accuracy of DGA data clustering. Then, an exponential form of the membership function is proposed to obtain monotony with respect to distance, thereby improving the dissolved gas data clustering. Likewise, a similarity function to determine the degree of membership is derived. Test results for large datasets show that the improved clustering algorithm can be successfully applied for DGA-data-based transformer fault detection.

Sign in / Sign up

Export Citation Format

Share Document