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.

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.

Marlim R3D: A realistic model for controlled-source electromagnetic simulations — Phase 2: The controlled-source electromagnetic data set

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. E293-E299
Author(s):  
Jorlivan L. Correa ◽  
Paulo T. L. Menezes
Keyword(s):  
A Priori ◽  
Synthetic Data ◽  
Realistic Model ◽  
Earth Model ◽  
Data Sets ◽  
Data Set ◽  
Geoelectric Model ◽  
Controlled Source ◽  
The North ◽  
Electromagnetic Simulations

Synthetic data provided by geoelectric earth models are a powerful tool to evaluate a priori a controlled-source electromagnetic (CSEM) workflow effectiveness. Marlim R3D (MR3D) is an open-source complex and realistic geoelectric model for CSEM simulations of the postsalt turbiditic reservoirs at the Brazilian offshore margin. We have developed a 3D CSEM finite-difference time-domain forward study to generate the full-azimuth CSEM data set for the MR3D earth model. To that end, we fabricated a full-azimuth survey with 45 towlines striking the north–south and east–west directions over a total of 500 receivers evenly spaced at 1 km intervals along the rugged seafloor of the MR3D model. To correctly represent the thin, disconnected, and complex geometries of the studied reservoirs, we have built a finely discretized mesh of [Formula: see text] cells leading to a large mesh with a total of approximately 90 million cells. We computed the six electromagnetic field components (Ex, Ey, Ez, Hx, Hy, and Hz) at six frequencies in the range of 0.125–1.25 Hz. In our efforts to mimic noise in real CSEM data, we summed to the data a multiplicative noise with a 1% standard deviation. Both CSEM data sets (noise free and noise added), with inline and broadside geometries, are distributed for research or commercial use, under the Creative Common License, at the Zenodo platform.

Joint inversion of potential-fields data over the DO-27 kimberlite pipe using a Gaussian mixture model prior

2020 ◽  
Vol 8 (4) ◽  
pp. SS47-SS62
Author(s):  
Thibaut Astic ◽  
Dominique Fournier ◽  
Douglas W. Oldenburg
Keyword(s):  
Gaussian Mixture Model ◽  
Mixture Model ◽  
Joint Inversion ◽  
Gravity Data ◽  
Physical Property ◽  
Gaussian Mixture ◽  
Kimberlite Pipe ◽  
Magnetic Data ◽  
High Porosity ◽  
Rock Types

We have carried out petrophysically and geologically guided inversions (PGIs) to jointly invert airborne and ground-based gravity data and airborne magnetic data to recover a quasi-geology model of the DO-27 kimberlite pipe in the Tli Kwi Cho (also referred to as TKC) cluster. DO-27 is composed of three main kimberlite rock types in contact with each other and embedded in a granitic host rock covered by a thin layer of glacial till. The pyroclastic kimberlite (PK), which is diamondiferous, and the volcanoclastic kimberlite (VK) have anomalously low density, due to their high porosity, and weak magnetic susceptibility. They are indistinguishable from each other based upon their potential-field responses. The hypabyssal kimberlite (HK), which is not diamondiferous, has been identified as highly magnetic and remanent. Quantitative petrophysical signatures for each rock unit are obtained from sample measurements, such as the increasing density of the PK/VK unit with depth and the remanent magnetization of the HK unit, and are represented as a Gaussian mixture model (GMM). This GMM guides the PGI toward generating a 3D quasi-geology model with physical properties that satisfies the geophysical data sets and the petrophysical signatures. Density and magnetization models recovered individually yield volumes that have physical property combinations that do not conform to any known petrophysical characteristics of the rocks in the area. A multiphysics PGI addresses this problem by using the GMM as a coupling term, but it puts a volume of the PK/VK unit at a location that is incompatible with geologic information from drillholes. To conform to that geologic knowledge, a fourth unit is introduced, PK-minor, which is petrophysically and geographically distinct from the main PK/VK unit. This inversion produces a quasi-geology model that presents good structural locations of the diamondiferous PK unit and can be used to provide a resource estimate or decide the locations of future drillholes.

An attempt to formulate well‐posed questions in gravity: Application of linear inverse techniques to mining exploration

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1781-1793 ◽  
Author(s):  
Vincent Richard ◽  
Roger Bayer ◽  
Michel Cuer
Keyword(s):  
Linear Programming ◽  
Gravity Data ◽  
A Priori ◽  
Massive Sulfide ◽  
Sulfide Deposit ◽  
Exploration Process ◽  
Programming Techniques ◽  
Priori Information ◽  
Mining Exploration ◽  
Well Posed

The aim of this paper is to use linear inverse theory to interpret gravity surveys in mining exploration by incorporating a priori information on the densities and data in terms of Gaussian or uniform probability laws. The Bayesian approach and linear programming techniques lead to the solution of well‐posed questions resulting from the exploration process. In particular, we develop a method of measuring the possible heterogeneity within a given domain by using linear programming. These techniques are applied to gravity data taken over the massive sulfide deposit of Neves Corvo (Portugal). We show how crude constraints on the densities lead to a first estimation of the location of sources, while further geologic constraints allow us to estimate the heterogeneity and to put definite bounds on the ore masses.

Focusing joint inversion of gravity and magnetic data using a clustering stabilizer in a space of weighted parameters

2020 ◽  
Vol 224 (2) ◽  
pp. 1344-1359
Author(s):  
Zhengwei Xu ◽  
Guangui Zou ◽  
Qianqian Wei ◽  
Junqi Tian ◽  
Hemin Yuan
Keyword(s):  
Joint Inversion ◽  
Model Space ◽  
Massive Sulfide ◽  
Realistic Model ◽  
Magnetic Data ◽  
Inversion Algorithm ◽  
Model Studies ◽  
Structural Correlation ◽  
Gravity And Magnetic ◽  
Gravity And Magnetic Data

SUMMARY This paper develops a minimum-support focusing stabilizer to perform a joint inversion of the vertical components of gravity and magnetic data using fuzzy c-means clustering (FCM) with the regularized Newton method in a space of weighted parameters. Not only does this joint inversion technology arrive at the conditionally well-posed traditional potential field inversion, but it also increases the structural correlation between multiple inverted models. The FCM and the focusing stabilizer make it possible to balance the convergence of the data space (D) and the model space (M), guiding multimodal geophysical parameters toward assigned petrophysical values, which makes the results more stable and realistic. Two model studies are presented to illustrate the method, a simple synthetic model with two rectangular bodies in a homogenous background and a realistic model of the Volcanogenic Massive Sulfide (VMS) deposits in northeastern New Brunswick, Canada. These models demonstrate that the new focusing joint inversion algorithm produces better images than traditional methods because the FCM function uses the structural correlation of density contrast and magnetic susceptibility as constraints.

Isostatic constraint for 2D nonlinear gravity inversion on rifted margins

Geophysics ◽  
2019 ◽  
Vol 85 (1) ◽  
pp. G17-G34
Author(s):  
B. Marcela S. Bastos ◽  
Vanderlei C. Oliveira Jr.
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Rifted Margins ◽  
Isostatic Equilibrium ◽  
Priori Information ◽  
Pelotas Basin ◽  
Nonlinear Gravity

We have developed a nonlinear gravity inversion for simultaneously estimating the basement and Moho geometries, as well as the depth of the reference Moho along a profile crossing a passive rifted margin. To obtain stable solutions, we impose smoothness on basement and Moho, force them to be close to previously estimated depths along the profile and also impose local isostatic equilibrium. Different from previous methods, we evaluate the information of local isostatic equilibrium by imposing smoothness on the lithostatic stress exerted at depth. Our method delimits regions that deviate and those that can be considered in local isostatic equilibrium by varying the weight of the isostatic constraint along the profile. It also allows controlling the degree of equilibrium along the profile, so that the interpreter can obtain a set of candidate models that fit the observed data and exhibit different degrees of isostatic equilibrium. Our method also differs from earlier studies because it attempts to use isostasy for exploring (but not necessarily reducing) the inherent ambiguity of gravity methods. Tests with synthetic data illustrate the effect of our isostatic constraint on the estimated basement and Moho reliefs, especially at regions with pronounced crustal thinning, which are typical of passive volcanic margins. Results obtained by inverting satellite data over the Pelotas Basin, a passive volcanic margin in southern Brazil, agree with previous interpretations obtained independently by combining gravity, magnetic, and seismic data available to the petroleum industry. These results indicate that combined with a priori information, simple isostatic assumptions can be very useful for interpreting gravity data on passive rifted margins.

Structural inversion of gravity data using linear programming

Geophysics ◽  
2006 ◽  
Vol 71 (3) ◽  
pp. J41-J50 ◽  
Author(s):  
Tim van Zon ◽  
Kabir Roy-Chowdhury
Keyword(s):  
Linear Programming ◽  
Gravity Data ◽  
A Priori ◽  
Synthetic Data ◽  
Uniform Grid ◽  
Model Parameters ◽  
Data Set ◽  
Test Models ◽  
Structural Inversion ◽  
Value Decomposition

Structural inversion of gravity data — deriving robust images of the subsurface by delineating lithotype boundaries using density anomalies — is an important goal in a range of exploration settings (e.g., ore bodies, salt flanks). Application of conventional inversion techniques in such cases, using [Formula: see text]-norms and regularization, produces smooth results and is thus suboptimal. We investigate an [Formula: see text]-norm-based approach which yields structural images without the need for explicit regularization. The density distribution of the subsurface is modeled with a uniform grid of cells. The density of each cell is inverted by minimizing the [Formula: see text]-norm of the data misfit using linear programming (LP) while satisfying a priori density constraints. The estimate of the noise level in a given data set is used to qualitatively determine an appropriate parameterization. The 2.5D and 3D synthetic tests adequately reconstruct the structure of the test models. The quality of the inversion depends upon a good prior estimation of the minimum depth of the anomalous body. A comparison of our results with one using truncated singular value decomposition (TSVD) on a noisy synthetic data set favors the LP-based method. There are two advantages in using LP for structural inversion of gravity data. First, it offers a natural way to incorporate a priori information regarding the model parameters. Second, it produces subsurface images with sharp boundaries (structure).

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 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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