Inversion modeling of gravity with prismatic mass bodies

Geophysics ◽  
1991 ◽  
Vol 56 (9) ◽  
pp. 1365-1376 ◽  
Author(s):  
Tieng‐Chang Lee ◽  
Shawn Biehler
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Depth Resolution ◽  
Memory Storage ◽  
Inversion Algorithm ◽  
Sampling Window ◽  
Prismatic Bodies ◽  
The Fourier Transform ◽  
Priori Information ◽  
Forward And Inverse Modeling

A combined method for forward and inverse modeling of gravity data is presented. Based on the Fourier transform of Poisson’s equation, the forward modeling is suitable for observation points above, within, and below causative masses with any prescribed density distribution. The inversion is linearized in the spatial domain by superimposing numerous prismatic bodies, each having constant but different density, and fixed geometry. Our inversion algorithm adopts a sampling window to reduce memory storage and computations. Testing, with synthetic and field data, demonstrates that a successful inversion can be obtained from crudely estimated a priori density distributions and uncertainties. Lateral variations in density are well resolved but depth resolution often requires better constrained a priori information. Under various a priori conditions, our modeling indicates that sediment density tends to vary exponentially with depth in the San Jacinto basin, southern California.

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.

Three‐dimensional gravity inversion using simulated annealing: Constraints on the diapiric roots of allochthonous salt structures

Geophysics ◽  
2001 ◽  
Vol 66 (5) ◽  
pp. 1438-1449 ◽  
Author(s):  
Seiichi Nagihara ◽  
Stuart A. Hall
Keyword(s):  
Simulated Annealing ◽  
Gulf Of Mexico ◽  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Inversion Method ◽  
A Priori Information ◽  
Final Density ◽  
Smoothing Effects ◽  
Priori Information

In the northern continental slope of the Gulf of Mexico, large oil and gas reservoirs are often found beneath sheetlike, allochthonous salt structures that are laterally extensive. Some of these salt structures retain their diapiric feeders or roots beneath them. These hidden roots are difficult to image seismically. In this study, we develop a method to locate and constrain the geometry of such roots through 3‐D inverse modeling of the gravity anomalies observed over the salt structures. This inversion method utilizes a priori information such as the upper surface topography of the salt, which can be delineated by a limited coverage of 2‐D seismic data; the sediment compaction curve in the region; and the continuity of the salt body. The inversion computation is based on the simulated annealing (SA) global optimization algorithm. The SA‐based gravity inversion has some advantages over the approach based on damped least‐squares inversion. It is computationally efficient, can solve underdetermined inverse problems, can more easily implement complex a priori information, and does not introduce smoothing effects in the final density structure model. We test this inversion method using synthetic gravity data for a type of salt geometry that is common among the allochthonous salt structures in the Gulf of Mexico and show that it is highly effective in constraining the diapiric root. We also show that carrying out multiple inversion runs helps reduce the uncertainty in the final density model.

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.

A Fast Rational Model Approach to Parametric Spectral Estimation—Part I: The Algorithm

1990 ◽  
Vol 112 (3) ◽  
pp. 321-327 ◽  
Author(s):  
S. D. Fassois
Keyword(s):  
Spectral Estimation ◽  
A Priori ◽  
Inverse Function ◽  
Memory Storage ◽  
Rational Model ◽  
Arma Process ◽  
Sufficient Statistic ◽  
Guaranteed Stability ◽  
Local Extrema ◽  
Priori Information

A novel, fast rational model (ARMA) approach to parametric spectral estimation, based on correlation-type and guaranteed-stability versions of the Suboptimum Maximum Likelihood scheme that utilizes a quadratic approximation of the negative log-likelihood about an initial estimate in the MA parameter subspace, inverse function estimates, and fundamental ARMA process properties, is introduced. The proposed approach is exclusively based on linear operations, uses the autocovariance function as a “sufficient statistic,” and overcomes the main drawbacks/limitations of alternative approaches by offering high accuracy, minimal computational and memory storage requirements, no need for a priori information, mathematically guaranteed stability (and therefore the capability of estimating all types of spectra, including those characterized by sharp valleys), and complete elimination of the local extrema problem by yielding a unique estimate that is shown to asymptotically converge to the true spectrum. The paper is divided into two parts: The basic form of the proposed approach is derived in the first part, whereas in the second (Fassois, 1990), its consistency is proven, two guaranteed-stability versions developed, and its performance evaluated via numerical simulations and comparisons with standard techniques.

scholarly journals 3D stochastic inversion of gravity data using cokriging and cosimulation

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. I1-I10 ◽  
Author(s):  
Pejman Shamsipour ◽  
Denis Marcotte ◽  
Michel Chouteau ◽  
Pierre Keating
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Inversion Method ◽  
Geostatistical Techniques ◽  
Priori Information ◽  
Surface Geology ◽  
Synthetic Models ◽  
Secondary Variable ◽  
Good Agreement

A new application has been developed, based on geostatistical techniques of cokriging and conditional simulation, for the 3D inversion of gravity data including geologic constraints. The necessary gravity, density, and gravity-density covariance matrices are estimated using the observed gravity data. Then the densities are cokriged or simulated using the gravity data as the secondary variable. The model allows noise to be included in the observations. The method is applied to two synthetic models: a short dipping dike and a stochastic distribution of densities. Then some geologic information is added as constraints to the cokriging system. The results show the ability of the method to integrate complex a priori information. The survey data of the Matagami mining camp are considered as a case study. The inversion method based on cokriging is applied to the residual anomaly to map the geology through the estimation of the density distribution in this region. The results of the inversion and simulation methods are in good agreement with the surface geology of the survey region.

3D controlled-source electromagnetic imaging of gas hydrates: Insights from the Pelotas Basin offshore Brazil

2019 ◽  
Vol 7 (4) ◽  
pp. SH111-SH131 ◽  
Author(s):  
Raghava Tharimela ◽  
Adolpho Augustin ◽  
Marcelo Ketzer ◽  
Jose Cupertino ◽  
Dennis Miller ◽  
...  
Keyword(s):  
Gas Hydrates ◽  
Gas Hydrate ◽  
A Priori ◽  
Inversion Algorithm ◽  
Near Surface ◽  
Bottom Simulating Reflector ◽  
Controlled Source ◽  
Lateral Extent ◽  
Priori Information ◽  
Pelotas Basin

Mapping of natural gas hydrate systems has been performed successfully in the past using the controlled-source electromagnetic (CSEM) method. This method relies on differentiating resistive highly saturated free gas or hydrate-bearing host sediment from a less resistive low-saturated gas or brine-bearing host sediments. Knowledge of the lateral extent and resistivity variations (and hence the saturation variations) within sediments that host hydrates is crucial to be able to accurately quantify the presence of saturated gas hydrates. A 3D CSEM survey (PUCRS14) was acquired in 2014 in the Pelotas Basin offshore Brazil, with hydrate resistivity mapping as the main objective. The survey was acquired within the context of the CONEGAS research project, which investigated the origin and distribution of gas hydrate deposits in the Pelotas Basin. We have inverted the acquired data using a proprietary 3D CSEM anisotropic inversion algorithm. Inversion was purely CSEM data driven, and we did not include any a priori information in the process. Prior to CSEM, interpretation of near-surface geophysical data including 2D seismic, sub-bottom profiler, and multibeam bathymetry data indicated possible presence of gas hydrates within features identified such as faults, chimneys, and seeps leading to pockmarks, along the bottom simulating reflector and within the gas hydrate stability zone. Upon integration of the same with CSEM-derived resistivity volume, the interpretation revealed excellent spatial correlation with many of these features. The interpretation further revealed new features with possible hydrate presence, which were previously overlooked due to a lack of a clear seismic and/or multibeam backscatter signature. In addition, features that were previously mapped as gas hydrate bearing had to be reinterpreted as residual or low-saturated gas/hydrate features, due to the lack of significant resistivity response associated with them. Furthermore, we used the inverted resistivity volume to derive the saturation volume of the subsurface using Archie’s equation.

A continuation approach to regularization of ill-posed problems with application to crosswell-traveltime tomography

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE337-VE351 ◽  
Author(s):  
Kenneth P. Bube ◽  
Robert T. Langan
Keyword(s):  
A Priori ◽  
Real Data ◽  
Inversion Algorithm ◽  
Surface Reflection ◽  
Traveltime Tomography ◽  
Ill Posed ◽  
Priori Information ◽  
The Many ◽  
Derivatives Of

In most geometries in which seismic-traveltime tomography is applied (e.g., crosswell, surface-reflection, and VSP), determination of the slowness field using only traveltimes is not a well-conditioned problem. Nonuniqueness is common. Even when the slowness field is uniquely determined, small changes in measured traveltimes can cause large errors in the computed slowness field. A priori information often is available — well logs, initial rough estimates of slowness from structural geology, etc. — and can be incorporated into a traveltime-inversion algorithm by using penalty terms. To further regularize the problem, smoothing constraints also can be incorporated using penalty terms by penalizing derivatives of the slowness field. What weights to use on the penalty terms is a major decision, particularly the smoothing-penalty weights. We use a continuation approach in selecting the smoothing-penalty weights. Instead of using fixed smoothing-penalty weights, we decrease them step by step, using the slowness model computed with the previous, larger weights as the initial slowness model for the next step with the new, smaller weights. This continuation approach can solve synthetic problems more accurately than does one that uses fixed smoothing-penalty weights, and it appears to yield more features of interest in real-data applications of traveltime tomography. We have formulated guidelines for making the many choices needed to implement this continuation strategy effectively and have developed specific choices for crosswell-traveltime tomography.

Practical applications of uniqueness theorems in gravimetry: Part II—Pragmatic incorporation of concrete geologic information

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 795-800 ◽  
Author(s):  
Valéria C. F. Barbosa ◽  
João B. C. Silva ◽  
Walter E. Medeiros
Keyword(s):  
Gravity Data ◽  
A Priori ◽  
Gravity Inversion ◽  
Solution Stability ◽  
Practical Applications ◽  
Density Distributions ◽  
Alternative Method ◽  
True Source ◽  
Priori Information ◽  
Simply Connected

We illustrate the importance of establishing solution uniqueness through mathematical restrictions reflecting a source attribute. We also illustrate the validity and utility of a guideline derived in an accompanying paper for constructing sound gravity inversion methods for the class of sources presenting either homogeneous or depth‐independent density distributions. The two‐part guideline is (1) to introduce a priori information favoring uniqueness, either by assuming that a nonnull density distribution depending only on x and y is confined to the interior of a horizontal slab with known position or by limiting the class of possible solutions to homogeneous, simply connected polygons (or polyhedra) with known density, displaying no fancy shapes and no curling apophyses at their borders, and (2) to introduce information favoring solution stability by estimating only the features of the source which may be resolved by the data. Following the guideline, we apply different methods to gravity data using interpretation models consisting of a grid of cells on the x‐y and x‐z planes. In both cases the estimates are very close to the true synthetic source. The data produced by the distribution varying with x and z are also inverted using the method, which minimizes the norm of the first‐order derivative of the density. This constraint does not reflect a true source attribute but is strong enough to stabilize the solution and to guarantee its uniqueness. Because of the strong bias imposed to the solution, the estimated distribution, although unique and stable, is far from the true source, concentrating most of the anomalous mass at the surface. Finally, we present an alternative method which redistributes the estimated anomalous mass downward. To be effective, this technique requires prior knowledge about the source depth to the top. In addition, the source should not be too small and deep. Although being able to produce good results, this alternative method requires a great dose of the interpreter's art.

Innovative Approach to Information Search by Example of a Patent Analysis of an Important Substitution Plan

2020 ◽  
pp. 143-157
Author(s):  
Maria A. Milkova
Keyword(s):  
Information Search ◽  
Topic Modeling ◽  
Cognitive Biases ◽  
A Priori ◽  
Import Substitution ◽  
Innovative Approach ◽  
Iterative Search ◽  
Comprehensive Picture ◽  
Priori Information ◽  
Selection Of

Nowadays the process of information accumulation is so rapid that the concept of the usual iterative search requires revision. Being in the world of oversaturated information in order to comprehensively cover and analyze the problem under study, it is necessary to make high demands on the search methods. An innovative approach to search should flexibly take into account the large amount of already accumulated knowledge and a priori requirements for results. The results, in turn, should immediately provide a roadmap of the direction being studied with the possibility of as much detail as possible. The approach to search based on topic modeling, the so-called topic search, allows you to take into account all these requirements and thereby streamline the nature of working with information, increase the efficiency of knowledge production, avoid cognitive biases in the perception of information, which is important both on micro and macro level. In order to demonstrate an example of applying topic search, the article considers the task of analyzing an import substitution program based on patent data. The program includes plans for 22 industries and contains more than 1,500 products and technologies for the proposed import substitution. The use of patent search based on topic modeling allows to search immediately by the blocks of a priori information – terms of industrial plans for import substitution and at the output get a selection of relevant documents for each of the industries. This approach allows not only to provide a comprehensive picture of the effectiveness of the program as a whole, but also to visually obtain more detailed information about which groups of products and technologies have been patented.

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