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.

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).

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.

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.

Interpretation of borehole gravity data of the Lalor volcanogenic massive sulfide deposit, Snow Lake, Manitoba, Canada

2015 ◽  
Vol 3 (3) ◽  
pp. T145-T154 ◽  
Author(s):  
Ernst Schetselaar ◽  
Pejman Shamsipour
Keyword(s):  
Gravity Data ◽  
Hanging Wall ◽  
Bouguer Anomaly ◽  
Massive Sulfide ◽  
Geological Mapping ◽  
Sulfide Deposit ◽  
Massive Sulfide Deposit ◽  
Volcanogenic Massive Sulfide ◽  
Volcanogenic Massive Sulfide Deposit ◽  
Gamma Density

We have acquired borehole gravity data along five drillholes intersecting the Lalor volcanogenic massive sulfide deposit hosted in the eastern Flin Flon greenstone belt at Snow Lake, Manitoba, Canada. Inverted apparent interval density (IAID) logs were calculated from the borehole gravity data and compared with lithofacies and [Formula: see text] logs; the latter of which is a geochemical proxy for differentiating volcanic rocks of felsic to mafic composition. The IAID anomalies predominantly reflect alternating mafic and felsic volcanic rock units in the footwall and hanging wall of the massive sulfide deposit. IAID lows are associated with [Formula: see text] highs that correspond to rhyolite and rhyodacite intervals in the hanging wall. IAID lows with associated [Formula: see text] peaks in the footwall occur within intervals of gneiss and schist formed by metamorphism of hydrothermally altered rocks, suggesting that these IAID lows still reflect the felsic composition of their volcanic protoliths. A significant peak-to-peak Bouguer anomaly of 0.66 mGal caused by an estimated excess mass of 0.7 mT can be correlated with gamma-gamma density signature of the main sulfide ore zone in three boreholes. This anomaly is aligned with the ore zone after restoring the displacement along a northeast-dipping structure. When integrated with drillhole lithology and lithogeochemistry logs, gravity borehole data can, in addition to the direct detection of mineralization, be used as a subsurface geological mapping tool.

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.

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.

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