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.

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.

scholarly journals A new lidar inversion method using a surface reference target applied to the backscattering coefficient and lidar ratio retrievals of a fog-oil plume at short range

2020 ◽  
Vol 13 (4) ◽  
pp. 1921-1935
Author(s):  
Florian Gaudfrin ◽  
Olivier Pujol ◽  
Romain Ceolato ◽  
Guillaume Huss ◽  
Nicolas Riviere
Keyword(s):  
Short Range ◽  
A Priori ◽  
Inversion Method ◽  
Backscattering Coefficient ◽  
Reference Target ◽  
Lidar Measurements ◽  
Lidar Ratio ◽  
Aerosol Plume ◽  
Good Agreement

Abstract. In this paper, a new elastic lidar inversion equation is presented. It is based on the backscattering signal from a surface reference target (SRT) rather than that from a volumetric layer of reference (Rayleigh molecular scatterer) as is usually done. The method presented can be used when the optical properties of such a layer are not available, e.g., in the case of airborne elastic lidar measurements or when the lidar–target line is horizontal Also, a new algorithm is described to retrieve the lidar ratio and the backscattering coefficient of an aerosol plume without any a priori assumptions about the plume. In addition, our algorithm allows a determination of the instrumental constant. This algorithm is theoretically tested, viz. by means of simulated lidar profiles and then using real measurements. Good agreement with available data in the literature has been found.

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.

scholarly journals Retrieval of Canopy component temperatures through Bayesian inversion of directional thermal measurements

2009 ◽  
Vol 6 (2) ◽  
pp. 3007-3040 ◽  
Author(s):  
J. Timmermans ◽  
W. Verhoef ◽  
C. van der Tol ◽  
Z. Su
Keyword(s):  
Sensitivity Analysis ◽  
Surface Temperature ◽  
A Priori ◽  
Inversion Method ◽  
Success Rates ◽  
Brightness Temperatures ◽  
Ill Posed ◽  
Priori Information ◽  
The Individual ◽  
High Level

Abstract. In remote sensing evapotranspiration is estimated using a single surface temperature. This surface temperature is an aggregate over multiple canopy components. The temperature of the individual components can differ significantly, introducing errors in the evapotranspiration estimations. The temperature aggregate has a high level of directionality. An inversion method is presented in this paper to retrieve four canopy component temperatures from directional brightness temperatures. The Bayesian method uses both a priori information and sensor characteristics to solve the ill-posed inversion problem. The method is tested using two case studies: 1) a sensitivity analysis, using a large forward simulated dataset, and 2) in a reality study, using two datasets of two field campaigns. The results of the sensitivity analysis show that the Bayesian approach is able to retrieve the four component temperatures from directional brightness temperatures with good success rates using multi-directional sensors (ℜspectra≈0.3, ℜgonio≈0.3, and ℜAATSR≈0.5), and no improvement using mono-angular sensors (ℜ≈1). The results of the experimental study show that the approach gives good results for high LAI values (RMSEgrass=0.50 K, RMSEwheat=0.29 K, RMSEsugar beet=0.75 K, RMSEbarley=0.67 K), but for low LAI values the measurement setup provides extra disturbances in the directional brightness temperatures, RMSEyoung maize=2.85 K, RMSEmature maize=2.85 K. As these disturbances, were only present for two crops and can be eliminated using masked thermal images the method is considered successful.

scholarly journals Retrieval of canopy component temperatures through Bayesian inversion of directional thermal measurements

2009 ◽  
Vol 13 (7) ◽  
pp. 1249-1260 ◽  
Author(s):  
J. Timmermans ◽  
W. Verhoef ◽  
C. van der Tol ◽  
Z. Su
Keyword(s):  
Sensitivity Analysis ◽  
A Priori ◽  
Inversion Method ◽  
Success Rates ◽  
Brightness Temperatures ◽  
Single Temperature ◽  
Ill Posed ◽  
Priori Information ◽  
The Individual ◽  
High Level

Abstract. Evapotranspiration is usually estimated in remote sensing from single temperature value representing both soil and vegetation. This surface temperature is an aggregate over multiple canopy components. The temperature of the individual components can differ significantly, introducing errors in the evapotranspiration estimations. The temperature aggregate has a high level of directionality. An inversion method is presented in this paper to retrieve four canopy component temperatures from directional brightness temperatures. The Bayesian method uses both a priori information and sensor characteristics to solve the ill-posed inversion problem. The method is tested using two case studies: 1) a sensitivity analysis, using a large forward simulated dataset, and 2) in a reality study, using two datasets of two field campaigns. The results of the sensitivity analysis show that the Bayesian approach is able to retrieve the four component temperatures from directional brightness temperatures with good success rates using multi-directional sensors (Srspectra≈0.3, Srgonio≈0.3, and SrAATSR≈0.5), and no improvement using mono-angular sensors (Sr≈1). The results of the experimental study show that the approach gives good results for high LAI values (RMSEgrass=0.50 K, RMSEwheat=0.29 K, RMSEsugar beet=0.75 K, RMSEbarley=0.67 K); but for low LAI values the results were unsatisfactory (RMSEyoung maize=2.85 K). This discrepancy was found to originate from the presence of the metallic construction of the setup. As these disturbances, were only present for two crops and were not present in the sensitivity analysis, which had a low LAI, it is concluded that using masked thermal images will eliminate this discrepancy.

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.

Inversion of magnetotelluric data for 2D structure with sharp resistivity contrasts

Geophysics ◽  
2004 ◽  
Vol 69 (1) ◽  
pp. 78-86 ◽  
Author(s):  
Catherine de Groot‐Hedlin ◽  
Steven Constable
Keyword(s):  
Real Data ◽  
Fixed Number ◽  
Inversion Method ◽  
Magnetotelluric Data ◽  
2D Structure ◽  
Discrete Values ◽  
Modeling Code ◽  
Occam Inversion ◽  
Synthetic Models ◽  
Good Agreement

We have developed a linearized algorithm to invert noisy 2‐D magnetotelluric data for subsurface conductivity structures represented by smooth boundaries defining sharp resistivity contrasts. We solve for both a fixed number of subsurface resistivities and for the boundary locations between adjacent units. The boundary depths are forced to be discrete values defined by the mesh used in the forward modeling code. The algorithm employs a Lagrange multiplier approach in a manner similar to the widely used Occam method. The main difference is that we penalize variations in the boundary depths, rather than in resistivity contrasts between a large number of adjacent blocks. To reduce instabilities resulting from the breakdown of the linear approximation, we allow an option to penalize contrasts in the resistivities of adjacent units. We compare this boundary inversion method to the smooth Occam inversion for two synthetic models, one that includes a conductive wedge between two resistors and another that includes a resistive wedge between two conductors. The two methods give good agreement for the conductive wedge, but the solutions differ for the more poorly resolved resistive wedge, with the boundary inversion method giving a more geologically realistic result. Application of the boundary inversion method to the resistive Gemini subsalt petroleum prospect in the Gulf of Mexico indicates that the shape of this salt feature is accurately imaged by this method, and that the method remains stable when applied to real data.

Joint interpretation and uncertainty analysis of petrophysical properties in unconventional shale reservoirs

2015 ◽  
Vol 3 (1) ◽  
pp. SA33-SA49 ◽  
Author(s):  
Qinshan Yang ◽  
Carlos Torres-Verdín
Keyword(s):  
Joint Inversion ◽  
A Priori ◽  
Estimation Method ◽  
Monte Carlo Algorithm ◽  
Posteriori Probability ◽  
Inversion Method ◽  
A Posteriori ◽  
A Priori Information ◽  
Core Data ◽  
Priori Information

Interpretation of hydrocarbon-bearing shale is subject to great uncertainty because of pervasive heterogeneity, thin beds, and incomplete and uncertain knowledge of saturation-porosity-resistivity models. We developed a stochastic joint-inversion method specifically developed to address the quantitative petrophysical interpretation of hydrocarbon-bearing shale. The method was based on the rapid and interactive numerical simulation of resistivity and nuclear logs. Instead of property values themselves, the estimation method delivered the a posteriori probability of each property. The Markov-chain Monte Carlo algorithm was used to sample the model space to quantify the a posteriori distribution of formation properties. Additionally, the new interpretation method allows the use of fit-for-purpose statistical correlations between water saturation, salt concentration, porosity, and electrical resistivity to implement uncertain, non-Archie resistivity models derived from core data, including those affected by total organic carbon (TOC). In the case of underdetermined estimation problems, i.e., when the number of measurements was lower than the number of unknowns, the use of a priori information enabled plausible results within prespecified petrophysical and compositional bounds. The developed stochastic interpretation technique was successfully verified with data acquired in the Barnett and Haynesville Shales. Core data (including X-ray diffraction data) were combined into a priori information for interpretation of nuclear and resistivity logs. Results consisted of mineral concentrations, TOC, and porosity together with their uncertainty. Eighty percent of the core data was located within the 95% credible interval of estimated mineral/fluid concentrations.

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