2-D inversion of gravity data using sources laterally bounded by continuous surfaces and depth‐dependent density

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1128-1141 ◽  
Author(s):  
Juan García‐Abdeslem
Keyword(s):  
Sensitivity Analysis ◽  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Data Sets ◽  
Nonlinear Inversion ◽  
Correlation Matrices ◽  
Significant Difference ◽  
Dependent Density

A description is given of numerical methods for 2-D gravity modeling and nonlinear inversion. The forward model solution is suitable for calculating the gravity anomaly caused by a 2-D source body with depth‐dependent density that is laterally bounded by continuous surfaces and can easily accommodate different kinds of geologic structures. The weighted and damped discrete nonlinear inverse method addressed here can invert both density and geometry of the source body. Both modeling and inversion methods are illustrated with several examples using synthetic and two field gravity data sets—one over a sulfide ore body and other across a sedimentary basin. A sensitivity analysis is carried out for the resulting solutions by means of the resolution, covariance, and correlation matrices, providing insight into the capabilities and limitations of the inversion method. The inversion of synthetic data provides meaningful results, showing that the method is robust in the presence of noise. Its sensitivity analysis indicates an almost perfect resolution and small covariance, but high correlation between some parameters. Differences in the asperity aspect of the inverted‐field data sets turned out to be important for the inversion capabilities of the algorithm, making a significant difference in the resolution achieved, its covariance, and the degree of correlation among parameters.

A Bayesian approach to modeling 2D gravity data using polygons

Geophysics ◽  
2017 ◽  
Vol 82 (1) ◽  
pp. G1-G21 ◽  
Author(s):  
William J. Titus ◽  
Sarah J. Titus ◽  
Joshua R. Davis
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Gravity Inversion ◽  
Limiting Factor ◽  
Data Sets ◽  
Data Set ◽  
Local Optima ◽  
Occupancy Probability ◽  
Compute Model ◽  
Parameter Values

We apply a Bayesian Markov chain Monte Carlo formalism to the gravity inversion of a single localized 2D subsurface object. The object is modeled as a polygon described by five parameters: the number of vertices, a density contrast, a shape-limiting factor, and the width and depth of an encompassing container. We first constrain these parameters with an interactive forward model and explicit geologic information. Then, we generate an approximate probability distribution of polygons for a given set of parameter values. From these, we determine statistical distributions such as the variance between the observed and model fields, the area, the center of area, and the occupancy probability (the probability that a spatial point lies within the subsurface object). We introduce replica exchange to mitigate trapping in local optima and to compute model probabilities and their uncertainties. We apply our techniques to synthetic data sets and a natural data set collected across the Rio Grande Gorge Bridge in New Mexico. On the basis of our examples, we find that the occupancy probability is useful in visualizing the results, giving a “hazy” cross section of the object. We also find that the role of the container is important in making predictions about the subsurface object.

3-D resistivity inversion using the finite‐element method

Geophysics ◽  
1994 ◽  
Vol 59 (12) ◽  
pp. 1839-1848 ◽  
Author(s):  
Yutaka Sasaki
Keyword(s):  
Finite Element ◽  
Approximate Method ◽  
Synthetic Data ◽  
Computation Time ◽  
Inversion Method ◽  
Data Sets ◽  
Near Surface ◽  
Partial Derivatives ◽  
Homogeneous Half Space ◽  
Resistivity Inversion

With the increased availability of faster computers, it is now practical to employ numerical modeling techniques to invert resistivity data for 3-D structure. Full and approximate 3-D inversion methods using the finite‐element solution for the forward problem have been developed. Both methods use reciprocity for efficient evaluations of the partial derivatives of apparent resistivity with respect to model resistivities. In the approximate method, the partial derivatives are approximated by those for a homogeneous half‐space, and thus the computation time and memory requirement are further reduced. The methods are applied to synthetic data sets from 3-D models to illustrate their effectiveness. They give a good approximation of the actual 3-D structure after several iterations in practical situations where the effects of model inadequacy and topography exist. Comparisons of numerical examples show that the full inversion method gives a better resolution, particularly for the near‐surface features, than does the approximate method. Since the full derivatives are more sensitive to local features of resistivity variations than are the approximate derivatives, the resolution of the full method may be further improved when the finite‐element solutions are performed more accurately and more efficiently.

Gravity data as a tool for detecting faults: In-depth enhancement of subtle Almada’s basement faults, Brazil

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. B59-B68 ◽  
Author(s):  
Valeria C. Barbosa ◽  
Paulo T. Menezes ◽  
João B. Silva
Keyword(s):  
Gravity Data ◽  
Synthetic Data ◽  
Normal Fault ◽  
Northeastern Brazil ◽  
Normal Faults ◽  
Gravity Inversion ◽  
Inversion Method ◽  
Basement Faults ◽  
Depth Enhancement ◽  
Fault Displacement

We demonstrate the potential of gravity data to detect and to locate in-depth subtle normal faults in the basement relief of a sedimentary basin. This demonstration is accomplished by inverting the gravity data with the constraint that the estimated basement relief presents local abrupt faults and is smooth elsewhere. We inverted the gravity data from the onshore Almada Basin in northeastern Brazil, and we mapped several normal faults whose locations and plane geometries were already known from seismic imaging. The inversion method delineated well both the discontinuities with small or large slips and a sequence of step faults. Using synthetic data, we performed a systematic search of normal fault slips versus fault displacement depths to map the fault-detectable region in this space. This mapping helps to assess the ability of gravity inversion to detect normal faults. Mapping shows that normal faults with small [Formula: see text], medium (about [Formula: see text]), and large (about [Formula: see text]) vertical slips can be detected if the maximum midpoint depths of the fault planes are smaller than 1.8, 3.8, and [Formula: see text], respectively.

Integration of seismic and gravity data — A case study from the western Gulf of Mexico

2015 ◽  
Vol 3 (4) ◽  
pp. SAC99-SAC106 ◽  
Author(s):  
Irina Filina ◽  
Nicholas Delebo ◽  
Gopal Mohapatra ◽  
Clayton Coble ◽  
Gary Harris ◽  
...  
Keyword(s):  
Gulf Of Mexico ◽  
Gravity Field ◽  
Gravity Model ◽  
Seismic Velocity ◽  
Gravity Data ◽  
Public Domain ◽  
Gravity Modeling ◽  
Data Sets ◽  
Gardner Equation ◽  
Well Data

A 3D gravity model was developed in the western Gulf of Mexico in the East Breaks and Alaminos Canyon protraction areas. This model integrated 3D seismic, gravity, and well data; it was constructed in support of a proprietary seismic reprocessing project and was updated iteratively with seismic. The gravity model was built from seismic horizons of the bathymetry, salt layers, and the acoustic basement; however, the latter was only possible to map in seismic data during the latest iterations. In addition, a deep layer representing the Moho boundary was derived from gravity and constrained by public-domain refraction data. A 3D density distribution was derived from the seismic velocity volume using a modified Gardner equation. The modification comprised imposing a depth dependency on the Gardner coefficient, which is constant in the classic Gardner equation. The modified coefficient was derived from well data in the study area and public-domain velocity-density data sets. The forward-calculated gravity response of the composed density model was then compared with the observed gravity field, and the mismatch was analyzed jointly by a seismic interpreter and a gravity modeler. Adjustments were then made to the gravity model to ensure that the resultant salt model was geologically reasonable and supported by gravity, seismic, and well data sets. The output of the gravity modeling was subsequently applied to the next phase of seismic processing. Overall, this integration resulted in a more robust salt model, which has led to significant improvements in subsalt seismic imaging. The analysis of the regional trend in the observed gravity field suggested that a stretched continental crust underlay our seismic reprocessing area, with an oceanic-continental transition zone located to the southeast of our reprocessing region.

scholarly journals Generating high-fidelity synthetic patient data for assessing machine learning healthcare software

2020 ◽  
Vol 3 (1) ◽  
Author(s):  
Allan Tucker ◽  
Zhenchen Wang ◽  
Ylenia Rotalinti ◽  
Puja Myles
Keyword(s):  
Machine Learning ◽  
Sensitivity Analysis ◽  
Synthetic Data ◽  
Patient Data ◽  
Data Sets ◽  
Outlier Analysis ◽  
Ground Truth Data ◽  
Machine Learning Classifiers ◽  
Learning Classifiers ◽  
Graphical Modelling

Abstract There is a growing demand for the uptake of modern artificial intelligence technologies within healthcare systems. Many of these technologies exploit historical patient health data to build powerful predictive models that can be used to improve diagnosis and understanding of disease. However, there are many issues concerning patient privacy that need to be accounted for in order to enable this data to be better harnessed by all sectors. One approach that could offer a method of circumventing privacy issues is the creation of realistic synthetic data sets that capture as many of the complexities of the original data set (distributions, non-linear relationships, and noise) but that does not actually include any real patient data. While previous research has explored models for generating synthetic data sets, here we explore the integration of resampling, probabilistic graphical modelling, latent variable identification, and outlier analysis for producing realistic synthetic data based on UK primary care patient data. In particular, we focus on handling missingness, complex interactions between variables, and the resulting sensitivity analysis statistics from machine learning classifiers, while quantifying the risks of patient re-identification from synthetic datapoints. We show that, through our approach of integrating outlier analysis with graphical modelling and resampling, we can achieve synthetic data sets that are not significantly different from original ground truth data in terms of feature distributions, feature dependencies, and sensitivity analysis statistics when inferring machine learning classifiers. What is more, the risk of generating synthetic data that is identical or very similar to real patients is shown to be low.

scholarly journals Marquardt inverse modeling of the residual gravity anomalies due to simple geometric structures: A case study of chromite deposit

2019 ◽  
Vol 49 (2) ◽  
pp. 153-180 ◽  
Author(s):  
Ata Eshaghzadeh ◽  
Alireza Dehghanpour ◽  
Sanaz Seyedi Sahebari
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Synthetic Data ◽  
Vertical Cylinder ◽  
Gravity Anomalies ◽  
Horizontal Cylinder ◽  
Inversion Method ◽  
Chromite Deposit ◽  
Different Shapes

Abstract In this paper, an inversion method based on the Marquardt’s algorithm is presented to invert the gravity anomaly of the simple geometric shapes. The inversion outputs are the depth and radius parameters. We investigate three different shapes, i.e. the sphere, infinite horizontal cylinder and semi-infinite vertical cylinder for modeling. The proposed method is used for analyzing the gravity anomalies from assumed models with different initial parameters in all cases as the synthetic data are without noise and also corrupted with noise to evaluate the ability of the procedure. We also employ this approach for modeling the gravity anomaly due to a chromite deposit mass, situated east of Sabzevar, Iran. The lowest error between the theoretical anomaly and computed anomaly from inverted parameters, determine the shape of the causative mass. The inversion using different initial models for the theoretical gravity and also for real gravity data yields approximately consistent solutions. According to the interpreted parameters, the best shape that can imagine for the gravity anomaly source is the vertical cylinder with a depth to top of 7.4 m and a radius of 11.7 m.

Fast 2D inversion of large borehole EM induction data sets with an efficient Fréchet-derivative approximation

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. E75-E91 ◽  
Author(s):  
Gong Li Wang ◽  
Carlos Torres-Verdín ◽  
Jesús M. Salazar ◽  
Benjamin Voss
Keyword(s):  
Electrical Resistivity ◽  
Synthetic Data ◽  
Large Data ◽  
Inversion Method ◽  
Central Component ◽  
Data Sets ◽  
Spatial Distributions ◽  
Desktop Computer ◽  
Data Set ◽  
Uncertainty Estimator

In addition to reliability and stability, the efficiency and expediency of inversion methods have long been a strong concern for their routine applications by well-log interpreters. We have developed and successfully validated a new inversion method to estimate 2D parametric spatial distributions of electrical resistivity from array-induction measurements acquired in a vertical well. The central component of the method is an efficient approximation to Fréchet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion. To further enhance the overall efficiency of the inversion, we combined the new approximation with both the improved numerical mode-matching method and domain decomposition. Examples of application with synthetic data sets show that the new methodis computer efficient and capable of retrieving original model re-sistivities even in the presence of noise, performing equally well in both high and low contrasts of formation resistivity. In thin resistive beds, the new inversion method estimates more accurate resistivities than standard commercial deconvolution software. We also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately [Formula: see text] of CPU time on a desktop computer. In addition to 2D parametric spatial distributions of electrical resistivity, the new inversion method provides a qualitative indicator of the uncertainty of estimated parameters based on the estimator’s covariance matrix. The uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfit lies within the measurement error (noise).

Gravity modeling for crustal-scale models of rifted continental margins using a constrained 3D inversion method

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. G25-G39 ◽  
Author(s):  
Meixia Geng ◽  
J. Kim Welford ◽  
Colin G. Farquharson ◽  
Xiangyun Hu
Keyword(s):  
Weighting Function ◽  
Gravity Data ◽  
A Priori ◽  
Probabilistic Approach ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Continental Margins ◽  
Linear Equality Constraints ◽  
Boundary Information ◽  
Regional Gravity

We have developed a new constrained inversion method that is based on a probabilistic approach for resolving crustal structure from regional gravity data. The smoothness of estimated structures is included in the inversion by using a model covariance matrix, and the sparse boundary information obtained from seismic data is incorporated in the inversion by using linear equality constraints. Moreover, constraints on the average anomalous densities expected for different crustal layers are applied instead of using a depth-weighting function. Bathymetric data and sediment thicknesses are included in the inversion by using an a priori model. Using the proposed method, model structures with sharp boundaries can be obtained while the existing boundary information and sparse seismic constraints are honored. We determine through a synthetic example and a real-world example that the proposed constrained inversion method is a valid tool for studying crustal-scale structures.

The 4-D microgravity method for waterflood surveillance: A model study for the Prudhoe Bay reservoir, Alaska

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 78-87 ◽  
Author(s):  
Jennifer L. Hare ◽  
John F. Ferguson ◽  
Carlos L. V. Aiken ◽  
Jerry L. Brady
Keyword(s):  
Total Mass ◽  
Least Squares Method ◽  
Gravity Data ◽  
Water Injection ◽  
Gravity Modeling ◽  
Inversion Method ◽  
Model Parameters ◽  
Worst Case ◽  
Inverse Models ◽  
Prudhoe Bay

Forward and inverse gravity modeling is carried out on a suite of reservoir simulations of a proposed water injection in the Prudhoe Bay reservoir, Alaska. A novel surveillance technique is developed in which surface gravity observations are used to monitor the progress of a gas cap waterflood in the reservoir at 8200-ft (2500-m) depth. This cost‐effective method requires that high‐precision gravity surveys be repeated over periods of years. Differences in the gravity field with time reflect changes in the reservoir fluid densities. Preliminary field tests at Prudhoe Bay indicates survey accuracy of 5–10 μGal can be achieved for gravity data using a modified Lacoste & Romberg “G” type meter or Scintrex CG-3M combined with the NAVSTAR Global Positioning System (GPS). Forward gravity modeling predicts variations in surface measurements of 100 μGal after 5 years of water injection, and 180–250 μGal after 15 years. We use a constrained least‐squares method to invert synthetic gravity data for subsurface density distributions. The modeling procedure has been formulated and coded to allow testing of the models for sensitivity to gravity sampling patterns, noise types, and various constraints on model parameters such as density, total mass, and moment of inertia. Horizontal‐feature resolution of the waterflood is about 5000 ft (1520 m) for constrained inverse models from synthetic gravity with 5 μGal standard deviation (SD) noise. The inversion method can account for total mass of injected water to within a few percent. Worst‐case scenarios result from inversion of gravity data which are contaminated by high levels (greater than 10–15 μGal SD) of spatially correlated noise, in which case the total mass estimate from inverse models may over or underestimate the mass by 10–20%. The results of the modeling indicate that inversion of time‐lapse gravity data is a viable technique for the monitoring of reservoir gas cap waterfloods.

Amplitude variation with angle inversion using the exact Zoeppritz equations — Theory and methodology

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. N1-N15 ◽  
Author(s):  
Lixia Zhi ◽  
Shuangquan Chen ◽  
Xiang-yang Li
Keyword(s):  
Parameter Extraction ◽  
Tikhonov Regularization Method ◽  
Inversion Method ◽  
Data Sets ◽  
Nonlinear Inversion ◽  
S Wave ◽  
Amplitude Variation ◽  
Highly Nonlinear ◽  
Amplitude Variation With Angle ◽  
Dominant Frequencies

To overcome the weaknesses of conventional prestack amplitude variation with angle inversion based on various linear or quasi-linear approximations, we have conducted a nonlinear inversion method using the exact Zoeppritz matrix (EZAI). However, the inversion using the exact Zoeppritz matrix was highly nonlinear and often unstable, if not properly treated. To tackle these issues, we have used an iteratively regularizing Levenberg-Marquardt scheme (IRLM), which regularizes the inversion problem within an algorithm that minimizes the misfit between the observed and the modeled data at the same time by incorporating the Tikhonov regularization method. As a result, the new EZAI method solved using the IRLM scheme is feasible for seismic data sets with large incidence angles, even up to or beyond the critical angle as well as strong parameter contrasts. Single and multilayered synthetic examples were used to test these features. These tests also showed that EZAI is robust on noisy gathers for parameter extraction and has weak dependence on the initial model. For the influence of inaccurate amplitudes, dominant frequencies, and phase angles, we found that EZAI is less sensitive to the variation in amplitude and phase shifts than to the dominant frequencies. Specifically, the inversion results of EZAI for P- and S-wave velocities and density were reliable if the inaccurate range for the amplitude was within 20% or the angle of the phase shift was no more than 20°. The superiority of EZAI makes it a very promising method for the estimation of subsurface elastic parameters.

Sign in / Sign up

Export Citation Format

Share Document