2D modeling and inversion of gravity data using density contrast varying with depth and source–basement geometry described by the Fourier series

Geophysics ◽  
2003 ◽  
Vol 68 (6) ◽  
pp. 1909-1916 ◽  
Author(s):  
Juan García‐Abdeslem
Keyword(s):  
Fourier Series ◽  
Gravity Data ◽  
Forward Modeling ◽  
Density Contrast ◽  
Nonlinear Inversion ◽  
Bouguer Gravity ◽  
Data Set ◽  
Cubic Polynomial ◽  
Broad Variety ◽  
And Inversion

A method is developed for 2D forward modeling and nonlinear inversion of gravity data. The forward modeling calculates the gravity anomaly caused by a 2D source body with an assumed depth‐dependent density contrast given by a cubic polynomial. The source body is bounded at depth by a smooth, curvilinear surface given by the Fourier series, which represents the basement. The weighted and damped discrete nonlinear inverse method presented here can invert gravity data to infer the geometry of the source body. The use of the Fourier series to define the basement geometry allows the interpreter to reconstruct a broad variety of geometries for the geologic structures using a small number of free parameters. Both modeling and inversion methods are illustrated with examples using field gravity data across the San Jacinto graben in southern California and across the Sayula basin in Jalisco, Mexico. The inversion of the San Jacinto graben residual Bouguer gravity data yields results compatible with those from previous interpretations of the same data set, suggesting that this geologic structure accommodates about 2.5 km of sediments. The inversion of the residual Bouguer gravity data across the Sayula basin suggests a maximum of 1‐km‐thick sedimentary infill.

Frequency‐domain acoustic‐wave modeling and inversion of crosshole data: Part II—Inversion method, synthetic experiments and real‐data results

Geophysics ◽  
1995 ◽  
Vol 60 (3) ◽  
pp. 796-809 ◽  
Author(s):  
Zhong‐Min Song ◽  
Paul R. Williamson ◽  
R. Gerhard Pratt
Keyword(s):  
Frequency Domain ◽  
Real Data ◽  
Forward Modeling ◽  
Two Dimensions ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Data Set ◽  
Wave Inversion ◽  
Full Wave ◽  
And Inversion

In full‐wave inversion of seismic data in complex media it is desirable to use finite differences or finite elements for the forward modeling, but such methods are still prohibitively expensive when implemented in 3-D. Full‐wave 2-D inversion schemes are of limited utility even in 2-D media because they do not model 3-D dynamics correctly. Many seismic experiments effectively assume that the geology varies in two dimensions only but generate 3-D (point source) wavefields; that is, they are “two‐and‐one‐half‐dimensional” (2.5-D), and this configuration can be exploited to model 3-D propagation efficiently in such media. We propose a frequency domain full‐wave inversion algorithm which uses a 2.5-D finite difference forward modeling method. The calculated seismogram can be compared directly with real data, which allows the inversion to be iterated. We use a descents‐related method to minimize a least‐squares measure of the wavefield mismatch at the receivers. The acute nonlinearity caused by phase‐wrapping, which corresponds to time‐domain cycle‐skipping, is avoided by the strategy of either starting the inversion using a low frequency component of the data or constructing a starting model using traveltime tomography. The inversion proceeds by stages at successively higher frequencies across the observed bandwidth. The frequency domain is particularly efficient for crosshole configurations and also allows easy incorporation of attenuation, via complex velocities, in both forward modeling and inversion. This also requires the introduction of complex source amplitudes into the inversion as additional unknowns. Synthetic studies show that the iterative scheme enables us to achieve the theoretical maximum resolution for the velocity reconstruction and that strongly attenuative zones can be recovered with reasonable accuracy. Preliminary results from the application of the method to a real data set are also encouraging.

Fast iterative equivalent-layer technique for gravity data processing: A method grounded on excess mass constraint

Geophysics ◽  
2017 ◽  
Vol 82 (4) ◽  
pp. G57-G69 ◽  
Author(s):  
Fillipe C. L. Siqueira ◽  
Vanderlei C. Oliveira Jr. ◽  
Valéria C. F. Barbosa
Keyword(s):  
Mass Distribution ◽  
Least Squares Method ◽  
Gravity Data ◽  
Vertical Component ◽  
Forward Modeling ◽  
Computational Effort ◽  
Data Set ◽  
Gravity Station ◽  
Layer Technique ◽  
Equivalent Layer

We have developed a new iterative scheme for processing gravity data using a fast equivalent-layer technique. This scheme estimates a 2D mass distribution on a fictitious layer located below the observation surface and with finite horizontal dimensions composed by a set of point masses, one directly beneath each gravity station. Our method starts from an initial mass distribution that is proportional to the observed gravity data. Iteratively, our approach updates the mass distribution by adding mass corrections that are proportional to the gravity residuals. At each iteration, the computation of the residual is accomplished by the forward modeling of the vertical component of the gravitational attraction produced by all point masses setting up the equivalent layer. Our method is grounded on the excess of mass and on the positive correlation between the observed gravity data and the masses on the equivalent layer. Mathematically, the algorithm is formulated as an iterative least-squares method that requires neither matrix multiplications nor the solution of linear systems, leading to the processing of large data sets. The time spent on the forward modeling accounts for much of the total computation time, but this modeling demands a small computational effort. We numerically prove the stability of our method by comparing our solution with the one obtained via the classic equivalent-layer technique with the zeroth-order Tikhonov regularization. After estimating the mass distribution, we obtain a desired processed data by multiplying the matrix of the Green’s functions associated with the desired processing by the estimated mass distribution. We have applied the proposed method to interpolate, calculate the horizontal components, and continue gravity data upward (or downward). Testing on field data from the Vinton salt dome, Louisiana, USA, confirms the potential of our approach in processing large gravity data set over on undulating surface.

2.5-D forward modeling and inversion of time domain IP method

2017 ◽  
Vol 70 (0) ◽  
pp. 69-79
Author(s):  
Hideki Mizunaga ◽  
Kiyotaka Ishinaga
Keyword(s):  
Time Domain ◽  
Forward Modeling ◽  
And Inversion

scholarly journals Development of a semi-parametric PAR (Photosynthetically Active Radiation) partitioning model for the United States, version 1.0

2014 ◽  
Vol 7 (5) ◽  
pp. 2477-2484 ◽  
Author(s):  
J. C. Kathilankal ◽  
T. L. O'Halloran ◽  
A. Schmidt ◽  
C. V. Hanson ◽  
B. E. Law
Keyword(s):  
United States ◽  
Elevation Angle ◽  
Model Performance ◽  
Diffuse Radiation ◽  
The United States ◽  
Polynomial Model ◽  
Coefficient Of Determination ◽  
Data Set ◽  
Cubic Polynomial ◽  
Solar Elevation Angle

Abstract. A semi-parametric PAR diffuse radiation model was developed using commonly measured climatic variables from 108 site-years of data from 17 AmeriFlux sites. The model has a logistic form and improves upon previous efforts using a larger data set and physically viable climate variables as predictors, including relative humidity, clearness index, surface albedo and solar elevation angle. Model performance was evaluated by comparison with a simple cubic polynomial model developed for the PAR spectral range. The logistic model outperformed the polynomial model with an improved coefficient of determination and slope relative to measured data (logistic: R2 = 0.76; slope = 0.76; cubic: R2 = 0.73; slope = 0.72), making this the most robust PAR-partitioning model for the United States currently available.

Enabling isotropic reflectivity modeling and inversion in anisotropic media

2021 ◽  
Vol 40 (4) ◽  
pp. 267-276
Author(s):  
Peter Mesdag ◽  
Leonardo Quevedo ◽  
Cătălin Tănase
Keyword(s):  
Synthetic Data ◽  
Anisotropic Media ◽  
Forward Modeling ◽  
Seismic Inversion ◽  
Stratified Medium ◽  
Effective Parameters ◽  
Elastic Parameters ◽  
Pp Wave ◽  
Anisotropic Elastic ◽  
And Inversion

Exploration and development of unconventional reservoirs, where fractures and in-situ stresses play a key role, call for improved characterization workflows. Here, we expand on a previously proposed method that makes use of standard isotropic modeling and inversion techniques in anisotropic media. Based on approximations for PP-wave reflection coefficients in orthorhombic media, we build a set of transforms that map the isotropic elastic parameters used in prestack inversion into effective anisotropic elastic parameters. When used in isotropic forward modeling and inversion, these effective parameters accurately mimic the anisotropic reflectivity behavior of the seismic data, thus closing the loop between well-log data and seismic inversion results in the anisotropic case. We show that modeling and inversion of orthorhombic anisotropic media can be achieved by superimposing effective elastic parameters describing the behavior of a horizontally stratified medium and a set of parallel vertical fractures. The process of sequential forward modeling and postinversion analysis is exemplified using synthetic data.

Inversion and uncertainty estimation of gravity data using simulated annealing: An application over Lake Vostok, East Antarctica

Geophysics ◽  
2005 ◽  
Vol 70 (1) ◽  
pp. J1-J12 ◽  
Author(s):  
Lopamudra Roy ◽  
Mrinal K. Sen ◽  
Donald D. Blankenship ◽  
Paul L. Stoffa ◽  
Thomas G. Richter
Keyword(s):  
Simulated Annealing ◽  
Gravity Data ◽  
A Priori ◽  
Model Space ◽  
Uncertainty Estimation ◽  
East Antarctica ◽  
Airborne Gravity ◽  
Model Parameters ◽  
Data Set ◽  
Lake Vostok

Interpretation of gravity data warrants uncertainty estimation because of its inherent nonuniqueness. Although the uncertainties in model parameters cannot be completely reduced, they can aid in the meaningful interpretation of results. Here we have employed a simulated annealing (SA)–based technique in the inversion of gravity data to derive multilayered earth models consisting of two and three dimensional bodies. In our approach, we assume that the density contrast is known, and we solve for the coordinates or shapes of the causative bodies, resulting in a nonlinear inverse problem. We attempt to sample the model space extensively so as to estimate several equally likely models. We then use all the models sampled by SA to construct an approximate, marginal posterior probability density function (PPD) in model space and several orders of moments. The correlation matrix clearly shows the interdependence of different model parameters and the corresponding trade-offs. Such correlation plots are used to study the effect of a priori information in reducing the uncertainty in the solutions. We also investigate the use of derivative information to obtain better depth resolution and to reduce underlying uncertainties. We applied the technique on two synthetic data sets and an airborne-gravity data set collected over Lake Vostok, East Antarctica, for which a priori constraints were derived from available seismic and radar profiles. The inversion results produced depths of the lake in the survey area along with the thickness of sediments. The resulting uncertainties are interpreted in terms of the experimental geometry and data error.

Three-dimensional magnetotelluric axial anisotropic forward modeling and inversion

2018 ◽  
Vol 153 ◽  
pp. 75-89 ◽  
Author(s):  
Hui Cao ◽  
Kunpeng Wang ◽  
Tao Wang ◽  
Boguang Hua
Keyword(s):  
Three Dimensional ◽  
Forward Modeling ◽  
And Inversion
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