Inline delayed-shot migration in tilted elliptical-cylindrical coordinates

Geophysics ◽  
2010 ◽  
Vol 75 (5) ◽  
pp. S187-S197 ◽  
Author(s):  
Jeffrey Shragge ◽  
Guojian Shan
Keyword(s):  
Impulse Response ◽  
Seismic Data ◽  
Finite Difference Methods ◽  
Computational Cost ◽  
Coordinate Systems ◽  
Geologic Structure ◽  
Data Set ◽  
Implicit Finite Difference ◽  
Wavefield Extrapolation ◽  
Generalized Coordinate

Riemannian wavefield extrapolation, a one-way wave-equation method for propagating seismic data on generalized coordinate systems, is extended to inline delayed-shot migration using 3D tilted elliptical-cylindrical (TEC) coordinate meshes. Compared to Cartesian geometries, TEC coordinates are more conformal to the shape of inline delayed-source impulse response, which allows the bulk of wavefield energy to propagate at angles lower to the extrapolation axis, thus improving global propagation accuracy. When inline coordinate tilt angles are well matched to the inline source ray parameters, the TEC coordinate extension affords accurate propagation of both steep-dip and turning-wave components important for successfully imaging complex geologic structure. Wavefield extrapolation in TEC coordinates is no more complicated than propagation in elliptically anisotropic media and can be handled by existing implicit finite-difference methods. Impulse response tests illustrate the phase accuracy of the method and show that the approach is free of numerical anisotropy. Migration tests from a realistic 3D wide-azimuth synthetic derived from a field Gulf of Mexico data set demonstrate the imaging advantages afforded by the technique, including the improved imaging of steeply dipping salt flanks at a reduced computational cost.

Regularization and datuming of seismic data by weighted, damped least squares

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. U67-U76 ◽  
Author(s):  
Robert J. Ferguson
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Synthetic Data ◽  
Real Data ◽  
Structural Data ◽  
Irregular Sampling ◽  
Data Set ◽  
Near Surface ◽  
Damped Least Squares ◽  
Wavefield Extrapolation

The possibility of improving regularization/datuming of seismic data is investigated by treating wavefield extrapolation as an inversion problem. Weighted, damped least squares is then used to produce the regularized/datumed wavefield. Regularization/datuming is extremely costly because of computing the Hessian, so an efficient approximation is introduced. Approximation is achieved by computing a limited number of diagonals in the operators involved. Real and synthetic data examples demonstrate the utility of this approach. For synthetic data, regularization/datuming is demonstrated for large extrapolation distances using a highly irregular recording array. Without approximation, regularization/datuming returns a regularized wavefield with reduced operator artifacts when compared to a nonregularizing method such as generalized phase shift plus interpolation (PSPI). Approximate regularization/datuming returns a regularized wavefield for approximately two orders of magnitude less in cost; but it is dip limited, though in a controllable way, compared to the full method. The Foothills structural data set, a freely available data set from the Rocky Mountains of Canada, demonstrates application to real data. The data have highly irregular sampling along the shot coordinate, and they suffer from significant near-surface effects. Approximate regularization/datuming returns common receiver data that are superior in appearance compared to conventional datuming.

Prestack imaging of seismic data using Lp iterative reweighted least-squares wavefield extrapolation filters in the frequency-space domain

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. V243-V252
Author(s):  
Wail A. Mousa
Keyword(s):  
Least Squares ◽  
Seismic Data ◽  
Least Squares Method ◽  
Filter Design ◽  
Finite Impulse Response ◽  
Weighted Least Squares ◽  
Data Set ◽  
Frequency Space ◽  
Wavefield Extrapolation ◽  
Iterative Reweighted Least Squares

A stable explicit depth wavefield extrapolation is obtained using [Formula: see text] iterative reweighted least-squares (IRLS) frequency-space ([Formula: see text]-[Formula: see text]) finite-impulse response digital filters. The problem of designing such filters to obtain stable images of challenging seismic data is formulated as an [Formula: see text] IRLS minimization. Prestack depth imaging of the challenging Marmousi model data set was then performed using the explicit depth wavefield extrapolation with the proposed [Formula: see text] IRLS-based algorithm. Considering the extrapolation filter design accuracy, the [Formula: see text] IRLS minimization method resulted in an image with higher quality when compared with the weighted least-squares method. The method can, therefore, be used to design high-accuracy extrapolation filters.

Optimized implicit finite-difference and Fourier finite-difference migration for VTI media

Geophysics ◽  
2009 ◽  
Vol 74 (6) ◽  
pp. WCA189-WCA197 ◽  
Author(s):  
Guojian Shan
Keyword(s):  
Dispersion Relation ◽  
Finite Difference ◽  
Weighted Least Squares ◽  
Taylor Series Expansion ◽  
Relative Dispersion ◽  
Data Set ◽  
Isotropic Media ◽  
Implicit Finite Difference ◽  
Wavefield Extrapolation ◽  
Vti Media

Propagation velocity of seismic waves in heterogeneous VTI media depends not only on spatial location but also on their propagation direction, which leads to a much more complex dispersion relation than in isotropic media. As a result, designing implicit finite-difference (FD) schemes for wavefield extrapolation in anisotropic media through analytic Taylor-series expansion is more difficult. Implicit FD and Fourier finite-difference (FFD) schemes are developed for vertical transversely isotropic (VTI) media based on function fitting. The dispersion relation of VTI media is approximated with a rational function and its coefficients are estimated by weighted least-squares optimization. Because these coefficients are functions of Thomsen anisotropy parameters ([Formula: see text] and [Formula: see text]) and vary laterally in heterogeneous VTI media, they are calculated before wavefield extrapolation and stored in a table. Implicit FD and FFD schemes for VTI media are almost the same as for isotropic media, except that coefficients are looked up in a precalculated table. Impulse responses and relative dispersion-relation error show that accuracy of the FD scheme for VTI media is similar to its counterpart in isotropic media. Application to a synthetic data set showed that implicit FD and FFD can handle laterally varying VTI media.

Prestack wave-equation depth migration in elliptical coordinates

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. S169-S175 ◽  
Author(s):  
Jeff Shragge ◽  
Guojian Shan
Keyword(s):  
Coordinate Systems ◽  
Data Set ◽  
Depth Migration ◽  
Prestack Migration ◽  
Oblate Spheroidal ◽  
2D Imaging ◽  
Elliptical Coordinates ◽  
The One ◽  
Wavefield Extrapolation ◽  
Root Operator

We extend Riemannian wavefield extrapolation (RWE) to prestack migration using 2D elliptical-coordinate systems. The corresponding 2D elliptical extrapolation wavenumber introduces only an isotropic slowness model stretch to the single-square-root operator. This enables the use of existing Cartesian finite-difference extrapolators for propagating wavefields on elliptical meshes. A poststack migration example illustrates advantages of elliptical coordinates for imaging turning waves. A 2D imaging test using a velocity-benchmark data set demonstrates that the RWE prestack migration algorithm generates high-quality prestack migration images that are more accurate than those generated by Cartesian operators of the equivalent accuracy. Even in situations in which RWE geometries are used, a high-order implementation of the one-way extrapolator operator is required for accurate propagation and imaging. Elliptical-cylindrical and oblate-spheroidal geometries are potential extensions of the analytical approach to 3D RWE-coordinate systems.

Riemannian wavefield extrapolation: Nonorthogonal coordinate systems

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. T11-T21 ◽  
Author(s):  
Jeffrey Chilver Shragge
Keyword(s):  
Wave Propagation ◽  
Spherical Geometry ◽  
Coordinate Systems ◽  
Propagation Theory ◽  
Mesh Smoothing ◽  
Computational Overhead ◽  
Wavefield Extrapolation ◽  
2D And 3D ◽  
Smoothing Procedure ◽  
Generalized Coordinate

Riemannian wavefield extrapolation (RWE) is used to model one-way wave propagation on generalized coordinate meshes. Previous RWE implementations assume that coordinate systems are defined by either orthogonal or semiorthogonal geometry. This restriction leads to situations where coordinate meshes suffer from problematic bunching and singularities. Nonorthogonal RWE is a procedure that avoids many of these problems by posing wavefield extrapolation on smooth, but generally nonorthogonal and singularity-free, coordinate meshes. The resulting extrapolation operators include additional terms that describe nonorthogonal propagation. These extra degrees of complexity, however, are offset by smoother coefficients that are more accurately implemented in one-way extrapolation operators. Remaining coordinate mesh singularities are then eliminated using a differential mesh smoothing procedure. Analytic extrapolation examples and the numerical calculation of 2D and 3D Green’s functions for cylindrical and near-spherical geometry validate the nonorthogonal RWE propagation theory. Results from 2D benchmark testing suggest that the computational overhead associated with the RWE approach is roughly 35% greater than Cartesian-based extrapolation.

Azimuth moveout for 3-D prestack imaging

Geophysics ◽  
1998 ◽  
Vol 63 (2) ◽  
pp. 574-588 ◽  
Author(s):  
Biondo Biondi ◽  
Sergey Fomel ◽  
Nizar Chemingui
Keyword(s):  
Integral Operator ◽  
Impulse Response ◽  
Constant Velocity ◽  
Computational Cost ◽  
Data Set ◽  
Depth Migration ◽  
Prestack Migration ◽  
Migration Operator ◽  
Time Space ◽  
Strong Curvature

We introduce a new partial prestack‐migration operator called “azimuth moveout” (AMO) that rotates the azimuth and modifies the offset of 3-D prestack data. Followed by partial stacking, AMO can reduce the computational cost of 3-D prestack imaging. We have successfully applied AMO to the partial stacking of a 3-D marine data set over a range of offsets and azimuths. When AMO is included in the partial‐stacking procedure, high‐frequency steeply dipping energy is better preserved than when conventional partial‐stacking methodologies are used. Because the test data set requires 3-D prestack depth migration to handle strong lateral variations in velocity, the results of our tests support the applicability of AMO to prestack depth‐imaging problems. AMO is a partial prestack‐migration operator defined by chaining a 3-D prestack imaging operator with a 3-D prestack modeling operator. The analytical expression for the AMO impulse response is derived by chaining constant‐velocity DMO with its inverse. Equivalently, it can be derived by chaining constant‐velocity prestack migration and modeling. Because 3-D prestack data are typically irregularly sampled in the surface coordinates, AMO is naturally applied as an integral operator in the time‐space domain. The AMO impulse response is a skewed saddle surface in the time‐midpoint space. Its shape depends on the amount of azimuth rotation and offset continuation to be applied to the data. The shape of the AMO saddle is velocity independent, whereas its spatial aperture is dependent on the minimum velocity. When the azimuth rotation is small (⩽20°), the AMO impulse response is compact, and its application as an integral operator is inexpensive. Implementing AMO as an integral operator is not straightforward because the AMO saddle may have a strong curvature when it is expressed in the midpoint coordinates. An appropriate transformation of the midpoint axes to regularize the AMO saddle leads to an effective implementation.

Stochastic nonlinear inversion of seismic data for the estimation of petroelastic properties using the ensemble smoother and data reparameterization

Geophysics ◽  
2018 ◽  
Vol 83 (3) ◽  
pp. M25-M39 ◽  
Author(s):  
Mingliang Liu ◽  
Dario Grana
Keyword(s):  
Seismic Data ◽  
Reservoir Characterization ◽  
Computational Cost ◽  
Rock Physics ◽  
Inversion Method ◽  
Nonlinear Inversion ◽  
Seismic Velocities ◽  
Reservoir Properties ◽  
Data Set ◽  
Ensemble Smoother

We have developed a new stochastic nonlinear inversion method for seismic reservoir characterization studies to jointly estimate elastic and petrophysical properties and to quantify their uncertainty. Our method aims to estimate multiple reservoir realizations of the entire set of reservoir properties, including seismic velocities, density, porosity, mineralogy, and saturation, by iteratively updating the initial ensemble of models based on the mismatch between their seismic response and the measured seismic data. The initial models are generated using geostatistical methods and the geophysical forward operators include rock-physics relations and a seismic forward model. The optimization is achieved using an iterative ensemble-based algorithm, namely, the ensemble smoother with multiple data assimilation, in which each iteration is based on a Bayesian updating step. The advantages of the proposed method are that it can be applied to nonlinear inverse problems and it can provide an ensemble of solutions from which we can quantify the uncertainty of the model properties of interest. To reduce the computational cost of the inversion, we perform the optimization in a lower dimensional data space reparameterized by singular value decomposition. The proposed methodology is validated on a synthetic case in which the set of petroelastic properties is recovered with satisfactory accuracy. Then, we applied the inversion method to a real seismic data set from the Norne field in the Norwegian Sea.

Angle-domain common-image gathers in generalized coordinates

Geophysics ◽  
2009 ◽  
Vol 74 (3) ◽  
pp. S47-S56 ◽  
Author(s):  
Jeff Shragge
Keyword(s):  
Large Angle ◽  
Synthetic Data ◽  
Opening Angle ◽  
Coordinate Systems ◽  
Data Set ◽  
Enhanced Sensitivity ◽  
Cartesian Geometry ◽  
Definition Of ◽  
Spatially Varying ◽  
Generalized Coordinate

The theory of angle-domain common-image gathers (ADCIGs) is extended to migrations performed in generalized 2D coordinate systems. I have developed an expression linking the definition of reflection opening angle to differential traveltime operators and spatially varying weights derived from the non-Cartesian geometry. Generalized-coordinate ADCIGs can be calculated directly using Radon-based offset-to-angle approaches for coordinate systems satisfying the Cauchy-Riemann differentiability criteria. The canonical examples of tilted-Cartesian, polar, and elliptical coordinates can be used to illustrate the ADCIG theory. I have compared analytically and numerically generated image volumes for a set of elliptically shaped reflectors. Experiments with a synthetic data set showed that elliptical-coordinate ADCIGs better resolve the reflection opening angles of steeply dipping structure, relative to conventional Cartesian image volumes, because of improved large-angle propagation and enhanced sensitivity to steep structural dips afforded by coordinate system transformations.

scholarly journals A Computational Protocol Combining DFT and Cheminformatics for Prediction of pH-Dependent Redox Potentials

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 3978
Author(s):  
Rocco Peter Fornari ◽  
Piotr de Silva
Keyword(s):  
Organic Molecules ◽  
Ph Value ◽  
Computational Cost ◽  
Legendre Transform ◽  
Good Prediction ◽  
Redox Potentials ◽  
Free Energies ◽  
Hybrid Functional ◽  
Data Set ◽  
State Changes

Discovering new materials for energy storage requires reliable and efficient protocols for predicting key properties of unknown compounds. In the context of the search for new organic electrolytes for redox flow batteries, we present and validate a robust procedure to calculate the redox potentials of organic molecules at any pH value, using widely available quantum chemistry and cheminformatics methods. Using a consistent experimental data set for validation, we explore and compare a few different methods for calculating reaction free energies, the treatment of solvation, and the effect of pH on redox potentials. We find that the B3LYP hybrid functional with the COSMO solvation method, in conjunction with thermal contributions evaluated from BLYP gas-phase harmonic frequencies, yields a good prediction of pH = 0 redox potentials at a moderate computational cost. To predict how the potentials are affected by pH, we propose an improved version of the Alberty-Legendre transform that allows the construction of a more realistic Pourbaix diagram by taking into account how the protonation state changes with pH.

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