An Interblock Conductivity Scheme for Finite Difference Models of Steady Unsaturated Flow in Heterogeneous Media

1995 ◽  
Vol 31 (11) ◽  
pp. 2883-2889 ◽  
Author(s):  
A. J. Desbarats
Keyword(s):  
Finite Difference ◽  
Heterogeneous Media ◽  
Unsaturated Flow

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

Optimum split-step Fourier 3D depth migration: Developments and practical aspects

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S167-S175 ◽  
Author(s):  
Jianfeng Zhang ◽  
Linong Liu
Keyword(s):  
Finite Difference ◽  
Heterogeneous Media ◽  
Fourier Transforms ◽  
Computational Cost ◽  
Fourier Method ◽  
Approximate Algorithm ◽  
Wide Angle ◽  
Data Set ◽  
Depth Migration ◽  
Varying Coefficients

We present an efficient scheme for depth extrapolation of wide-angle 3D wavefields in laterally heterogeneous media. The scheme improves the so-called optimum split-step Fourier method by introducing a frequency-independent cascaded operator with spatially varying coefficients. The developments improve the approximation of the optimum split-step Fourier cascaded operator to the exact phase-shift operator of a varying velocity in the presence of strong lateral velocity variations, and they naturally lead to frequency-dependent varying-step depth extrapolations that reduce computational cost significantly. The resulting scheme can be implemented alternatively in spatial and wavenumber domains using fast Fourier transforms (FFTs). The accuracy of the first-order approximate algorithm is similar to that of the second-order optimum split-step Fourier method in modeling wide-angle propagation through strong, laterally varying media. Similar to the optimum split-step Fourier method, the scheme is superior to methods such as the generalized screen and Fourier finite difference. We demonstrate the scheme’s accuracy by comparing it with 3D two-way finite-difference modeling. Comparisons with the 3D prestack Kirchhoff depth migration of a real 3D data set demonstrate the practical application of the proposed method.

3D finite-difference dynamic-rupture modeling along nonplanar faults

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. SM123-SM137 ◽  
Author(s):  
Víctor M. Cruz-Atienza ◽  
Jean Virieux ◽  
Hideo Aochi
Keyword(s):  
Finite Difference ◽  
Boundary Conditions ◽  
Heterogeneous Media ◽  
Slip Rate ◽  
Quantitative Agreement ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Weight Functions ◽  
Dynamic Rupture ◽  
Fault Surface

Proper understanding of seismic emissions associated with the growth of complexly shaped microearthquake networks and larger-scale nonplanar fault ruptures, both in arbitrarily heterogeneous media, requires accurate modeling of the underlying dynamic processes. We present a new 3D dynamic-rupture, finite-difference model called the finite-difference, fault-element (FDFE) method; it simulates the dynamic rupture of nonplanar faults subjected to regional loads in complex media. FDFE is based on a 3D methodology for applying dynamic-rupture boundary conditions along the fault surface. The fault is discretized by a set of parallelepiped fault elements in which specific boundary conditions are applied. These conditions are applied to the stress tensor, once transformed into a local fault referenceframe. Numerically determined weight functions multiplying particle velocities around each element allow accurate estimates of fault kinematic parameters (i.e., slip and slip rate) independent of faulting mechanism. Assuming a Coulomb-like slip-weakening friction law, a parametric study suggests that the FDFE method converges toward a unique solution, provided that the cohesive zone behind the rupture front is well resolved (i.e., four or more elements inside this zone). Solutions are free of relevant numerical artifacts for grid sizes smaller than approximately [Formula: see text]. Results yielded by the FDFE approach are in good quantitative agreement with those obtained by a semianalytical boundary integral method along planar and nonplanar parabola-shaped faults. The FDFE method thus provides quantitative, accurate results for spontaneous-rupture simulations on intricate fault geometries.

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