Staggered‐Grid High‐Order Finite‐Difference Method in Elastic Wave Simulation with Variable Grids and Local Time‐Steps

Huang, Chao; Dong, Liangguo

doi:10.1002/cjg2.1457

Cited by 19 publications

(10 citation statements)

References 14 publications

(7 reference statements)

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“…In transition zone, points in smaller step domain related to derivative calculation should be the same distance to central points with the relevant points in coarser step domain. In transition zone, modified spatial derivative difference scheme is [7]…”

Section: Finite Difference Scheme Of Gird Variation Methods With Pml Bmentioning

confidence: 99%

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A Finite‐Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

Sun¹,

Yin²

2011

Chinese J of Geophysics

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Heterogeneous media is a kind of multi‐scale media. The scale of the fracture reservoir could reach up to millimeter. Simulating a fractured carbonate model with finite‐difference method is calling for the same scale of sample steps. A finite‐difference method with high power of grid steps variation is presented here. Spatial and temporal sampling steps can be optimized according to material properties and model geometry. The ratio of grid steps could reach up to hundreds or more. We improve the method of numerical grid division in order to add more flexibility and efficiency to finite‐difference method with grid variation. The numerical results support that the method can describe heterogeneous media on millimeter scale accurately with efficiency, and the property made the method suitable for modeling cavity or fractured carbonate reservoirs.

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Section: Finite Difference Scheme Of Gird Variation Methods With Pml Bmentioning

confidence: 99%

“…Temporal steps could be changed along with spatial steps [4] . Ten-fold grid variation method could be seen in resent literature [7] .…”

Section: Introductionmentioning

confidence: 99%

A Finite‐Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

Sun¹,

Yin²

2011

Chinese J of Geophysics

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“…However, it is hard to determine which of the two schemes is more accurate and efficient. Although the SG scheme has sometimes been regarded as more precise than the CG scheme (Huang and Dong, 2009), there is also some theoretical and experimental proof in the literature that does not support this proposition. Moczo et al (2011) compared the accuracy of the different finite-difference schemes with respect to the P -wave to S-wave speed ratio using theoretical analysis and numerical experiments.…”

Section: Introductionmentioning

confidence: 99%

Second-order scalar wave field modeling with a first-order perfectly matched layer

Zhang

Chen

et al. 2018

Solid Earth

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Abstract. The forward modeling of a scalar wave equation plays an important role in the numerical geophysical computations. The finite-difference algorithm in the form of a second-order wave equation is one of the commonly used forward numerical algorithms. This algorithm is simple and is easy to implement based on the conventional grid. In order to ensure the accuracy of the calculation, absorption layers should be introduced around the computational area to suppress the wave reflection caused by the artificial boundary. For boundary absorption conditions, a perfectly matched layer is one of the most effective algorithms. However, the traditional perfectly matched layer algorithm is calculated using a staggered grid based on the first-order wave equation, which is difficult to directly integrate into a conventional-grid finite-difference algorithm based on the second-order wave equation. Although a perfectly matched layer algorithm based on the second-order equation can be derived, the formula is rather complex and intermediate variables need to be introduced, which makes it hard to implement. In this paper, we present a simple and efficient algorithm to match the variables at the boundaries between the computational area and the absorbing boundary area. This new boundary-matched method can integrate the traditional staggered-grid perfectly matched layer algorithm and the conventional-grid finite-difference algorithm without formula transformations, and it can ensure the accuracy of finite-difference forward modeling in the computational area. In order to verify the validity of our method, we used several models to carry out numerical simulation experiments. The comparison between the simulation results of our new boundary-matched algorithm and other boundary absorption algorithms shows that our proposed method suppresses the reflection of the artificial boundaries better and has a higher computational efficiency.

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“…However, due to using a nonuniform grid, these methods rely on either wavefield interpolation (i.e. upsampling) or varying weighting coefficients using Taylor expansion (Huang C and Dong LG, 2009). We know that Taylor expansion has high accuracy only when the variables are close to the expansion point; thus, the finite‐difference method using Taylor expansion would encounter numerical dispersions when using a nonuniform grid within a thick transition zone between a coarse grid and a fine grid.…”

Section: Introductionmentioning

confidence: 99%

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

Zhang¹,

Yao²

2017

Earth and Planetary Physics

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Numerical solver using a uniform grid is popular due to its simplicity and low computational cost, but would be unfeasible in the presence of tiny structures in large‐scale media. It is necessary to use a nonuniform grid, where upsampling the wavefield from the coarse grid to the fine grid is essential for reducing artifacts. In this paper, we suggest a local refinement scheme using the Fourier interpolation, which is superior to traditional interpolation methods since it is theoretically exact if the input wavefield is band limited. Traditional interpolation methods would fail at high upsampling ratios (say 50); in contrast, our scheme still works well in the same situations, and the upsampling ratio can be any positive integer. A high upsampling ratio allows us to greatly reduce the computational burden and memory demand in the presence of tiny structures and large‐scale models, especially for 3D cases.

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Staggered‐Grid High‐Order Finite‐Difference Method in Elastic Wave Simulation with Variable Grids and Local Time‐Steps

Cited by 19 publications

References 14 publications

A Finite‐Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

A Finite‐Difference Scheme Based on PML Boundary Condition with High Power Grid Step Variation

Second-order scalar wave field modeling with a first-order perfectly matched layer

Exact local refinement using Fourier interpolation for nonuniform-grid modeling

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