An Improved and Novel Approach for Frequency Domain Forward Modeling of GPR Data Using the Finite Difference Staggered Grid Technique

2021 ◽  
Author(s):  
Mrinal Kanti Layek ◽  
Probal Sengupta
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Forward Modeling ◽  
Staggered Grid ◽  
Novel Approach ◽  
Grid Technique

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

Solid Earth ◽  
2018 ◽  
Vol 9 (6) ◽  
pp. 1277-1298
Author(s):  
Xiaoyu Zhang ◽  
Dong Zhang ◽  
Qiong Chen ◽  
Yan Yang
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Forward Modeling ◽  
Perfectly Matched Layer ◽  
Second Order ◽  
Staggered Grid ◽  
Scalar Wave ◽  
First Order ◽  
Second Order Wave Equation ◽  
Boundary Absorption

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.

Forward Modeling of GPR Data by Unstaggered Finite Difference Frequency Domain (FDFD) Method: An Approach towards an Appropriate Numerical Scheme

2019 ◽  
Vol 24 (3) ◽  
pp. 487-496
Author(s):  
Mrinal Kanti Layek ◽  
Probal Sengupta
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Homogeneous Model ◽  
Fdtd Method ◽  
Forward Modeling ◽  
Difference Frequency ◽  
Complex Frequency ◽  
Numerical Schemes ◽  
Finite Difference Frequency Domain ◽  
Ground Penetrating

Forward modeling of ground penetrating radar (GPR) is an important part to the inversion/modeling of the observed data. The aim of this study is to establish specific numerical schemes for forward modeling of GPR data by finite difference frequency domain (FDFD) method which were originally developed for seismic or finite difference time domain (FDTD) method. A total number of six modified and improved FDFD techniques have been used to discretize the two-dimensional (2D) transverse electric (TE)-mode scalar wave equation in order to find the suitable method for this. These techniques include five-point classical to nine-point mixed unstaggered-grid configurations. The numerical schemes for three unsplit perfectly matched layer (PML) for nine-point mixed unstaggered-grid configurations are also presented. The applicability of these techniques is tested by using the underground models of relative permittivity and conductivity for the two cases of homogeneous and 2-cross models. GPR shot gather data for these two models are also produced for this study. The relative reflection errors of the numerical schemes are also estimated for the homogeneous model to comprehend the appropriate method for the modeling. The algorithm for complex-frequency shifted PML (CFSPML) gives the least error in case of the forward modeling of the GPR data.

Cosine-modulated window function-based staggered-grid finite-difference forward modeling

2017 ◽  
Vol 14 (1) ◽  
pp. 115-124 ◽  
Author(s):  
Jian Wang ◽  
Xiao-Hong Meng ◽  
Hong Liu ◽  
Wan-Qiu Zheng ◽  
Sheng Gui
Keyword(s):  
Finite Difference ◽  
Forward Modeling ◽  
Window Function ◽  
Staggered Grid

scholarly journals A hybrid finite-difference and integral-equation method for modeling and inversion of marine controlled-source electromagnetic data

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. E323-E336 ◽  
Author(s):  
Daeung Yoon ◽  
Michael S. Zhdanov ◽  
Johan Mattsson ◽  
Hongzhu Cai ◽  
Alexander Gribenko
Keyword(s):  
Integral Equation ◽  
Finite Difference ◽  
Electric Fields ◽  
Integral Equation Method ◽  
Numerical Differentiation ◽  
Forward Modeling ◽  
Staggered Grid ◽  
3D Inversion ◽  
Controlled Source ◽  
And Inversion

One of the major problems in the modeling and inversion of marine controlled-source electromagnetic (CSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward-modeling algorithms should be powerful and fast enough to be suitable for repeated use in hundreds of iterations of the inversion and for multiple transmitter/receiver positions. To this end, we have developed a novel 3D modeling and inversion approach, which combines the advantages of the finite-difference (FD) and integral-equation (IE) methods. In the framework of this approach, we have solved Maxwell’s equations for anomalous electric fields using the FD approximation on a staggered grid. Once the unknown electric fields in the computation domain of the FD method are computed, the electric and magnetic fields at the receivers are calculated using the IE method with the corresponding Green’s tensor for the background conductivity model. This approach makes it possible to compute the fields at the receivers accurately without the need of very fine FD discretization in the vicinity of the receivers and sources and without the need for numerical differentiation and interpolation. We have also developed an algorithm for 3D inversion based on the hybrid FD-IE method. In the case of the marine CSEM problem with multiple transmitters and receivers, the forward modeling and the Fréchet derivative calculations are very time consuming and require using large memory to store the intermediate results. To overcome those problems, we have applied the moving sensitivity domain approach to our inversion. A case study for the 3D inversion of towed streamer EM data collected by PGS over the Troll field in the North Sea demonstrated the effectiveness of the developed hybrid method.

GPU Elastic Modeling Using an Optimal Staggered-Grid Finite-Difference Operator

2018 ◽  
Vol 26 (02) ◽  
pp. 1850005 ◽  
Author(s):  
Jian Wang ◽  
Xiaohong Meng ◽  
Hong Liu ◽  
Wanqiu Zheng ◽  
Zhiwei Liu
Keyword(s):  
Finite Difference ◽  
Difference Operator ◽  
Waveform Inversion ◽  
Forward Modeling ◽  
Dominant Frequency ◽  
Window Function ◽  
Numerical Dispersion ◽  
Staggered Grid ◽  
Reverse Time ◽  
Time Migration

Staggered-grid finite-difference forward modeling in the time domain has been widely used in reverse time migration and full waveform inversion because of its low memory cost and ease to implementation on GPU, however, high dominant frequency of wavelet and big grid interval could result in significant numerical dispersion. To suppress numerical dispersion, in this paper, we first derive a new weighted binomial window function (WBWF) for staggered-grid finite-difference, and two new parameters are included in this new window function. Then we analyze different characteristics of the main and side lobes of the amplitude response under different parameters and accuracy of the numerical solution between the WBWF method and some other optimum methods which denotes our new method can drive a better finite difference operator. Finally, we perform elastic wave numerical forward modeling which denotes that our method is more efficient than other optimum methods without extra computing costs.

scholarly journals Second-order Scalar Wave Field Modeling with First-order Perfectly Matched Layer

2018 ◽  
Author(s):  
Xiaoyu Zhang ◽  
Dong Zhang ◽  
Qiong Chen ◽  
Yan Yang
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Forward Modeling ◽  
Perfectly Matched Layer ◽  
Second Order ◽  
Staggered Grid ◽  
Scalar Wave ◽  
First Order ◽  
Second Order Wave Equation ◽  
Boundary Absorption

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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