Laplace Domain Modeling of Power Components for Transient Converter-Grid Interaction Studies

We have developed a Laplace-domain full-waveform inversion technique based on a time-domain finite-difference modeling algorithm for efficient 3D inversions. Theoretically, the Laplace-domain Green’s function multiplied by a constant can be obtained regardless of the frequency content in the time-domain source wavelet. Therefore, we can use low-frequency sources and large grids for efficient modeling in the time domain. We Laplace-transform time-domain seismograms to the Laplace domain and calculate the residuals in the Laplace domain. Then, we back-propagate the Laplace-domain residuals in the time domain using a predefined time-domain source wavelet with the amplitude of the residuals. The back-propagated wavefields are transformed to the Laplace domain again to update the velocity model. The inversion results are long-wavelength velocity models on large grids similar to those obtained by the original approach based on Laplace-domain modeling. Inversion examples with 2D Gulf of Mexico field data revealed that the method yielded long-wavelength velocity models comparable with the results of the original Laplace-domain inversion methods. A 3D SEG/EAGE salt model example revealed that the 3D Laplace-domain inversion based on time-domain modeling method can be more efficient than the inversion based on Laplace-domain modeling using an iterative linear system solver.

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Efficient Laplace-domain modeling using an axis transformation technique

10.1190/segam2012-0565.1 ◽

2012 ◽

Author(s):

Wansoo Ha ◽

Changsoo Shin ◽

Taeyoung Ha

Keyword(s):

Domain Modeling ◽

Transformation Technique ◽

Laplace Domain

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Dispersion analysis of an average-derivative optimal scheme for Laplace-domain scalar wave equation

Geophysics ◽

10.1190/geo2013-0230.1 ◽

2014 ◽

Vol 79 (2) ◽

pp. T37-T42 ◽

Cited By ~ 7

Author(s):

Jing-Bo Chen

Keyword(s):

Wave Equation ◽

Dispersion Analysis ◽

Domain Modeling ◽

Scalar Wave ◽

Laplace Domain ◽

Optimal Scheme ◽

Point Scheme ◽

Sampling Intervals ◽

Grid Points ◽

Average Derivative

Laplace-domain modeling is an important foundation of Laplace-domain full-waveform inversion. However, dispersion analysis for Laplace-domain numerical schemes has not been completely established. This hampers the construction and optimization of Laplace-domain modeling schemes. By defining a pseudowavelength as a scaled skin depth, I establish a method for Laplace-domain numerical dispersion analysis that is parallel to its frequency-domain counterpart. This method is then applied to an average-derivative nine-point scheme for Laplace-domain scalar wave equation. Within the relative error of 1%, the Laplace-domain average-derivative optimal scheme requires four grid points per smallest pseudowavelength, whereas the classic five-point scheme requires 13 grid points per smallest pseudowavelength for general directional sampling intervals. The average-derivative optimal scheme is more accurate than the classic five-point scheme for the same sampling intervals. By using much smaller sampling intervals, the classic five-point scheme can approach the accuracy of the average-derivative optimal scheme, but the corresponding cost is much higher in terms of storage requirement and computational time.

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Efficient Laplace-domain modeling and inversion using an axis transformation technique

Geophysics ◽

10.1190/geo2011-0424.1 ◽

2012 ◽

Vol 77 (4) ◽

pp. R141-R148 ◽

Cited By ~ 4

Author(s):

Wansoo Ha ◽

Changsoo Shin

Keyword(s):

Wave Propagation ◽

Computation Time ◽

Dispersion Analysis ◽

Domain Modeling ◽

Memory Usage ◽

Regular Grid ◽

Transformation Technique ◽

Laplace Domain ◽

Domain Inversion ◽

And Inversion

We tested an axis-transformation technique for modeling wave propagation in the Laplace domain using a finite-difference method. This technique enables us to use small grids near the surface and large grids at depth. Accordingly, we can reduce the number of grids and attain computational efficiency in modeling and inversion in the Laplace domain. We used a dispersion analysis and comparisons between modeled wavefields obtained on the regular and transformed axes. We demonstrated in a synthetic Laplace-domain inversion technique shows that this method is efficient and yields a result comparable to that of a Laplace-domain inversion using a regular grid. In a synthetic inversion example, the memory usage reduced to less than 33%, and the computation time reduced to 39% of those required for the regular grid case using a logarithmic transformation function.

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