| The Perfectly Matched Layer(PML)is an efficient absorbing technique for numer-ical wave simulation.The complex frequency-shifted PML(CFS-PML)introduces two additional parameters in the stretching function to make the absorption frequency depen-dent.This frequency dependent absorption can help to suppress converted evanescent waves from near grazing incident waves,but does not efficiently absorb low frequency waves below the cutoff frequency.To absorbing both the evanescent waves and low fre-quency waves,the double-pole CFS-PML having two poles in the coordinate stretching function was developed in computational electromagnetism.Several studies have in-vestigated the performance of the double-pole CFS-PML for seismic wave simulations against narrowband seismic wavelet and did not find significant difference comparing to the CFS-PML.Another difficulty to apply the double-pole CFS-PML for real problems is that a practical strategy to set optimal parameter values has not be established.In this work,we study the performance of the double-pole CFS-PML for broadband seismic wave simulation.We find that when the maximum frequency to minimum frequency ratio is large,say more than 16,the CFS-PML will either fail to suppress the converted evanescent waves for grazing incident waves,or produce visible low frequency reflec-tion,depending on the parameter value.In contrast,the double-pole CFS-PML can simultaneously suppress the converted evanescent waves and avoid low frequency re-flections with proper parameter values.We analyze the different roles of the double-pole CFS-PML parameters and propose optimal selections of these parameters.Numerical tests show that the double-pole CFS-PML with the optimal parameters can generate the most satisfactory results for broadband seismic wave simulations.Configurations with point sources in a media which varies in only two dimensions(2D media)are referred as '2.5D problem'.To solve 2.5D problems,the full 3D finite difference method seismic wave simulation can be rather time-consuming.In order to reduce the computer memory and computational time,one can use several alternative methods to generate synthetic wavefield without using true 3D simulation.One cat-egory of methods are often referred as asymptotic filtering methods.These methods apply a filter to correct amplitudes and phases of 2D seismic waves to obtain approx-imate 3D solutions.Filtering methods are only strictly valid for simple homogeneous acoustic media in the far-field.They may be inaccurate at short range,or in complex media which leads to multiple,overlapping reflected phases.To overcome the draw-backs of filtering methods,one can apply another category of methods which are usu-ally called 2.5D modelling.2.5D modelling methods apply the Fourier transformation in the out-of-plane direction(y-axis)to transform the 3D governing equation to a series of 2D equations with different wavenumbers in y direction.By taking inverse Fourier transformation,the 2D solutions can reconstruct the 3D solutions.To our knowledge,although finite difference time domain 2.5D modelling are commonly considered as time-saving compared to full 3D modelling,there is no systematical research on its computational complexity.In fact,the computational complexity of 2.5D modelling depends on how many wavenumbers in y direction we have to calculate.We propose a principle to judge whether 2.5D modelling can save computational time or not.We propose a new method,which is named as slice model 3D simulation to solve 2.5D problem efficiently.We prove that it is possible to simulate seismic wave in a very thin model to obtain accurate wavefield.The slice model 3D simulation is accurate while it needs less computer memory and computational time than conventional 3D simulation.We find the optimal CFS-PML parameters to absorb the near-gazing incident waves for 3D slice model method.We prove the accuracy of the slice model 3D simulation by applying it in complex media. |
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