Frequency response modelling of seismic waves using finite difference time domain with phase sensitive detection (TD-PSD)

Abstract

S U M M A R YThis paper describes an efficient approach for computing the frequency response of seismic waves propagating in 2-and 3-D earth models within which the magnitude and phase are required at many locations. The approach consists of running an explicit finite difference time domain (TD) code with a time harmonic source out to steady-state. The magnitudes and phases at locations in the model are computed using phase sensitive detection (PSD). PSD does not require storage of time-series (unlike a fast Fourier transform), reducing its memory requirements. Additionally, the response from multiple sources can be obtained from a single finite difference run by encoding each source with a different frequency. For 2-D models with many sources, this time domain phase sensitive detection (TD-PSD) approach has a higher arithmetic complexity than direct solution of the finite difference frequency domain (FD) equations using nested dissection re-ordering (FD-ND). The storage requirements for 2-D finite difference TD-PSD are lower than FD-ND. For 3-D finite difference models, TD-PSD has significantly lower arithmetic complexity and storage requirements than FD-ND, and therefore, may prove useful for computing the frequency response of large 3-D earth models.

Multi‐source least‐squares reverse time migration

“…In this case, the above integration should be carried out from T to 2T where T = 2π dω (Nihei and Li, 2006). DigitizingP (ω s , g) yields a supergather containing the blended full wavefields.…”

“…Nihei and Li (2006) proposed to use a time-domain finite-difference method to obtain the single frequency response of a point source in a velocity model. Compared to the conventional frequency domain method, their method has significantly lower arithmetic complexity and storage requirements in the 3D case.…”

“…Following Nihei and Li (2006) and Sirgue et al (2008), the single frequency response of a velocity model v(x) for a shot at s can be modelled with the time-domain finitedifference method by solving the equation…”

Seismic Waves - Research and Analysis

“…The last possible approach to compute monochromatic wavefields is to perform the modeling in the time domain and extract the frequency-domain solution, either by discrete Fourier transform in the loop over the time steps (Sirgue et al, 2008) or by phase-sensitivity detection once the steady-state regime has been reached (Nihei & Li, 2007). An arbitrary number of frequencies can be extracted within the loop over time steps at a minimal extra cost.…”

Least-squares reverse time migration of marine data with frequency-selection encoding

“…The frequency-selection encoding strategy can also be applied to least-squares reverse time migration with the time-domain single frequency simulation method proposed by Nihei and Li (2007), where the time-domain simulations are performed with a single-frequency source instead of the conventional broadband source, so that the single-frequency response of the medium to a point source can be extracted from the wavefield after it reaches steady state. Compared to the conventional frequencydomain director solver, their method has significantly lower arithmetic complexity and storage requirements in the 3D case (Nihei and Li, 2007;Sirgue et al, 2008).…”