Frequency response modelling of seismic waves using finite difference time domain with phase sensitive detection (TD–PSD) |
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Authors: | Kurt T Nihei Xiaoye Li |
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Institution: | Earth Sciences Division, Lawrence Berkeley National Laboratory;now at Chevron ETC, 6001;Bollinger Canyon Rd., San Ramon, CA 94583, USA. E-mail: Computational Research Division, Lawrence Berkeley National Laboratory, 1;Cyclotron Rd., MS 50F-1650, Berkeley, CA 94720, USA |
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Abstract: | This 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. |
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Keywords: | finite-difference methods numerical techniques seismic modelling |
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