Transmission effects of localized variations of Earth's visco-acoustic parameters

Visco-Acoustic Modeling

For this study, several seismic experiments were simulated using many different geologic visco-acoustic models. The models are parametrized by three fields for velocity, density, and Q-factor (i.e. the Q-factor for the peak frequency in the source wavelet used). Direct wave-equation modeling was conducted using time-domain finite differencing of the linearized wave equation for Newtonian fluids (Mavko et al., 2003). Finite differencing was explicit in time, and the spatial derivatives were computed in the Fourier domain to attain better accuracy.

A problem with using the linearized wave equation for Newtonian fluids is the acausality, which was observed as negative time shifts in some of our test cases (see Figure 1). Those time shifts, however, are extremely small and can be observed only after dense resampling, which is unreasonable considering the accuracy of our numerical modeling. For this study, only the time shifts of the maximum absolute amplitude are considered.

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Figure 1. Distortions of a wavelet after passing an absorption anomaly. The amplitude drop as a function of Q-factor is accompanied by a wavelet stretch and a shift of the zero crossing. [CR]

Transmission effects of localized variations of Earth's visco-acoustic parameters