implemented layer by layer (Robinson, 1979;Bano, 1996). These phase inverse Q-filter algorithms can be used to eliminate the phase distortion caused by velocity dispersion and are stable without conditions (Robinson, 1979 and1982;Bickel and Natarajan, 1985) but the amplitude effect due to energy attenuation was neglected. Moreover, the amplitude compensation operator is an exponential function of frequency and traveltime. As a result, for deeper layers, the inverse Q-filter amplifies the noise level causing instability in the seismic band and undesirable artifacts in the solution (Wang, 2002;Zhang, 2006). Wang (2002) proposed a gain-limited inverse Q-filter amplitude compensation operator. This algorithm controls the inverse Q-filter noise from different depths by choosing a Q-dependent time-variant frequency threshold. However, using empirical formulas, it is difficult to approach the true time-variant threshold frequency.In this paper, we present a stable wavefield continuation approach to inverse Q-filtering assuming the subsurface media to be a layered-earth Q model. For each individual

Implicit finite-difference (IFD) extrapolation operator and plane wave migration in TTI media are studied in this paper. Compared to isotropic and VTI media, the dispersion relation of TTI media is much more complicated. It is difficult to get the explicit expression of the dispersion relations. It needs no longer only a symmetrical even function like isotropic and VTI media but also an odd function to express the dispersion relations. We design TTI medium IFD wave-field extrapolation operator and solve operator coefficients by nonlinear optimization method. We combine the theory of plane wave migration in isotropic media with the IFD operator in TTI media and extend plane wave migration to TTI media. Comparing the dispersion curves and migration impulse response of the IFD extrapolation operator with the theoretical solution verifies the high accuracy of the operator. Synthetic P-wave data from full elastic TTI equation modeling followed by polarization analysis verifies the accuracy and effectiveness of the method.

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