Chapter 2: PS imaging operators

Chapter 2 described three operators for imaging of converted-wave data. The first operator, PS Normal Moveout, a non-hyperbolic moveout equation for converted waves. This equation is in terms of the effective velocity, and the P-to-S velocity ratio. However, for offset-to-depth ratio less than 0.6, the moveout of converted waves can be approximated by the hyperbolic moveout equation.

The second operator, PS-DMO, is an operator in the frequency wavenumber log-stretch domain. Since this operator is stationary in the time log-stretch domain, the use of FFT in both directions is possible. Additionally, the f-k log-stretch PS-DMO operator is computationally efficient. PS-DMO is accurate kinematicly and also handles the amplitudes for steeply dipping reflections more accurately than existing PS-DMO operators.

The first two operators transform the data into an image that is in the time ($\tau$) domain. Both PS-NMO and PS-DMO have several limitations, PS-NMO is not a valid transformation in geologically complex areas. Also, PS-DMO uses an approximation for the CMP to CCP correction that depends on $\gamma$, which is a difficult parameter to determine from the data. Therefore, the appropiate operator is the wave-equation-based migration operator, since the dimensions of the model space are depth, image-midpoint, and image-offset, that as seen in the Chapters 3, and 5, this domain is the most appropiate to image PS data.