DMO after logarithmic stretching

Matthias Schwab

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ABSTRACT

DMO stacks seismic offset data by honoring the reflector dips. This method can be an attractive compromise between computationally expensive prestack migration and inaccurate NMO. The DMO process implemented here is accurate for any constant velocity medium. The algorithm is velocity independent in the sense that it does not assume a certain velocity value. The DMO step prepares the data for an NMO step. The subsequent NMO facilitates an improved velocity analysis and stack, since it does not require a flat reflector assumption. Logarithmic stretching and Fourier transformation along the time axis reduce the 3D DMO operator to a midpoint and frequency invariant 2D operator. The duality properties of the Fourier transformation and the band limitation of our signal allow an efficient representation of the logarithmically scaled traces. In this article I present the kinematics of the basic DMO operator. I outline a program based on logarithmic resampling in temporal frequency, followed by 2D convolution over constant-frequency planes. The proposed DMO algorithm is highly parallel and should lend itself to a very efficient implementation.