Angle-dependent reflectivity estimation

David E. Lumley

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ABSTRACT

I derive an analytical least-squares inverse solution to the problem of estimating angle-dependent reflectivity from prestack seismic reflection data. The reflection coefficients and the reflection angles are estimated simultaneously directly from the prestack seismic reflection data, without a priori knowledge of geologic structure or dip. I define a forward theory which relates angle-dependent reflection data to a generalized reflectivity model combining elements of Zoeppritz plane wave reflection and Rayleigh-Sommerfeld diffraction. The l₂ inverse solutions for reflectivity and reflection angle are then derived by a standard application of stationary phase and Gauss-Newton gradient optimization, and naturally incorporate l₂ compensation for limited data acquisition aperture, source and receiver directivity, geometric spreading, transmission loss, and high-frequency intrinsic Q attenuation. Uncompensated reflectivity amplitude errors include coherent noise (e.g., multiples, surface waves, etc.), steep-dip operator spatial aliasing, migration velocity error, and data mute zones. The method is validated on a synthetic data example in the presence of dips up to 30 degrees, and should prove to be a useful component of seismic prestack amplitude analysis (AVO) and impedance inversion.