Applying accurate gradients of seismic wave reflection coefficients (SWRC) to the inversion of seismic wave velocities

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Through solving the Zoeppritz’s partial derivative equations, we have obtained accurate partial derivatives of reflected coefficients of seismic wave with respect to P- and S-wave velocities. With those partial derivatives, a multi-angle inversion is developed for seismic wave velocities. Numerical examples of different formation models show that if the number of iterations goes over 10, the relative error of inversion results is less than 1%, whether or not there is interference among the reflection waves. When we only have the reflected seismograms of P-wave, and only invert for velocities of P-wave, the multi-angle inversion is able to obtain a high computation precision. When we have the reflected seismograms of both P-wave and VS-wave, and simultaneously invert for the velocities of P-wave and VS-wave, the computation precisions of VS-wave velocities improves gradually with the increase of the number of angles, but the computation precision of P-wave velocities becomes worse. No matter whether the reflected seismic waves from the different reflection interface are coherent or non-coherent, this method is able to achieve a higher computation precision. Because it is based on the accurate solution of the gradient of SWRCs without any additional restriction, the multi-angle inversion method can be applied to seismic inversion of total angles. By removing the difficulties caused by simplified Zoeppritz formulas that the conventional AVO technology struggles with, the multi-angle inversion method extended the application range of AVO technology and improved the computation precision and speed of inversion of seismic wave velocities.