P-wave impedance, S-wave impedance and density from linear AVO inversion: Application to VSP data from Alberta
Faranak Mahmoudian, Gary F. Margrave
In AVO (amplitude variation with offset) inversion the amplitudes of compressional and converted shear surface seismic data are inverted both separately and jointly to provide three parameters - the physical properties of compressional impedance, shear impedance, and density. Physical property information obtained from seismic data can be useful in imaging subsurface structure, either by directly detecting changes in the subsurface, or as an aid in the interpretation of seismic reflection data. The approximated Zoeppritz equation is least-squares fitted to the amplitude of all traces of a common midpoint gather (PP data) and a common converted point gather (PS data) at each depth sample to obtain the bandlimited reflectivity of the three parameter traces. Then, the reflectivity traces are integrated to obtain the three parameter traces, with the missing low-frequency components provided from well log information.
The three parameters, especially the density, cannot be accurately resolved from AVO data due to the ill-posed nature of the inverse problem. The damped SVD (singular value decomposition) method has been utilized to stabilize the AVO inversion. The examination of the resolution matrix, after adding a damping factor, demonstrates that the shear velocity contributes more than the compressional velocity to improving the density estimate for the study area data, namely VSP data from a Red Deer coal bed methane site.
In the joint inversion, the converted shear wave data dominates in estimating the shear impedance and density and appears promising in providing shear impedance and density estimates from the PS inversion alone. In addition, in the joint inversion, the compressional data dominates in estimating the compressional impedance and provides a good estimate for the compressional impedance in the PP inversion alone.