Abstract: Seismic acoustic impedance linear inversion algorithm is studied. Based on Cauchy criteria, the regularized sparse inversion can be made by using pre-conditional conjugate gradient algorithm (PCGA) in simultaneously iterative inversion of reflection factor and wavelet. For solving the inversion problem by PCGA, it is better to solve the original linear system rather than the normalized system for the good matrix condition number. The initial wavelet estimation and acoustic impedance interpretation methods are presented. The real data verification shows that the wavelet, reflection factor and acoustic impedance given by PCGA are more accurate, quicker convergent and value stable than the existing direct sparse inversion method.

Key words: seismic acoustic impedance, Cauchy criteria, iterative inversion, pre-conditional conjugate gradient