ESTIMATION OF PHASE VELOCITIES AND Q-FACTORS FROM ZERO-OFFSET, VERTICAL SEISMIC PROFILE DATA

In seismic processing, we face the problem of characterizing the effec t of anelastic attenuation on the seismic signal during propagation. T o solve this problem, approximate physical properties of the porous fl uid-filled rock are needed. We give a strategy for estimating effectiv e parameters governing absorption and dispersion of waves in viscoelas tic media by inverting zero-offset vertical seismic profiling (VSP) da ta acquired in a medium with plane horizontal layers. The VSP data are filtered such that all energy except for the direct downgoing wave an d the primary reflected wave from each interface is zeroed. This proce dure requires a model with layer thicknesses greater than a minimum li mit. A stack of thin layers must be replaced by a layer with average p hysical properties and with thickness exceeding the required minimum. The model parameter vector is partitioned into two vectors. The first contains the frequency-dependent complex propagation velocity in each layer, and is evaluated over the frequency band where the signal-to-no ise ratio is acceptable. In the second vector, the geophone-to-formati on coupling factors, which are assumed to be frequency-independent, ar e gathered. It is straightforward to determine both the frequency-depe ndent phase velocities and the frequency-dependent quality (Q-) factor s from the frequency-dependent propagation velocities. We assume that layer boundaries and layer densities can be obtained from well logs. W e give the equations for a simplified forward-modeling scheme and the equations for the solution of the nonlinear inverse problem. The algor ithm is applied to both synthetic and real data. Inversion of syntheti c data shows that the phase velocities can be satisfactorily estimated , and that Q-factors below approximately 50 are well-resolved, even fo r large errors in the geophone-to-formation coupling factors. The esti mated phase velocities from the real data behave fairly stable as a fu nction of frequency. The results for the quality factors are less conc lusive, but the low Q-factors may be of correct size.