Velocity and Q from reflection seismic data

This study has resulted in the discovery of an exact method for the theoretical formulation of the effects of intrinsic damping where the attenuation coefficient, alpha(nu), is an arbitrary function of the frequency nu. Absorption-dispersion pairs are computed using numerical Hilbert transformations; approximate analytical expressions that require the selection of arbitrary constants and cutoff frequencies are no longer necessary. The inverse problem is also investigated using singular value decomposition (SVD). The sparse matrices encountered in the acquisition of conventional reflection seismology data result in a system of linear equations of the form AX = B, with A the design matrix, X the solution vector, and B the data vector. A technique to improve the sparsity pattern prior to decomposition is described. From an application of the Q = 2 delta tau/pi delta W equation using reference reflections from shallower reflectors, crystalline rocks in South Carolina over the depth interval from about 5 to 10 km yield values of Q in the range Q = 250 to 300. Nonstandard recording geometries and vibroseis recording procedures are suggested to minimize matrix sparseness and increase the useable frequency bandwidth between zero and Nyquist. The direct detection of body wave dispersion by conventional vibroseis techniques may be useful to distinguish between those crustal volumes that are potentially seismogenic and those that are not. Such differences may be due to variations in fracture density and therefore water content in the crust.