Anisotropic frequency-dependent spreading of seismic waves from first-arrival vertical seismic profile data analysis

Abstract

A model of first-arrival amplitude decay combining geometric spreading, scattering, and inelastic dissipation is derived from a multioffset, 3D vertical seismic profile data set. Unlike the traditional approaches, the model is formulated in terms of path integrals over the rays and without relying on the quality factor ([Formula: see text]) for rocks. The inversion reveals variations of geometric attenuation (wavefront curvatures and scattering, [Formula: see text]) and the effective attenuation parameter ([Formula: see text]) with depth. Both of these properties are also found to be anisotropic. Scattering and geometric spreading (focusing and defocusing) significantly affect seismic amplitudes at lower frequencies and shallower depths. Statistical analysis of model uncertainties quantitatively measures the significance of these results. The model correctly predicts the observed frequency-dependent first-arrival amplitudes at all frequencies. This and similar models can be applied to other types of waves and should be useful for true-amplitude studies, including inversion, inverse [Formula: see text]-filtering, and amplitude variations with offset analysis. With further development of petrophysical models of internal friction and elastic scattering, attenuation parameters [Formula: see text] and [Formula: see text] should lead to constraints on local heterogeneity and intrinsic physical properties of the rock. These parameters can also be used to build models of the traditional frequency-dependent [Formula: see text] for forward and inverse numerical viscoelastic modeling.