Estimation Of Viscoelastic Paramenters From Zero-Offset Vsp Data

Abstract

There exist different expressions for seismic attenuation. We want to compare some of these models by doing parameter estimation on a zero-offset VSP dataset. The attenuation models are the Kolsky-Futterman model (Kolsky. 1956; Futtctman, 1962), the standard linear solid model (Ben-Menahcm and Sin&. 198 I L the power law (Strick. 1967), Azimi’s second and third law (Azimi et al., 196X), the Cole-Colt model (Colt and Cole. 1941). Miiller’s (1981) model and Kjartansson’s (1979) model. In the modeling scheme we have used the geometric ray approximation (Ursin and Arntsen. 1985). for point-source. vertical wave propagation in a 1-D viscoclastic medium with plane wave reflection coefticients. Amundsen and Mittet (1994) used the same modeling algorithm to invert for complex velocities in a set of layers using zero-offset VSP-data. They did inversion with respect to each frequency component of the complex velocity. Our approach is to assume a formula for the complex velocity and then invert for the parameters in a few homogeneous layers. The inversion algorithm has been tested on a VSP-datasct from a well in the North Sea for different attenuation models. By minimizing the error energy we estimate the parameters in the different models.