ANALYSIS OF REFLECTION TRAVEL-TIMES IN 3-D TRANSVERSELY ISOTROPIC HETEROGENEOUS MEDIA

A two-point ray-tracing technique for rays reflected from irregular, b ut smooth, interfaces in 3-D transversely isotropic heterogeneous medi a is developed. The method is based on Chebyshev parameterization of c urved segments of the reflected rays, of the reflectors, and of the ve locity and anisotropy distributions in the model. Chebyshev approximat ion also can describe the reflection traveltime surfaces to compress t raveltime data by replacing them with coefficients of the correspondin g Chebyshev series. The advantage of the proposed parameterization is that it gives traveltime as an explicit function of the model paramete rs. This explicitly provides the Frechet derivatives of the traveltime with respect to the model parameters. The Frechet derivatives are use d in two ways. First, a two-term Taylor series is constructed to relat e variations in the model parameters to the corresponding perturbation s in the traveltimes. This makes it possible, based on the results of a single ray tracing in a relatively simple model, to predict travelti mes for a range of more complicated models, without any additional ray tracing. Second, singular-value decomposition of the Frechet matrix d etermines the influence of various model parameters on common-source a nd common-midpoint traveltimes. The singular-value analysis shows that common-source traveltimes depend mainly on the reflector position and shape. The common-midpoint traveltimes also contain additional inform ation about lateral velocity heterogeneity and anisotropy. However, bo th of these parameters affect the traveltimes in similar ways and so u sually cannot be determined separately.