Inversion of seismic data in the τ‐p plane

Abstract

Seismic data can be transformed to the domain of intercept time and ray parameter without the artifical suppression of high frequencies caused by finite temporal and spatial sampling. These data can be analyzed to derive velocity‐depth information using the loci of the arrivals in the τ‐p plane. For limited source‐receiver offsets, the parameters of the best single ellipse approximating the true τ‐p reflection trajectory can be used to derive an approximate velocity‐depth function. We show that this is equivalent to Dix's (1955) hyperbolic traveltime approximation. When large aspect ratios are involved, the path formed by the postcritical reflection and refraction arrivals can be used directly to derive the velocity function. We consider both of these inversion methods as the initial step required to implement an inversion procedure that utilizes both pre‐ and postcritical reflection and refraction arrivals by an exact "normal moveout" correction in τ‐p. This approach is computationally efficient and is the equivalent to a ray traced normal moveout correction in X‐T.