An integrated approach to lithologic inversion—Part I: Theory

For the complex problem of lithologic inversion a new formalism is proposed, using a spatial distribution of seismic velocities ([Formula: see text]) and densities (ρ) as input. At each subsurface grid point, the inversion result consists of the most likely lithotype (gas, sand, shale, etc.) together with its related litho parameters (frame strength, porosity, etc.). The inversion method is based on the Bayesian theory of parameter estimation, allowing specification of inaccuracies in the input and the incorporation of geological knowledge. An important advantage of the proposed inversion method is that for each practical situation the necessary accuracy of [Formula: see text], [Formula: see text] and ρ can be predetermined to distinguish between specific lithotypes or to estimate a specific litho parameter with a prespecified accuracy. For instance, inversion results show that water saturation can only be estimated for an unrealistic accurate input. On the other hand, for the estimation of porosities it is generally sufficient to have compressional velocities available with a realistic accuracy.

Approximation of B-Spline Geometries With Lower Degree Representations

Exchange of data between geometric modeling systems of different inherent capabilities frequently requires approximate conversion of high degree, piecewise, polynomial curves and surface patches to lower degree representations. The objective of this work is to provide reliable methods for the approximation of high-order B-spline curves and surface patches by low-order B-spline representations. Our method guarantees a prespecified accuracy at all isoparametric points of the curve and patch, a critical feature for accurate exchange of data.