Method of Multivariate Seismic Tomography Based on Stochastic Analysis of Input Data Reliability

Abstract

Seismic tomography is one of the main tools for obtaining a depth velocity model. Its result largely determines the estimated geometry of oil and gas reservoir. Tomography is a deterministic procedure and does not provide an opportunity to assess the reliability of the results. However, in fact these results directly affect the subsequent economic decisions. For this reason, the aim of the current work is to develop a method of multivariate tomography which allows to determine the reliability of the results. The paper considers several factors of multivariance. Factor of input data quality is generally considered and stochastic averages tool is proposed for estimating input data reliability. Typically, input data estimation involves calculating supergathers. Usage of equivalent weights for supergathers accumulation means that all gathers have an equivalent quality but in practice this is far from the truth due to various regular noises. Replacing weights by random ones is equivalent to filtering with random kernel. These means assigning a random confidence levels to input gathers. This allows to generate many realizations of the input data for inverse problem. Also incorporation of tomography smoothness parameters variation to inverse problem is proposed. Such approach differs from traditional ones where these parameters are set by a specialist based on purely personal ideas. All together this allows to generate many realizations of depth velocity model and estimate its reliability. The proposed method of multivariate tomography doesn't use the known statistical distributions of the input data errors, thus, it is the most general and realistic. Its result can be utilized in the assessment of economic risks.