Seismic Data Conditioning and Inversion with Bayesian Methods and Dynamic Time-Warping

Seismic studies are carried out with the aim of delineating resolved images of the subsurface, however as the wave propagates through the earth, energy and resolution diminish. Amplitude attenuates and velocity disperses due to earth’s viscoelasticity resulting in distorted images of the subsurface stratigraphic layers and geological structures. Deconvolution (statistical or deterministic) is typically applied to correct for this distortion. The process for amplitude compensation is unstable at greater depths (or traveltime) due to the exponential function of time and frequency that boost ambient noise masking lower frequency signals. Absorption compensation is posed as an inverse problem and stabilized with the L1-norm deterministically and stochastically with two sparsity-promoting hierarchical prior distributions (Normal-Jeffreys and automatic relevance determination). The Normal-Jeffreys prior computes a sparse model that estimates observational noise variance which regularizes the solution.
Moreover, Amplitude variation with offset (AVO) processing workflows are carefully designed to preserve relative amplitude between offset gathers in preparation for reservoir characterization studies. But in the event where these traces are not aligned or production effects from a time-lapse causes time-shifts, offset traces can be re-adjusted with a dynamic time-warping (DTW) algorithm which is superior to linear time-shifts such as windowed-cross correlation. DTW re-alignment reveal the better correlation of elastic attributes when compared with upscaled well-logs. Seismically-derived elastic properties alone are not useful to a reservoir scientist. Often interest lies in rock-physics models that can quantify elastic property variation with effective pressure at all porosities. Proposed moduli-velocity model in conjunction with Gassmann model is utilized to invert for dynamic petrophysical properties (water saturation and pressure changes). A computationally-efficient mixture density neural network (MDN) which finds optimal parameters of a Gaussian mixture model is utilized for the 3D petrophysical analysis of the Norne field time-lapse dataset. The saturation inversion volume shows a decrease from the survey 2003 to the survey 2006.