Seismic repeatability, normalized rms, and predictability

Abstract

Time-lapse data are increasingly used to study production-induced changes in the seismic response of a reservoir as part of a reservoir management program. However, residual differences in the repeated time-lapse data that are independent of changes in the subsurface geology impact the effectiveness of the method. These differences depend on many factors such as signature control, streamer positioning, and recording fidelity differences between the two surveys. Such factors may be regarded as contributing to the time-lapse noise and any effort designed to improve the time-lapse signal-to-noise ratio must address the quantifiable repeatability of the seismic survey. Although there are counter-examples (for example, Johnston et al., 2000), minimization of the acquisition footprint and repeatability of the geometry to equalize residual footprints in both surveys are considered important. This has been a key objective in the development of point receiver acquisition systems. In this study, which develops the analysis from Kragh and Christie (2001), we examine the use of two repeatability metrics in assessing the similarity of two sets of repeat 2D lines acquired with a marine point receiver system. In one repeat set, no streamer positioning control was in use; in the other repeat set, positioning differences were minimized using the streamer positioning control. There does not appear to be a standard measure of repeatability, defined as a metric, to quantify the likeness of two traces. One commonly used metric is the normalized rms difference of the two traces, at and bt within a given window t1-t2: the rms of the difference divided by the average rms of the inputs, and expressed as a percentage: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[NRMS = \frac{200 {\times} RMS(a\_{t} {-} b\_{t})}{RMS(a\_{t}) {+} RMS(b\_{t})}\] \end{document} where the rms operator is defined as: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[RMS(x\_{t}) = \sqrt{\frac{{\Sigma}^{t\_{2}}\_{t\_{1}}(x_{t})^{2}}{N}}\] \end{document} and N is the number of samples in the interval t1-t2. The values of nrms are not intuitive and …