A nonlinear signal detector for enhancement of noisy seismic record sections

Abstract

In an area of complicated structure a stacked record section is likely to be characterized by a low signal‐to‐noise ratio, even after substantial velocity analysis and other processing. The interpreter identifies signals showing phase coherence across many traces at physically allowable velocities and compiles them into a line drawing. We have developed a nonlinear filter designed to mimic this process, which passes only signals showing spatial coherence and having slowness within an allowed range. In this algorithm, called the “SSD filter,” overlapping M-trace windows are converted into a p-τ representation, obtained by multiplying the stack along the relevant slant line by the smoothed semblance. The results from all windows are composited in the p-τ domain, then retransformed into x-t. The principal tunable parameter is the width M of the correlation window, adjusted to provide an output which agrees well with the event picks made by an experienced interpreter on a test panel of data. The method was developed to enable production of cleaned‐up sections from the often noisy stacks produced in deep crustal seismic studies. An example from the COCORP Southern Appalachian profile illustrates how removal of incoherent noise from the stacked section substantially enhances the quality of the migrated section.

Recognition and reconstruction of coherent energy with application to deep seismic reflection data

“…The local τ -p (intercept time-apparent dip or slowness) transform has already been used several times to extract laterally coherent signals (see, e.g., Harlan et al, 1984, andKong et al, 1985).…”

“…Following Kong et al (1985), the seismic section φ(x, t)i s divided into N partly overlapping subsections φ n (x, t)o fK traces each, which are transformed to the τ -p domain:…”

“…Among these are the skeletonization method (Le and Nyland, 1990;Lu and Cheng, 1990), the statistical method of Hansen et al (1988), methods using local τ -p analyses (Harlan et al, 1984;Kong et al, 1985), and spatial-prediction filtering (Hornbostel, 1991;Abma and Claerbout, 1995).…”

“…The methods actually computing the local τ -p transforms use it either as a focusing measure (Harlan et al, 1984) or in combination with semblance (Kong et al, 1985). The first method uses the τ -p transform to obtain the desired amplitude distributions of noise and signals needed for the recognition and extraction of samples containing the highest percentage of signal, whereas in the second method semblance-weighted slant stacks are used to emphasize and extract laterally coherent signals.…”

“…Fortunately, it is not difficult to adapt the recognition technique to estimate missing data. We propose two methods: (1) the application of the reconstruction method of Kong et al (1985) using semblance-weighted slant stacks after recognition, and (2) direct application of the recognition technique in the τ -p domain. Unfortunately, these methods again require the assumption of locally linear events.…”