Nonstationarity: patching

Nonstationarity: patching

Jon Claerbout

There are many reasons for cutting data planes or image planes into overlapping pieces (patches), operating on the pieces, and then putting them back together again, as depicted in Figure 1. The earth's dip varies with lateral location and depth. The dip spectrum and spatial spectrum thus also varies. The dip itself is the essence of almost all earth mapping, and its spectrum plays an important role in the estimation any earth properties. In statistical estimation theory, the word to describe changing statistical properties is ``nonstationary''.

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Figure 1. Decomposing a wall of information into windows (also called patches). Left is an example of a 2-D space input to module patch. Right shows a close-up of the output (top left corner).

We begin this chapter with basic patching concepts along with supporting utility code. The language of this chapter, patch, overlap, window, wall, is two-dimensional, but it may as well be three-dimensional, cube, subcube, brick, or one-dimensional, line, interval. We sometimes use the language of windows on a wall. But since we usually want to have overlapping windows, better imagery would be to say we assemble a quilt from patches.

The codes are designed to work in any number of dimensions. After developing the infrastructure, we examine some two-dimensional, time- and space-variable applications: adaptive steep-dip rejection, noise reduction by prediction, and segregation of signals and noises.

Nonstationarity: patching