In filtering applications, input seismic data are commonly divided into smaller subsets which we refer to as patches (which are also referred to as windows, gates, and other things). The data are assumed to be approximately stationary within a patch, but due to practical limits on patch size, it may not be possible to avoid nonstationarity and poor results in some patches. This is often true where the data are strongly curved (for spatial filtering) or noisy.
An alternative to independent patches is nonstationary filtering. SEP has applied nonstationary filtering to numerous problems in recent reports, including groundroll suppression Brown et al. (1999), multiple suppression Clapp and Brown (1999), tomography regularization Clapp and Biondi (1998), deconvolution Claerbout (1997), and interpolation Crawley (1999); Fomel (1999). Nonstationary PEFs do not have patch-size limitations, so we may shrink patches down to arbitrary size and shape. To control the potentially huge null space, we regularize the set of filters to ensure that PEFs located at similar data coordinates have similar coefficients. This implements the assumption that dips in the data may change everywhere, but do so smoothly. Besides being small, these new patches are fundamentally different in that they are not independent problems, but related to each other via the regularization. To distinguish them from the old independent patches, we call them ``micropatches''.
We have a great deal of freedom in deciding the size and shape of our micropatches, and in implementing the regularization. This paper motivates and describes my implementation.