Static correction using blind channel identification

Near-surface variations can be very complex and may distort amplitudes and arrival times of the reflections events from target reflectors. Near-surface complexities include topographic variations, near-surface irregularities, variations in soil conditions and the weathered layer.
These perturbations generally have a significant impact on seismic recordings. Although there is a general agreement that near-surface distortions are very complex and we usually rely on a rather simplified parameterization to compensate for these perturbations. Determinatin of time shifts is generally referred to as static corrections and residual static correction. Underlying concept of static corrections is the assumption that a simple time shift of an entire seismic trace will yield the seismic record that would have been observed if the geophones had been placed on the reference datum. Hence, static time shifts corrections are assumed to be surface consistent. Surface consistencymeans that the effects associated with a particular source or receiver affect all wave types similarly, regardless of the direction of propagation.
Conventional methods of static time shift corrections need information on velocities and depths of near-surface layers to determine and compensate the time shifts. These methods rely on simple models for near-surface layers.
In this paper, we develop an approach to compensate for complex time shift using blind channel identification, as it does not use near-surface information. The blind channel identification deals with the recovery of either the input signal or the channel response from the observed transmitted signal only. This method differs from conventional methods for seismic deconvolution. The latter resolve the undetermined nature of the problem by making assumptions about the reflectivity sequence (whiteness, sparsity) and/or the seismic wavelet (minimum phase/ zero phase). The blind channel identification method does not rely on these assumptions. It uses multichannel recordings to fully constrain the problem and is therefore purely data driven.
Many recent blind channel estimation techniques exploitsubspace structures of observation. The key idea in subspace methods of blind channel identification that the channel vector (or part of the channel vector) is in a one dimensional subspace of a block of noiseless observations. These methods, which are often referred to as subspace algorithms, have the attractive property that the channel estimates can often be obtained in a closed form from optimizing a quadratic cost function.
We use blind channel identification to estimate for near-surface source and receiver perturbations. These perturbations are parameterized as finite-impulse response (FIR) filters, and are referred to as the channels. Because the channels describe the near-surface perturbations, we can estimate time shifts from correlation of the channels.
We applied the method to synthetic data and to part of a field data set acquired in an area with significant near-surface heterogeneity. The application of new static corrections greatly improves the trace-to-trace consistency in prestack data. The procedure delineates reflection events that are difficult to detect prior to the application of new static corrections. Based on these results, we conclude that the new static corrections can successfully remove complex time shifts from land seismic data. The field data example demonstrates that the new static corrections can greatly enhance the imaging capabilities of land seismic data.