Filtering > Wiener filter: spiking deconvolution

In seismic reflection, when we record the seismic impulsion emitted by the source device, we generally conduct the signatures' processing to bring back the signature of each shot to a desired signal. This operation allows compensating energy variations at each shot, and modifying the impulsion to improve the resolution. This operation can be done in marine seismic because the signature is recorded in a homogeneous environment (water). This operation can also be done in well seismic (VSP) where the source and a reference sensor occupy permanent positions during the whole length of acquisition. This processing is called signature deconvolution. Any deconvolution is sensitive to noise. A method classically used and relatively robust to noise is the deconvolution with the Wiener filter. The Wiener filter allows passing from a given signal to a desired signal. The Wiener filter is a filter which minimizes (least squares conditions) the difference between the desired signal and the signal estimated by the filter. The desired filter can be a Dirac impulsion. In this case, a geophysician talks of Spiking deconvolution.