Hands-off seismic wavelet compression

Seismic data for imaging the subsurface layers of the Earth are often modeled as a convolution of a source wavelet and a reflectivity sequence of the propagation medium. The process of separating these two signals is called deconvolution. It is often performed by applying a filter that compresses the wavelet to a delta function. Such a filter is estimated using some a priori knowledge of the wavelet. The author shows that this filter can be determined, theoretically, without a priori knowledge of the wavelet and with no assumptions in regards to its statistical properties. Such a process is referred as hands-off deconvolution. The author formulates this as an optimization problem and shows that it can be solved using a constrained least-squares minimization technique. The solution can be shown to reduce to an eigenvalue problem. Several examples will be used to illustrate the result