Euclid and the art of wavelet estimation, Part II: Robust algorithm and field‐data examples

Abstract

In this second part of a two‐part work, a more robust algorithm is derived and used for the estimation of the seismic wavelet as the common signal of two or more seismic traces. It is based on the properties of the eigenvectors with zero eigenvalue of a matrix derived in the first part, whose elements are the samples of the autocorrelation functions and crosscorrelation functions of these seismic traces for a number of lags. The noise resistance of this algorithm is illustrated by means of a synthetic‐data example and then demonstrated on field data. In one field‐data example, the so‐called Euclid wavelet is compared with one derived deterministically by means of an impedance log. The other example relates three quite different Euclid wavelets determined in three different time zones on a seismic line to one another by showing that their differences can be explained by absorption.

A fast algorithm for sparse multichannel blind deconvolution

“…In contrast, SMBD and other multichannel approaches seek to directly determine the reflectivity (Rietsch, 1997a(Rietsch, , 1997bKaaresen and Taxt, 1998;Kazemi and Sacchi, 2014). As we will see, this difference also helps to explain the reduced computational complexity of our approach.…”

“…Of particular interest to this paper are the so-called multichannel blind deconvolution methods (Wiggins, 1978;Xu et al, 1995;Inouye and Sato, 1996;Rietsch, 1997aRietsch, , 1997bKaaresen and Taxt, 1998;Ding and Li, 2001;Ram et al, 2010). The term multichannel comes from the fact that these methods are applied when we have several observations of a certain signal, and each observation goes through a different channel.…”

Wavelet Estimation via Sparse Multichannel Blind Deconvolution

“…Euclid method estimates the reflectivity by estimating the eigenvector associated to the minimum non-zero eigenvalue of A T A Rietsch (1997a). A small amount of noise in the data makes the solution impractical for real data applications Rietsch (1997b). The addition of a noise term in our signal model leads to Ax = e .…”

“…Euclid deconvolution is a member of the plethora of methods that have been proposed for blind deconvolution of seismic data. The method was first discussed in the geophysical literature by Rietsch (1997a) and tested with real data examples in Rietsch (1997b). The method has also been investigated by Xu et al (1995) and Liu and Malvar (2001) in communication theory and deconvolution of reverberations.…”

Beyond Receiver Functions: Green's Function Estimation by Transdimensional Inversion and Its Application to OBS Data

“…They use an equation that directly relates P component records to the corresponding SV record for a model subsurface structure. The equation is similar to the concept of multichannel deconvolution proposed in the field of geophysical exploration (Kazemi & Sacchi, 2014;Rietsch, 1997aRietsch, , 1997b. Using this equation, they invert for subsurface seismic velocity structure by performing a direct search over many models.…”