Luc T. Ikelle

Multidimensional signature deconvolution and free-surface multiple elimination of marine multicomponent ocean-bottom seismic data

This paper presents a wave-equation method for multidimensional signature deconvolution (designature) and elimination of free-surface related multiples (demultiple) in four-component (4C) ocean-bottom seismic data. The designature/demultiple method has the following characteristics: it preserves primary amplitudes while attenuating free-surface related multiples; it requires no knowledge of the sea floor-parameters and the subsurface; it requires information only of the local density and acoustic wave propagation velocity just above the sea floor; it accommodates source arrays; and no information (except location) of the physical source array, its volume, and its radiation characteristics (wavelet) is required. Designature is an implicit part of the demultiple process; hence, the method is capable of transforming recorded reflection data excited by any source array below the sea surface into free-surface demultipled data that would be recorded from a point source with any desired signature. In addition, the incident wavefield is not subtracted from the data prior to free-surface demultiple; hence, separation of incident and scattered fields is not an issue as it is for most other free-surface demultiple schemes. The designature/demultiple algorithm can be divided into two major computational steps. First, a multidimensional deconvolution operator, inversely proportional to the time derivative of the downgoing part of the normal component of the particle velocity just above the sea floor, is computed. Second, an integral equation is solved to find any component of the designatured, free-surface demultipled multicomponent field. When the geology is horizontally layered, the designature and free-surface demultiple scheme greatly simplifies and lends itself toward implementation in the τ –p domain or frequency–wavenumber domain as deterministic deconvolution of common shot gathers (or common receiver gathers when source array variations are negligible).

Source signature estimation based on the removal of first‐order multiples

The estimation of the source signature is often one of the necessary first steps in the processing of seismic reflection data, especially if the processing chain includes prestack multiple removal. However, most methods for source estimation are based on poststack data or assume that the earth is 1-D. In this work, a new source estimation method for prestack data is presented. It consists of finding the source signature that permits the removal of events attributable to the first‐order free‐surface reflections (i.e., first‐order multiples). The method exploits the formulation of the relationship between the free‐surface reflections and the source signature as a scattering Born series. In this formulation, the order of the scattering series coincides with that of the free‐surface reflections, and the series is constructed exclusively with seismic data and the source signature without any knowledge of the subsurface other than the velocity of sea water. By restricting the problem to first‐order free‐surface...

Linearized inversion of multioffset seismic reflection data in the omega -K domain

In the acoustic approximation, the Earth is described using only density and bulk modulus. Assuming smooth density variations, reflections can be described using a single function—the velocity of compressional waves. If a reference model which is close enough to the actual Earth is known, the problem of estimating the medium velocity from the observed data can be linearized. Using a least‐squares formulation and working in the ω-k domain, the linearized inverse problem for a homogeneous reference medium can be solved by a noniterative algorithm which is economically competitive with prestack migration. Numerical tests with synthetic and real data demonstrate the feasibility and the numerical stability of the method. The numerical results compare well with those obtained by migration of unstacked data, although superior results will only be obtained when the physics of the problem (including elastic versus acoustic effects, three‐dimensional propagation, and accurate source estimation) will realistically b...

An example of seismic time picking by third‐order bicoherence

Conventional seismic time-delay estimation relies on the crosscorrelation that quantifies the similarities between two measurements in the second-order time domain. When the noise correlation in the measurements is considerable, the correlation peak can be substantially distorted, resulting in imprecise and even biased estimation of the time delay. The synthetic data computed by Ikelle et al. (1993) and Ikelle and Yung (1994) in their studies of wave propagation through random media provide a good example of data with considerable noise correlation. In picking the arrival times in this data set, we found that the crosscorrelation technique suffers both from the severely restricted signal bandwidth and from the presence of coda. Here we present an alternative approach involving high-resolution nonparametric time-delay estimation in the third-order domain.

Using even terms of the scattering series for deghosting and multiple attenuation of ocean‐bottom cable data

Inverse scattering multiple attenuation (ISMA) is a method of removing free‐surface multiple energy while preserving primary energy. The other key feature of ISMA is that no knowledge of the subsurface is required in its application. I have adapted this method to multicomponent ocean‐bottom cable data (i.e., to arrays of sea‐floor geophones and hydrophones) by selecting a subseries made of even terms of the current scattering series used in the free‐surface multiple attenuation of conventional marine surface seismic data (streamer data). This subseries approach allows me to remove receiver ghosts (receiver‐side reverberations) and free‐surface multiples (source‐side reverberations) in multicomponent OBC data. I have processed each component separately. As for the streamer case, my OBC version of ISMA preserves primary energy and does not require any knowledge of the subsurface. Moreover, the preprocessing steps of muting for the direct wave and interpolating for missing near offsets are no longer needed. ...

Multiple attenuation and P/S splitting of multicomponent OBC data at a heterogeneous sea floor

Abstract One of the benefits of dual-sensor (hydrophone and geophone) recordings in ocean bottom cable (OBC) experiments is that hydrophone data and geophone data can be combined to attenuate receiver-side reverberations in both data types or combined to split geophone data into upgoing P-and S-waves, albeit after applying appropriate scaling filters. Most of the formulae currently used to compute these scaling filters assume, sometimes implicitly, that the sea floor is horizontally flat. We present a generalization of these formulae to cases where the sea floor is arbitrarily heterogeneous. Heterogeneities can be due to the topography of the sea floor as well as laterally varying medium parameters along the sea floor. The novelty here is that our derivations are based on the elastodynamic representation theorem instead of plane wave decomposition. For the particular case where the medium parameters are constant along the receiver spread at a dipping sea floor, the resulting scaling filters are explicit and identical to those obtained by plane wave decomposition analysis. The results of our formulation can be used either for multiple attenuation or P/S splitting or both.

Kirchhoff scattering series: Insight into the multiple attenuation method

There are two basic integral equations used to represent wavefields in theoretical seismology: the Lippmann‐Schwinger integral equation and the representation theorem. The Born scattering series currently used for attenuating free‐surface multiples has been derived from the Lippmann‐Schwinger integral equation. Similarly, we have used the representation theorem here to derive a Kirchhoff scattering series for attenuating free‐surface multiples in towed‐streamer data.The Kirchhoff series for attenuating free‐surface multiples is, in theory, equivalent to the Born series; most important, like the Born series, it does not require any knowledge of the subsurface. However, it still provides useful insight into the multiple‐attenuation methods because the form of some quantities involved in the Kirchhoff series is different from the form in the Born series. For example, in towed‐streamer seismic data, the Kirchhoff series requires measurements of the vertical derivative of the pressure field in addition to the ...

Linearized inversion of multioffset seismic reflection data in the omega -K domain; depth-dependent reference medium

The computation of synthetic seismograms can be linearized with respect to a reference medium that issno close to the actual medium. Using a least‐squares formulation, the inverse problem can then be set up as a problem of quadratic optimization. The inverse problem is greatly simplified if the reference medium is symmetric. For a homogeneous reference medium, a rigorous and economic solution can be obtained by Fourier transforming all spatial variables. In particular, the solution can be obtained through an explicit formula that does not require the resolution of any linear system (as is the case when not working in the Fourier domain). However, the assumption of a homogeneous reference medium is generally not realistic. In some situations, the reference medium can be depth‐dependent. It can then be shown that by Fourier transforming time and all spatial variables except depth, the inverse problem also has an elegant and economic solution. If δm(x,z) is the (unknown) difference between the reference medi...

Potential impacts of vertical cable (VC)

Traditionally, the quality of land seismic data has been poor due to the energy trapped in the low‐velocity layers in the shallow subsurface. These low‐velocity zones generate ground roll and statics which interfere with primary reflection data. Also, undersampling, poor coupling, and imprecise orientation of multicomponent geophones result in low signal‐to‐noise ratio. In this paper we demonstrated how vertical cable (VC) technology can overcome these problems.

AVO-A response of an anisotropic half-space bounded by a dipping surface for P-P, P-SV and P-SH data

We analyze amplitude variations with offsets and azimuths AVO-A of an anisotropic half-space bounded by a dipping surface. By analyzing the response of a dipping reflector instead of a horizontal one, we integrate the fundamental problem of lateral heterogeneity vs. anisotropy into our study. This analysis is limited to the three scattering modes that dominate . ocean bottom seismic OBS data: P-P, P-SV and P-SH. When the overburden is assumed isotropic, the AVO-A of each of these three scattering modes can be cast in terms of a Fourier series of azimuths, f, in general form, 4 R f s F q F cos nf q G sin nf , wx