Kurt Eggenberger

Crossline wavefield reconstruction from multicomponent streamer data: Part 2 — Joint interpolation and 3D up/down separation by generalized matching pursuit

Computation of the 3D upgoing/downgoing separated wavefield at any desired position within a marine streamer spread is enabled by multicomponent streamers that can measure the crossline and vertical components of water-particle motion in addition to the pressure. We introduce the concept of simultaneous interpolation and deghosting and describe a new technique, generalized matching pursuit (GMP), to achieve this. This method is based on the matching-pursuit technique and iteratively reconstructs the signal as a combination of optimal basis functions. In the GMP method, the basis functions describing the unknown 3D upgoing wavefield are filtered by appropriate forward ghost operators before being matched to the multicomponent measurements. As a data-dependent method, GMP can operate on data samples that are highly aliased in the crossline direction without relying on assumptions about seismic events such as linearity. The technique is naturally suitable for data with only a small number of samples that may be irregularly spaced. We demonstrate the efficacy and robustness of the GMP method on several synthetic data sets of increasing complexity and in the presence of noise.

Crossline wavefield reconstruction from multicomponent streamer data: Part 1 — Multichannel interpolation by matching pursuit (MIMAP) using pressure and its crossline gradient

We introduce a technique that uses multicomponent seismic measurements to reconstruct the seismic wavefield at any desired crossline position between towed streamers. This method, called multichannel interpolation by matching pursuit (MIMAP), operates on pressure and crossline particle-motion measurements. It is based on the matching-pursuit technique and iteratively reconstructs the signal as a combination of optimal basis functions. Being a data-dependent technique, MIMAP can interpolate severely aliased data without assumptions about seismic events such as linearity or the model related to the seismic wavefield. MIMAP has the capability to perform well in the presence of irregular sampling and is robust when only a small number of samples are available. Using synthetic data examples, we show that the new method has the potential to interpolate signals that are sampled at realistic crossline streamer spacing and in the presence of noise.

Matching Pursuit Methods Applied to Multicomponent Marine Seismic Acquisition – The Issue of Crossline Aliasing

In this work we analyze the theoretical aspects of spatial aliasing in the crossline direction in marine seismic acquisition. We also explain the benefits of the additional measurements acquired by a multicomponent towed streamer, able to measure the three components of the particle velocity vector in addition to the pressure wavefield. We propose matching pursuit based techniques to reconstruct a 3D full bandwidth seismic wavefield on a fine receiver grid. The techniques that we describe process multicomponent seismic data; they calculate the desired 3D wavefield with satisfactory quality despite the severe aliasing that affects each of the individual input measurements in the crossline direction.

Mitigation of streamer noise impact in multicomponent streamer wavefield reconstruction

where ρ is the density of the medium. It is known (Linden, 1959) that the crossline component of the pressure gradient, Py, gives an important contribution in recovering from the cross-line aliasing, allowing the multi-channel reconstruction in the crossline direction of the seismic pressure. The MIMAP technique (Multichannel Interpolation by Matching Pursuit, Vassallo et al., 2010), has been proposed to exploit the anti-aliasing potential of two-component seismic data, P and Py, in realistic acquisition settings. It has also been discovered that the combined use of pressure, crossline and vertical component of the pressure gradient, P, Py and Pz, gives even more benefit, as it allows joint-interpolation and 3D deghosting of severely aliased data (Ozbek et al., 2010). Ozbek et al. (2010) introduced Generalized Matching Pursuit (GMP) as a technique to achieve this. Both MIMAP and GMP rely on the combination of measurements of different nature: in this paper we describe how this combination needs to take into account the differences between the signals and the noise characteristics that are observed on multicomponent marine measurements.

Parametric Matching Pursuit Methods to Reconstruct Seismic Data Acquired with Multichannel Sampling

In marine seismic data acquisition, multichannel sampling can occur in various scenarios, including over/under streamers, multicomponent streamer, and multicomponent ocean-bottom node. In these various multichannel sampling scenarios, each channel outputs samples of a filtered version of a seismic wavefield. These filters are different for each channel; the data are often coarsely and irregularly sampled. The objective is to reconstruct the unknown wavefield from the multichannel samples. In this paper, we discuss how parametric matching pursuit methods can be extended to solve such reconstruction problems. We give two examples based on data that a multicomponent streamer could record and show the form the reconstruction problem takes when two- and three-component data are available.

On the Role of Priors in Generalized Matching Pursuit to Reconstruct Wavefields from Multicomponent Streamer Data

In conventional single-component data acquisition, a common way to solve the problem of reconstructing aliased seismic data is to use priors that are computed at low frequencies and applied at high frequencies. In contrast, parametric matching pursuit methods such as Generalized Matching Pursuit applied on multicomponent data do not need priors in most conditions to achieve accurate reconstruction under aliasing. In this paper, we examine how and when soft priors can provide further robustness to multichannel matching pursuit algorithms. We illustrate our concepts on synthetic data generated by finite-difference modelling and on data acquired by a 3D-4C towed cable array. We find that multicomponent data allow matching pursuit algorithms to compute and use the priors in ways that are not possible with single-component data. For instance, the priors can be estimated by matching pursuit within an intermediate temporal frequency band, where the signal-to-noise ratios of all the components are high, while the data are already subject to spatial aliasing. The priors generated at these intermediate frequencies can then be used at higher frequencies where the aliasing is stronger, and also at lower frequencies, still aliased and affected by stronger noise.

Crossline Wavefield Reconstruction From Multi-component Streamer Data: Multichannel Interpolation By Matching Pursuit

We introduce a new technique that uses multicomponent seismic measurements that would be recorded by a true multicomponent streamer to reconstruct the seismic wavefield at any desired position between streamers. This method, called Multichannel Interpolation by Matching Pursuit (MIMAP), operates on pressure and crossline particle motion measurements. As a data-dependent technique, MIMAP can interpolate severely aliased data without any assumptions about seismic events such as linearity or the model related to the seismic wavefield. MIMAP has the capability to perform well in the presence of irregular sampling and is robust even when only a small number of samples are available.

Evaluating Fidelity and Repeatability of Wavefields Reconstructed from Multicomponent Streamer Data

In marine time-lapse (4D) seismic data processing, each wavefield snapshot is usually interpolated onto a common grid to compensate for differences in acquisition, especially receiver, geometry. Because crossline sampling is usually sparse compared to inline sampling, and most mispositioning results from poor crossline repeatability from variable feathering, crossline interpolation is often aliased and causes 4D errors that increase with interpolation distance. Recent developments in multicomponent wavefield reconstruction hold promise for good amplitude fidelity, even for data that are spatially aliased to high order. In this paper we examine repeated data acquired by an experimental 3D-4C towed-cable array. Data from six crossline samples are reconstructed 1:12 and placed on a rectangular grid uniformly sampled at 6.25 m inline and crossline. Wavefields are interpolated using pressure alone and compared with wavefields reconstructed from pressure, crossline gradient and vertical gradient. We find that 3C reconstruction has excellent fidelity, recapturing highly aliased diffractions which are lost by pressure-only interpolation. 3C reconstruction is also more repeatable, outperforming 1C reconstruction, where error correlates with midpoint mispositioning. Although the experimental 3D data have limited inline aperture, the level of repeatability achieved is extremely encouraging compared to full-aperture, pressure-only, 4D datasets at an equivalent stage of processing.

Increasing Spatial and Temporal Bandwidth with Multi-component Streamer Data

Increasing bandwidth is not only about temporal frequencies but also about spatial wavenumbers, in particular those which are poorly sampled in the cross-line direction with streamer separations of 16 to 24 times the inline sampling interval. In this talk, we present results from a test with a mini-3D array of prototype 4C marine streamers in which we use, in addition to the pressure, the vertical and crossline gradients of the pressure wavefield in order to reconstruct and 3D deghost the wavefield at arbitrary points within the aperture. From the experimental 3D survey, we show examples of spatial and temporal enhancement of wavefields reconstructed using a generalised matching pursuit algorithm, comparing pressure-only and multi-component reconstructions. We find that multicomponent reconstruction is able to de-alias high wavenumber diffractions, that are completely missed by a pressure-only matching pursuit algorithm with priors, and generate broad-band unmigrated timeslices with excellent resolution.

Flawless diamond reconstruction for simultaneous source separation

In this paper we prove that the recently introduced method of signal apparition optimally separates signals from interfering sources recorded during simultaneous source seismic data acquisition. By utilizing a periodic sequence of source signatures along one source line, that wavefield becomes separately partially visible in the spectral domain where it can be isolated from interfering signals, processed, and subtracted from the original recordings, thereby separating the wavefields from each other. Whereas other methods for simultaneous source separation can recover data in triangle-shaped region in the spectral domain, signal apparition allows for the exact separation of data in a diamond-shaped region that is twice as large thereby enabling superior reconstruction of separated wavefields throughout the entire data bandwidth. (Less)