Ralf Ferber

Robust Surface-consistent Deconvolution With Noise Suppression

A new extended method of surface-consistent deconvolution (s.-c. deconvolution) is presented that combines the benefits of trace-by-trace deconvolution and the strictly surface-consistent technique. The procedure employs the usual two steps: analysis (derivation of the model spectra) and application (actual operator design and deconvolution). In the application step, the spectrum of each trace is compared to its model. If the match is better than a given tolerance, the strictly s.-c. deconvolution is used. Otherwise, a “bad” trace has been detected, and an extra operator will be applied on top of the strictly surfaceconsistent operator. Additionally, the trace is flagged for optional surgical muting, to automatically edit the bad traces.

Quality Control And Bandwidth Optimization of Compact Fourier Interpolation Operators

Compact Fourier interpolation (COMFI) is a minimum mean-square-error interpolation algorithm that interpolates irregular data to arbitrary locations. We extend the basic algorithm, which has been known for some time (Yen, 1956; Hale, 1980; Chen and Allebach, 1987), to include bandwidth-optimization. By this, we mean that the interpolation operators only attempt to interpolate wavenumbers that are supported by the local sampling density. The maximum wavenumber that can be interpolated accurately is automatically determined. This extension is particularly important for seismic data, because the sampling density is often highly space-variant.

Two approaches for Q estimation and its application to seismic inversion

Summary In this paper, we present two complimentary approaches for interval Q estimation from surface seismic data. A layer-based approach and smooth solutions algorithms are presented and evaluated by comparing estimated Q from surface seismic data with VSP data. We also show how, by using a 3D attenuation estimation algorithm together with a time- and space-varying compensation algorithm (inverse Q filtering), we were able to derive an attenuation field an d to improve the wavelet stability as well as the P-impedance inversion results. The choice of attenuation estimation algorithm is related to the statistical nature of the attenuation field in the subsurface. Theory We consider the problem of plane-wave propagation in attenuating media characterized by a velocity, V, and quality factor, Q, as given by equation 1. ) ( / ) ( ) ( 1 ) , ( kx t i V x fQ o kx t i x o e e u e e u t x u = = ω ω π ω α . (1) We further assume that the relation between velocity, frequency, and quality factor can be characterized using the causal constant Q model of Futterman (1962),

Low-frequency signal enhancement by pseudo-Vz deghosting

We examine the estimation of the vertical component of particle motion (‘pseudo-Vz’) data from deep-tow streamer pressure data. The estimated data is then combined with the pressure data to attenuate the pressure ghost by a procedure referred to as pseudo-Vz deghosting. The notches created by the destructive interference of the up- and down-going waves at the receivers are shown to be ‘filled’ with information about the upgoing waves, thereby improving the signal-to-noise ratio. In addition, it is shown that even though they may not be present in the input data, by including sparsity constraints in the deghosting process, coherent and energetic signals at the low-frequency part of the spectrum can be estimated using this technique. The enhanced signals at notch frequencies provide broadband data. The proposed technique can be used, for example, for future deep-tow marine seismic data acquisition benefiting from higher signal-to-noise ratio at greater streamer depth, as well as in re-processing of existing data, for example in a time-lapse scenario, making them more comparable to future broadband data. We demonstrate the technique on a 2D deep-tow marine seismic data set acquired along a transect on the Sumatra subduction zone, in southwest Indonesia.

Is There Always Extra Bandwidth In Non-uniform Spatial Sampling?

We address the question of whether or not there always is a “bandwidth benefit” in non-uniform spatial sampling of geophysical data. Answering this question is, for example, important in the context of random sampling of seismic data, as it recently has been shown that there can be such a benefit under certain assumptions on the spectral structure of the data. Assume that a fixed number of sensors are placed either uniformly (i.e., on a regular grid) or nonuniformly (either randomly distributed or following any suitable non-uniform sampling scheme). The bandwidth supported by uniform sampling is that of the Nyquist wavenumbers corresponding to the sampling distances on the regular grid. The bandwidth supported by the nonuniform sampling we propose here refers to the maximum bandwidth of data that could be reconstructed by a linear operator at arbitrary sampling locations within the survey area without unacceptably high reconstruction error. Without making further assumptions on the spectral structure of the data, i.e., especially without assuming sparseness of the data spectrum, we will argue that we see no such bandwidth benefit in non-uniform sampling in the examples we have investigated.

L1 Pseudo-Vz Estimation and Deghosting of Single-component Marine Towed-streamer Data

We present a novel technique to estimate the data of the vertical component of particle motion from marine single-component pressure data. The particle motion data, bar an angle dependent obliquity factor, is computed by convolution of the output from L1 deconvolution of the pressure ghost wavelet with the corresponding ghost wavelet of the particle motion. The estimated particle motion data is then used in a conventional two-component technique for receiver ghost attenuation by combination with the original pressure-wave data. We applied our technique to deep-tow streamer data of a 3D over/sparse-under marine survey, in which six streamers were towed at a shallow depth, with two further streamers towed deeper. This data set enables us to compare the results from our single-component deghosting technique with optimum deghosting of the over/sparse-under data. We will show that our technique achieves improvements in bandwidth of the single-component pressure data, while not fully reaching the quality of the optimally deghosted data from the over/sparse-under survey.

Biwavenumber Transmission Function: A Powerful Tool For Characterizing Spectral Leakage And Aliasing In Nonuniform Sampling

We study spectral leakage and aliasing for the class of interpolators wherein the output is a linear combination of the sampled input. Spectral leakage is a fundamental problem in signal reconstruction from nonuniformly sampled data, and seismic acquisition geometries are often spatially aliased in at least one dimension. To analyze spectral leakage and aliasing, we demonstrate how the biwavenumber transmission function can be used to visualize how spectral input components are mapped in the interpolated output.