Prestack migration and/or inversion may be implemented in either the time or the frequency domain. In the frequency domain, it is possible to discretize the frequencies with a much larger sampling interval than that dictated by the sampling theorem and still obtain an imaging result that does not suffer from aliasing (wrap around) in the depth domain. The selection of input frequencies can be reduced when a range of offsets is available; this creates a redundancy of information in the wavenumber coverage of the target. In order to optimize the use of this information, we define a new discretization strategy that depends on the maximum effective offset present in the surface seismic survey: the larger the range of offsets, the fewer frequencies are required. The strategy, exact in a homogeneous 1D earth, selects frequencies by making use of the well-known effect of image stretch in normal-moveout (NMO) correction and in migration (usually considered detrimental for the imaging). The strategy is also useful in more general earth models: we apply it to the 2D Marmousi model and recover a continuous range of wavenumbers using only three input frequencies. The Marmousi inversion result accurately predicts all other data frequencies, demonstrating the redundancy of the data.

Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies

Collisional alignment and orientation of atomic outer shells I. Direct excitation by electron and atom impact

Electron scattering by molecules II. Experimental methods and data

Gas in an unconsolidated sand reservoir encased in shale often results in a dramatic increase in amplitude of the seismic reflection from the shale/gas-sand interface. Unfortunately, reflection amplitude appears not to vary linearly with water (brine) saturation, and thus cannot be used to estimate gas quantity. Previously presented theoretical velocity computations for a Tertiary sedimentary section, which demonstrate that compressional-wave velocity in an unconsolidated gas sand varies nonlinearly with brine saturation, qualitatively agree with laboratory velocity measurements on a sand specimen composed of pure quartz grains. However, significant departure of measured and theoretical velocities at high brine saturation indicates that the technique for partially saturating the sand specimen by flowing a gas-brine mixture through the specimen does not provide a sufficiently uniform distribution. The gas preferentially seeks larger pores. In a subsequent experiment on a specimen composed of spherical glass beads of nearly uniform size, the previous, as well as a modified, fluid injection technique was used. For the latter, brine only was injected into the pore space previously filled with a mixture of gas and brine in nearly equal proportions. This resulted in a more uniform distribution of the gas-brine mixture. For approximately equal brine saturations, this modified technique more » resulted in a measured compressional-wave velocity approximately one-half of the velocity measured for the previously used fluid injection technique. This result implies that if the gas-brine mixture is uniformly distributed in a reservoir, the fluid compressibility is the weighted-by-volume average of the constituent compressibilities. « less

Effect of brine-gas mixture on velocity in an unconsolidated sand reservoir. [Laboratory velocity measurements in unconsolidated sand at various brine saturations]

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Marchenko imagingMarchenko imaging

The succes of multiple suppression for seismic data often hinges on the accuracy with which the multiple behaviour can be predicted. This is especially true for interbed multiples where small details can be essential for distinguishing the multiples from surrounding primaries. In this paper we describe a new wave equation method of predicting interbed multiples from primary events. This scheme can be used to estimate multiples directly from measured data and has been incorporated into a new suppression technique.

Wave Equation Prediction And Removal of Interbed Multiples

Many prospective passive ocean margins are covered by large areas of basalts. These basalts are often extremely heterogeneous and scatter the seismic energy of the conventional seismic reflection system so that it becomes difficult to obtain information on deeper reflectors. Since high frequencies are scattered more than low frequencies, we argue that the acquisition system for sub-basalt targets should be modified to emphasize the low frequencies, using much larger airguns, and towing the source and receivers at about 20 m depth. In the summer of 2001 we obtained seismic reflection data over basalt in the northeast Atlantic using a system modified to enhance the low-frequency energy. These new data show deep reflections that are not visible on lines shot in the same places with a conventional system.

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Use of low frequencies for sub‐basalt imaging

Wave Equation Prediction and Removal of Interbed Multiples

Refraction surveys are a well-established method of imaging subsurface velocities, both in terms of the deep crustal structure at global scales and in the shallow near surface. These surveys generally involve deploying an array of receivers on the surface (or water bottom) and recording arrivals from a seismic source initiated at or near the surface.

/pdf/enhanced-refractor-imaging-by-supervirtual-interferometry-2ijlima2ls.pdf

Enhanced refractor imaging by supervirtual interferometry

This paper describes least-squares reverse-time migration. The method provides the exact adjoint operator pair for solving the linear inverse problem, thereby enhancing the convergence of gradient-based iterative linear inversion methods. In this formulation, modified source wavelets are used to correct the source signature imprint in the predicted data. Moreover, a roughness constraint is applied to stabilise the inversion and reduce high-wavenumber artefacts. It is also shown that least-squares migration implicitly applies a deconvolution imaging condition. Three numerical experiments illustrate that this method is able to produce seismic reflectivity images with higher resolution, more accurate amplitudes, and fewer artefacts than conventional reverse-time migration. The methodology is currently feasible in 2-D and can naturally be extended to 3-D when computational resources become more powerful.

Helmut Jakubowicz

Papers

Wave Equation Prediction And Removal of Interbed Multiples

Use of low frequencies for sub‐basalt imaging

Wave Equation Prediction and Removal of Interbed Multiples

Enhanced refractor imaging by supervirtual interferometry

Least‐squares reverse‐time migration in a matrix‐based formulation