Sean Crawley

Interpolation with smoothly nonstationary prediction-error filters

Building on the notions of time-variable filtering and the helix coordinate system, I develop software for filtersthat are smoothly variable in multiple dimensions, but that are quantized into large enough regions to be efficient. Multiscale prediction-error filters (PEFs) can estimate dips from recorded data and use the dip information to fillin unrecorded shot or receiver gathers. The data are typically divided into patches with approximately constant dips, with the requirement that the patches contain enough data samples to provide a sufficientnumber of fittingequations to determine all the coefficients of the filter. Each patch of data represents an independent estimation problem. Instead, I estimate a set of smoothly varying filtersin much smaller patches, as small as one data sample. They are more work to estimate, but the smoothly varying filtersdo give more accurate interpolation results than PEFs in independent patches, particularly on complicated data. To control the smoothness of the filters. I use filters like directional derivatives that Clapp et al. (1998) call “steering filters”. They destroy dips in easily adjusted directions. I use them in residual space to encourage dips in the specified directions. I describe the notion of “radial-steering filters” (Clapp et al. , 1999), i.e., steering filters oriented in the radial direction (lines of constant x t in t x space). Break a common-midpoint gather into pie shaped regions bounded by various values of x t . Such a pie-shaped region tends to have constant dip spectrum throughout the region so it is a natural region for smoothing estimates of dip spectra or of gathering statistics (via 2-D PEFs). In this paper I use smoothly variable PEFs to interpolate missing traces, though they may have many other uses. Finally, since noisy data can produce poor interpolation results, I deal with the separation of signal and noise along with missing data.

TTI reverse time migration using the pseudo-analytic method

Reverse time migration (RTM) was first introduced in the early 1980s (Whitmore, 1983), but was seemingly dormant until recent advances in computer hardware helped propel it onto the stage as a powerful depth-imaging method. RTM is now standard for areas where large velocity contrasts and/or steep dips pose a challenge, for instance below salt in the Gulf of Mexico. In recent years, where called for by the data, the migration tool of choice has gone from isotropic RTM to anisotropic RTM. The most common representations of anisotropy in sedimentary rocks are VTI (transverse isotropy with a vertical axis of symmetry) and TTI (tilted transverse isotropy). While isotropic and VTI RTM have become somewhat routine, TTI RTM remains challenging due to the complexity, stability, computational cost, and the difficulty in estimating the anisotropic parameters for TTI media.

3D TTI RTM Using the Pseudo-analytic Method

We use an extension of the pseudo-spectral method, called the pseudo-analytic method, to formulate a 3D TTI reverse time migration scheme. The pseudo-analytic method provides accurate, nearly non-dispersive wave propagation with a simple 2-order time-stepping scheme. The formulation is easily adapted to describe scalar wave propagation in VTI and TTI media. Our efficient TTI RTM scheme is free of the pseudo-shear wave artifacts that are normally associated with VTI and TTI formulations. We show 2D synthetic and 3D field data examples to illustrate the high-quality images that pseudo-analytic RTM produces.

A comparison of inversion results for two full-waveform methods that utilize the lowest frequencies in dual-sensor recordings

Summary In this abstract, we test the capability of full-waveform inversion to exploit the lowest frequencies available from dual-sensor, single-streamer recordings. Two different, time-domain methods are tested. The first method follows the “conventional” approach of iteratively updating interval velocity by using the gradient obtained from back-projected residuals between modelled and recorded data. The second method constructs perturbations in impedance from the gradient, which is then used to update the velocity. These methods are tested on 2-D and 3-D, synthetic data, using a wavelet with realistic bandwidth. They are also applied to field data for one cable from a dual-sensor field survey. Both this inversion and the synthetic inversion study indicate that features ~ 0.5 km can be accurately recovered at depths of a few kilometres using maximum offsets of only 8 km.

Shot interpolation for radon multiple suppression

Decreased CMP fold, such as that found in multi-source acquisition geometries, can hinder processing steps which benefit from well sampled CMP gathers, such as radon transforms. In two steps of linear least squares, multiscale prediction-error filters can estimate local dips from the recorded data and then use the dip information to fill in unrecorded shot or receiver gathers. In this paper I use multiscale, volumetric prediction-error filters to interpolate sparse, multiple-contaminated data. The increase in fold improves multiplesuppression results.

Velocity model building by wavefield-continuation imaging in the deepwater Gulf of Mexico

Wavefield-continuation-based migration algorithms that downward extrapolate the 3D prestack wavefield (commonly known as “wave-equation migration”) have been recently shown to produce better imaging results than Kirchhoff migration in many synthetic and real data cases (Popovici, 2000). Wavefield-continuation methods are potentially more accurate and robust because they are based on the full wave equation and not on an asymptotic solution based on ray theory. In addition, wavefield-continuation methods handle multipathing naturally in contrast to Kirchhoff methods, focusing and defocusing effects of velocity variations are correctly modeled, antialiasing is handled implicitly, and amplitudes are consistent with the wave equation.

Wave Equation Imaging Comparisons: Survey Sinking Vs. Shot Profile Methods

We examine the differences and similarities between the two common categories of wave-equation migration by looking at their mathematical formulations and examining their imaging results. We compare different implementations of shot profile and double square root downward continuation imaging in the context of the overall imaging challenge, including image accuracy, velocity model building, and the ability to generate prestack gathers. We examine the strengths and advantages of the methods by considering the approximations that go into them, the resulting images, and the relative costs of the methods.

DSR Wave-equation Migration For Steep And Overturned Events.

Wavefield-continuation migration algorithms deal nicely with complex velocity models, but have the disadvantage that they are typically implemented to perform only downward continuation. Energy in the wavefield that turns to 90° or more with respect to the vertical is lost. The result is that steep events may be lost from the image. We describe a method of coordinate rotation that enables steep events to be imaged by changing in a simple way from downward continuation to diagonal continuation. The sum of two or three such migrations produces an image with good imaging of steep and shallow dips.

Full-waveform Inversion By Pseudo-analytic Extrapolation

In this abstract, we examine the benefits of performing full-waveform inversion with a pseudo-analytic extrapolator. We first demonstrate the high kinematic accuracy of this extrapolator for a medium with strong, vertical transverse isotropy. We then show that under isotropic assumptions, an inversion performed with a high-order, space-time extrapolator can be gridded to yield results comparable to those obtained using pseudo-analytic extrapolation, but at four times the cost. Extrapolation by the pseudoanalytic method is thus the most efficient method currently available for performing 3-D full-waveform inversion assuming an acoustic medium.

Increasing the parallelism in common azimuth migration with overlap domain decomposition

Common azimuth migration is naturally parallel over the input frequency, but obvious parallelism ends there. In contrast to many other migration algorithms, the entire spatial extent of the input data migrates at once, usually with some mixed-domain operator. This can lead to a couple of complications. For a simple implementation, it caps the number of cores that can efficiently work on a single input frequency at the number that can share memory, commonly 4 or 8 on a current Linux cluster node. For a large, high frequency input data slice, more cpu power comes in handy.