Seismic diffractions are often considered noise and are intentionally or implicitly suppressed during processing. Diffraction-like events include true diffractions, wave conversions, or fracture waves which may contain valuable information about the subsurface and could be used for interpretation or imaging. Using synthetic and field data, we examine workflows to separate diffractions from reflections that allow enhancement of diffraction-like signals and suppression of reflections. The workflows consist of combinations of standard processing modules. Most workflows apply normal moveout corrections to flatten reflection hyperbolas, which eases their removal. We observe that the most effective techniques are the decomposition of seismic gathers into eigensections and flows based on Radon transformations.

S U M M A R YThe damage zone of a major fault can act as a low-velocity seismic waveguide. The fault-zone guided waves provide a potential method to constrain the in situ physical properties of the fault zone (FZ) at depth. Recently, there has been debate over the depth extent of observed fault waveguides and whether fault properties at seismogenic depth can be constrained by guided waves (GWs). To address these questions, elastic finite-difference synthetic seismograms were generated for fault-zone models that include an increase in seismic velocity with depth both inside and outside the FZ. Previous synthetic studies for a homogeneous fault showed that earthquakes off of the fault do not generate GWs unless the waveguide is restricted to a few kilometres depth. In contrast, earthquakes both inside and outside of a depth-varying fault waveguide generate strong GWs within the near-surface portion of the FZ. This is because the frequency-dependent trapping efficiency of the waveguide changes with depth. The nearsurface fault structure efficiently guides waves at lower frequencies than the deeper FZ. The low-frequency waves that are guided at the surface are not efficiently guided at greater depth, and therefore, travel as body waves. Fault structure at seismogenic depth requires the analysis of data at higher frequencies than the GWs that dominate at the surface and have been the subject of most previous investigations.

The paper presents a new approach to solve multiple scattering of acoustic waves in two dimensions. Traditionally wave fields are expanded into an orthogonal set of basis functions. Often these functions build a multipole. Unfortunately, these multipoles converge rather slowly for complex geometries. The new approach enhances convergence by including multiple multipoles into each region, allowing irregularities of the boundary to be resolved locally. The wave fields are expanded into a set of nonorthogonal basis functions. The incident wave field and the fields induces by the scatterers are matched in the least-square sense by evaluating the boundary conditions at discrete matching points along the domain boundaries. Due to the nonorthogonal expansions we choose more matching points than actually needed resulting in an overdetermined system which is solved in the least-squares sense. This allows an estimate of how well the expansion converges and can help to tune the scheme to enhance accuracy or reduce runtime. The idea of the multiple multipole can be extended by using more complicated basis functions which are closer to the solution sought. The resulting algorithm is a very general tool to solve relatively large and complex two-dimensional scattering problems.

This paper presents a new approach to solve scattering of elastic waves in two dimensions. Traditionally, wave fields are expanded into an orthogonal set of basis functions. Unfortunately, these expansions converge rather slowly for complex geometries. The new approach enhances convergence by summing multiple expansions with different centers of expansions. This allows irregularities of the boundary to be resolved locally from the neighboring center of expansion. Mathematically, the wave fields are expanded into a set of nonorthogonal basis functions. The incident wave field and the fields induced by the scatterers are matched by evaluating the boundary conditions at discrete matching points along the domain boundaries. Due to the nonorthogonal expansions, more matching points are used than actually needed, resulting in an overdetermined system which is solved in the least-squares sense. Since there are free parameters, such as location and number of expansion centers, as well as kind and orders of expansion functions used, numerical experiments are performed to measure the performance of different discretizations. An empirical set of rules governing the choice of these parameters is found from these experiments. The resulting algorithm is a very general tool to solve relatively large and complex two-dimensional scattering problems.

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S U M M A R YThe paper extends the multiple multipole method (MMP) to compute the multiple scattering effects from inclusions in a homogeneous full-space from two dimensions to three dimensions. MMP methods are based on a scattered wavefield model where the unknown weighting coefficients are determined from satisfying the boundary conditions at discrete matching points. The wavefield model is most commonly constructed from multiple spherical wavefunctions with different expansion centres, but any solution or approximation to the wave equation may also be used. Such an expansion is non-orthogonal and requires use of overdetermined matrix systems, but this system can be constructed rapidly because simple point matching without costly integration is sufficient. Furthermore, irregularities of the boundary are resolved locally from the nearest centre of expansion, which decouples different parts of the boundary, and thus, promotes rapid conversion with small numbers of expansion functions. The resulting algorithm is a very general tool to solve relatively large and complex 3-D scattering problems.

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Well logs show that heterogeneities occur at many different depth scales. This study examines the effects of these heterogeneities on the propagation of seismic waves, and specifically the dependence of reflection and transmission on the spatial scale content of the medium. Wavelet transformations are used to filter certain spatial scales from an acoustic sonic log. The scale‐filtered logs are used to construct layerstack models for which reflection and transmission seismograms are computed. The modified logs are also used to calculate frequency dependent reflection and transmission coefficients as functions of scale content. It is observed that features shorter than one‐fourth of the dominant wavelength have little effect on the reflection and transmission of seismic waves. Features larger than the dominant wavelength affect arrival times of individual packets within the wavetrain, but often these features hardly alter the overall appearance of individual wave packets. Reflection and transmission coda are primarily governed by heterogeneity at spatial scales similar to half the propagating wavelength. These scales appear to control the presence and shape of the events within the coda. The study also shows that the arrival times of packets at 1 kHz approach the theoretically expected value obtained from the harmonic velocity average, and the arrival times of packets below 1 Hz approach the theoretical value expected for the Backus average of the velocities.