Phase-weighted slant stacking for surface wave dispersion measurement

SUMMARY Surface wave retrieval from ambient noise records using seismic interferometry techniques has been widely used for multiscale shear wave velocity (Vs) imaging. One key step during Vs imaging is the generation of dispersion spectra and the extraction of a reliable dispersion curve from the retrieved surface waves. However, the sparse array geometry usually affects the ability for high-frequency (>1 Hz) seismic signals’ acquisition. Dispersion measurements are degraded by array response due to sparse sampling and often present smeared dispersion spectra with sidelobe artefacts. Previous studies usually focus on interferograms’ domain (e.g. cross-correlation function) and attempt to enhance coherent signals before dispersion measurement. We propose an alternative technique to explicitly deblur dispersion spectra through use of a phase-weighted slant-stacking algorithm. Numerical examples demonstrate the strength of the proposed technique to attenuate array responses as well as incoherent noise. Three different field examples prove the flexibility and superiority of the proposed technique: the first data set consists of ambient noise records acquired using a nodal seismometer array; the second data set utilizes distributed acoustic sensing (DAS) and a marine fibre-optic cable to acquire a similar ambient noise data set; the last data set is a vibrator-based active-source surface wave data. The enhanced dispersion measurements provide cleaner and higher-resolution spectra without distortions which will assist both human interpreters as well as ML algorithms in efficiently picking curves for subsequent Vs inversion.

Accelerating least-squares Kirchhoff time migration using beam methodology

Least-squares migration is an advanced imaging technique capable of producing images with improved spatial resolution, balanced illumination and reduced migration artifacts; however, the prohibitive computational cost poses a great challenge for its practical application. We have incorporated the beam methodology into the implementation of Kirchhoff time modeling/ migration and developed a fast common-offset least-squares Kirchhoff beam time migration (LSKBTM). Different from conventional Kirchhoff time modeling/migration in which the seismic data are modeled/migrated trace by trace, the mapping operation in Kirchhoff beam time modeling/migration is performed in terms of beam components and performed only at sparsely sampled beam centers. Therefore, the computational cost of LSKBTM is significantly reduced in comparison with that of least-square Kirchhoff time migration (LSKTM). In addition, based on the second-order Taylor expansion of the diffraction traveltime, we introduce a quadratic correction term into the inverse/forward local slant stacking, effectively enhancing the computational accuracy of LSKBTM. We have used both 2D synthetic and 3D field data examples to verify the effectiveness of the proposed method. The results show that LSKBTM can produce images comparable to that of LSKTM, but at considerably reduced computational cost.

Application of MASW Method for Evaluating Dynamic Properties of Lu-Liao-His Earth Dam

In the paper the shear wave velocity and Poisson’s ratio profile are studied using the MASW test. Slant stacking was adopted in experimental dispersion curve constructing. Theoretical dispersion curve can be constructed by thin layer stiffness matrix method. A real-parameter genetic algorithm is required to minimize the error between the theoretical and experimental dispersion curves. Test results show that spectrum using slant stacking shows the fundamental mode of Rayleigh wave in the frequency range from 15 Hz to 50Hz. To reduce the error of experimental and theoretical dispersion curve using real-parameter genetic algorithm is feasible. The results also show that the strata of Lu-Liao-His Earth Dam can be modeled as 3 soil layers with an underlying half space.

Dynamically Focused Gaussian Beams for Seismic Imaging

An initial study is performed in which dynamically focused Gaussian beams are investigated for seismic imaging. Focused Gaussian beams away from the source and receiver plane allow the narrowest and planar portions of the beams to occur at the depth of a specific target structure. To match the seismic data, quadratic phase corrections are required for the local slant stacks of the surface data. To provide additional control of the imaging process, dynamic focusing is investigated where all subsurface points are specified to have the same planar beam fronts. This gives the effect of using nondiffracting beams, but actually results from the use of multiple focusing depths for each Gaussian beam. However, now different local slant stacks must be performed depending on the position of the subsurface scattering point. To speed up the process, slant stacking of the local data windows is varied to match the focusing depths along individual beams when tracked back into the medium. The approach is tested with a simple model of 5-point scatterers which are then imaged with the data, and then to the imaging of a single dynamically focused beam for one shot gather computed from the Sigsbee2A model.

Directional illumination analysis using the local exponential frame

We have developed an efficient method of directional illumination analysis in the local angle domain using local exponential frame beamlets. The space-domain wavefields with different shot-receiver geometries are decomposed into the local angle domain by using the local exponential beamlets, which form a tight frame with the redundancy ratio two and are implemented by a linear combination of local cosine and local sine transforms. Because of the fast algorithms of the local cosine/sine transforms, this method is much more efficient than the previously used decomposition methods in directional illumination analysis, such as the local slant-stacking method and the Gabor-Daubechies frame method. The results of directional illumination (DI) maps and the acqui-sition dip responses (ADR) for the 2D SEG/EAGE salt model and the 45-shot 3D SEG/EAGE model demonstrated the validity and feasibility of our method. Compared with the illumination results using local slant-stacking decomposition, the new method produces illumination maps of similar quality, but it does so a few times faster. Furthermore, because of its high computational efficiency and saving in memory usage, the new method makes the 3D directional illumination analysis readily applicable in the industry.

3D plane-wave migration in tilted coordinates: A field data example

We have extended isotropic plane-wave migration in tilted coordinates to 3D anisotropic media and applied it on a Gulf of Mexico data set. Recorded surface data are transformed to plane-wave data by slant-stack processing in inline and crossline directions. The source plane wave and its corresponding slant-stacked data are extrapolated into the subsurface within a tilted coordinate system whose direction depends on the propagation direction of the plane wave. Images are generated by crosscorrelating these two wavefields. The shot sampling is sparse in the crossline direction, and the source generated by slant stacking is not really a plane-wave source but a phase-encoded source. We have discovered that phase-encoded source migration in tilted coordinates can image steep reflectors, using 2D synthetic data set examples. The field data example shows that 3D plane-wave migration in tilted coordinates can image steeply dipping salt flanks and faults, even though the one-way wave-equation operator is used for wavefield extrapolation.