A new paper is added to the collection of reproducible documents: Signal and noise separation in prestack seismic data using velocity-dependent seislet transform

The seislet transform is a wavelet-like transform that analyzes seismic data by following varying slopes of seismic events across different scales and provides a multiscale orthogonal basis for seismic data. It generalizes the discrete wavelet transform (DWT) in the sense that DWT in the lateral direction is simply the seislet transform with a zero slope. Our earlier work used plane-wave destruction (PWD) to estimate smoothly varying slopes. However, PWD operator can be sensitive to strong noise interference, which makes the seislet transform based on PWD (PWD-seislet transform) occasionally fail in providing a sparse multiscale representation for seismic field data. We adopt a new velocity-dependent (VD) formulation of the seislet transform, where the normal moveout equation serves as a bridge between local slope patterns and conventional moveout parameters in the common-midpoint (CMP) domain. The velocity-dependent (VD) slope has better resistance to strong random noise, which indicates the potential of VD seislets for random noise attenuation under 1D earth assumption. Different slope patterns for primaries and multiples further enable a VD-seislet frame to separate primaries from multiples when the velocity models of primaries and multiples are well disjoint. Results of applying the method to synthetic and field-data examples demonstrate that the VD-seislet transform can help in eliminating strong random noise. Synthetic and field-data tests also show the effectiveness of the VD-seislet frame for separation of primaries and pegleg multiples of different orders.

A new paper is added to the collection of reproducible documents: On anelliptic approximations for qP velocities in TI and orthorhombic media

Anelliptic approximations for phase and group velocities of qP waves in transversely isotropic (TI) media have been widely applied in various seismic data processing and imaging tasks. We revisit previously proposed approximations and suggest two improvements. The first improvement involves finding an empirical connection between anelliptic parameters along different fitting axes based on laboratory measurements of anisotropy of rock samples of different types. The relationship between anelliptic parameters observed is strongly linear suggesting a novel set of anisotropic parameters suitable for the study of qP-wave signatures. The second improvement involves suggesting a new functional form for the anelliptic parameter term to achieve better fitting along the horizontal axis. These modifications lead to improved three-parameter and four-parameter approximations for phase and group velocities of qP waves in TI media. In a number of model comparisons, the new three-parameter approximations appear to be more accurate than previous approximations with the same number of parameters. These modifications also serve as a foundation for an extension to orthorhombic media where qP velocities involve nine independent elastic parameters. However, as shown by previous researchers, qP wave propagation in orthorhombic media can be adequately approximated using just six combinations of those nine parameters. We propose novel six-parameter approximations for phase and group velocities for qP waves in orthorhombic media. The proposed orthorhombic phase-velocity approximation provides a more accurate alternative to previously known approximations and can find applications in full-wave modeling, imaging, and inversion. The proposed group-velocity approximation is also highly accurate and can find applications in ray tracing and velocity analysis.

A new paper is added to the collection of reproducible documents: Iterative deblending with multiple constraints based on shaping regularization

It has been shown previously that blended simultaneous-source data can be successfully separated using an iterative seislet thresholding algorithm. In this paper, I combine the iterative seislet thresholding with the local orthogonalization technique via the shaping regularization framework. During the iterations, the deblended data and its blending noise section are not orthogonal to each other, indicating that the noise section contains significant coherent useful energy. Although the leakage of useful energy can be retrieved by updating the deblended data from the data misfit during many iterations, I propose to accelerate the retrieval of leakage energy using iterative orthogonalization. It is the first time that multiple constraints are applied in an underdetermined deblending problem and the new proposed framework can overcome the drawback of low-dimensionality constraint in the traditional 2D deblending problem. Simulated synthetic and field data examples show superior performance of the proposed approach.