A new paper is added to the collection of reproducible documents: Simulating propagation of separated wave modes in general anisotropic media, Part II: qS-wave propagators

Shear waves, especially converted modes in multicomponent seismic data, provide significant information that allows better delineation of geological structures and characterization of petroleum reservoirs. Seismic imaging and inversion based upon the elastic wave equation involve high computational cost and many challenges in decoupling the wave modes and estimating so many model parameters. For transversely isotropic media, shear waves can be designated as pure SH and quasi-SV modes. Through two different similarity transformations to the Christoffel equation aiming to project the vector displacement wavefields onto the isotropic references of the polarization directions, we derive simplified second-order systems (i.e., pseudo-pure-mode wave equations) for SH- and qSV-waves, respectively. The first system propagates a vector wavefield with two horizontal components, of which the summation produces pure-mode scalar SH-wave data, while the second propagates a vector wavefield with a summed horizontal component and a vertical component, of which the final summation produces a scalar field dominated by qSV-waves in energy. The simulated SH- or qSV-wave has the same kinematics as its counterpart in the elastic wavefield. As explained in our previous paper (part I), we can obtain completely separated scalar qSV-wave fields after spatial filtering the pseudo-pure-mode qSV-wave fields. Synthetic examples demonstrate that these wave propagators provide efficient and flexible tools for qS-wave extrapolation in general transversely isotropic media.

Another old paper is added to the collection of reproducible documents: Multiple realizations using standard inversion techniques

When solving a missing data problem, geophysicists and geostatisticians have very similar strategies. Each use the known data to characterize the model’s covariance. At SEP we often characterize the covariance through Prediction Error Filters (PEFs) (Claerbout, 1998). Geostatisticians build variograms from the known data to represent the model’s covariance (Issaks and Srivastava, 1989). Once each has some measure of the model covariance they attempt to fill in the missing data. Here their goals slightly diverge. The geophysicist solves a global estimation problem and attempts to create a model whose covariance is equivalent to the covariance of the known data. The geostatistician performs kriging, solving a series of local estimation problem. Each model estimate is the linear combination of nearby data points that best fits their predetermined covariance estimate. Both of these approaches are in some ways exactly what we want: given a problem give me `the answer’…

A new paper is added to the collection of reproducible documents: Double sparsity dictionary for seismic noise attenuation

A key step in sparsifying signals is the choice of a sparsity-promoting dictionary. There are two basic approaches to design such a dictionary: the analytic approach and the learning-based approach. While the analytic approach enjoys the advantage of high efficiency, it lacks adaptivity to various data patterns. On the other hand, the learning-based approach can adaptively sparsify different datasets but has a heavier computational complexity and involves no prior-constraint pattern information for particular data. We propose a double sparsity dictionary (DSD) for seismic data in order to combine the benefits of both approaches. We provide two models to learn the DSD: the synthesis model and the analysis model. The synthesis model learns DSD in the data domain, and the analysis model learns DSD in the model domain. We give an example of the analysis model and propose to use the seislet transform and data-driven tight frame (DDTF) as the base transform and adaptive dictionary respectively in the DSD framework. DDTF obtains an extra structure regularization by learning dictionaries, while the seislet transform obtains a compensation for the transformation error caused by slope dependency. The proposed DSD aims to provide a sparser representation than the individual transform and dictionary and therefore can help achieve better performance in denoising applications. Although for the purpose of compression, the proposed DSD is less sparse than the seislet transform, it outperforms both seislet and DDTF in distinguishing signal and noise. Two simulated synthetic examples and three field data examples confirm a better denoising performance of the proposed approach.