Madagascar users are encouraged to try improving the results.
A new paper is added to the collection of reproducible documents: Full-waveform inversion using seislet regularization
Because of inaccurate, incomplete and inconsistent waveform records, full waveform inversion (FWI) in the framework of local optimization approach may not have a unique solution and thus remains an ill-posed inverse problem. To improve the robustness of FWI, we present a new model regularization approach, which enforces the sparsity of solutions in the seislet domain. The construction of seislet basis functions requires structural information, which can be estimated iteratively from migration images. We implement FWI with seislet regularization using nonlinear shaping regularization, and impose sparseness by applying soft thresholding on the updated model in the seislet domain at each iteration of the data fitting process. The main extra computational cost of the method relative to standard FWI is the cost of applying forward and inverse seislet transforms at each iteration. This cost is almost negligible compared to the cost of solving wave equations. Numerical tests using the synthetic Marmousi model demonstrate that seislet regularization can greatly improve the robustness of FWI by recovering high-resolution velocity models, particularly in the presence of strong crosstalk artifacts from simultaneous sources or strong random noise in the data.
The major new release of Madagascar, stable version 2.0 was made during the Madagascar school in Shanghai and features 25 new reproducible papers and significant other enhancements including complete examples of seismic field data processing.
According to the SourceForge statistics, the previous 1.7 stable distribution has been downloaded nearly 12,000 times. The top country (with 28% of all downloads) was USA, followed by China, Brazil, Germany, and Columbia.
The 2017 Madagascar School on Reproducible Computational Geophysics took place in Shanghai, China, on July 10-11 and was hosted by Professor Jiubing Cheng at Tongji University.
The school attracted nearly 80 participants from 12 different universities and 5 other research organizations. The program included lectures given by 6 different instructors and hands-on exercises on different topics in the use of the Madagascar software framework, as well as presentations sharing experience of different research groupd. The school materials are available on the website.
Earlier this year, on April 21-22, another school took place at the University of Houston and was hosted by SEG Wavelets, the local SEG student chapter. The school materials are available on the website.
We perform seismic diffraction imaging and time-migration velocity analysis by separating diffractions from specular reflections and decomposing them into slope components. We image slope components using migration velocity extrapolation in time-space-slope coordinates. The extrapolation is described by a convection-type partial differential equation and implemented in a highly parallel manner in the Fourier domain. Synthetic and field data experiments show that the proposed algorithms are able to detect accurate time-migration velocities by measuring the flatness of diffraction events in slope gathers for both single and multiple offset data.
A new paper is added to the collection of reproducible documents: Analytical path-summation imaging of seismic diffractions
Diffraction imaging aims to emphasize small subsurface objects, such as faults, fracture swarms, channels, etc. Similarly to classical reflection imaging, velocity analysis is crucially important for accurate diffraction imaging. Path-summation migration provides an imaging method, which produces an image of the subsurface without picking a velocity model. Previous methods of path-summation imaging involve a discrete summation of the images corresponding to all possible migration velocity distributions within a predefined integration range and thus involve a significant computational cost. We propose a direct analytical formula for path-summation imaging based on the continuous integration of the images along the velocity dimension, which reduces the cost to that of only two fast Fourier transforms. The analytic approach also enables automatic migration velocity extraction from diffractions using double path-summation migration framework. Synthetic and field data examples confirm the efficiency of the proposed techniques.
A new paper is added to the collection of reproducible documents: 3D generalized nonhyperboloidal moveout approximation
Moveout approximations are commonly used in velocity analysis and time-domain seismic imaging. We revisit the previously proposed generalized nonhyperbolic moveout approximation and develop its extension to the 3D multi-azimuth case. The advantages of the generalized approximation are its high accuracy and its ability to reduce to several other known approximations with particular choices of parameters. The proposed 3D functional form involves seventeen independent parameters instead of five as in the 2D case. These parameters can be defined by zero-offset traveltime attributes and four additional far-offset rays. In our tests, the proposed approximation achieves significantly higher accuracy than previously proposed 3D approximations.
sfseislet implements the 2-D seislet transform.
The seislet transform theory is descibed in the paper Seislet transform and seislet frame.
The following example from fpwd/teapot shows a 3-D seismic image before and after a seislet transform in the inline direction.
To perform the forward seislet transform, run sfseislet with the flag adj=y. To run the inverse transform, use adj=n. In a confusing choice of parameter names, inv= does not control the direction of the transform but the type of the weighting function used. Another control is provided by unit=.
A required auxiliary input is the dip field specified by dip=. If the dip was estimated using plane-wave destruction (sfdip), the order= parameter should be the same.
Different types of the seislet transform (specified by type=) correspond to different types of the corresponding digital wavelet transform. The choices are haar, linear, and biorthogonal.
A new paper is added to the collection of reproducible documents: Elastic wave-vector decomposition in heterogeneous anisotropic media
The goal of wave-mode separation and wave-vector decomposition is to separate full elastic wavefield into three wavefields with each corresponding to a different wave mode. This allows elastic reverse-time migration to handle of each wave mode independently . Several of the previously proposed methods to accomplish this task require the knowledge of the polarization vectors of all three wave modes in a given anisotropic medium. We propose a wave-vector decomposition method where the wavefield is decomposed in the wavenumber domain via the analytical decomposition operator with improved computational efficiency using low-rank approximations. The method is applicable for general heterogeneous anisotropic media. To apply the proposed method in low-symmetry anisotropic media such as orthorhombic, monoclinic, and triclinic, we define the two S modes by sorting them based on their phase velocities (S1 and S2), which are defined everywhere except at the singularities. The singularities can be located using an analytical condition derived from the exact phase-velocity expressions for S waves. This condition defines a weight function, which can be applied to attenuate the planar artifacts caused by the local discontinuity of polarization vectors at the singularities. The amplitude information lost because of weighting can be recovered using the technique of local signal-noise orthogonalization. Numerical examples show that the proposed approach provides an effective decomposition method for all wave modes in heterogeneous, strongly anisotropic media.