A new paper is added to the collection of reproducible documents: Diffraction imaging and time-migration velocity analysis using oriented velocity continuation
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.
10 previous programs of the month:
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.
A new paper is added to the collection of reproducible documents: Theory of interval traveltime parameter estimation in layered anisotropic media
Moveout approximations for reflection traveltimes are typically based on a truncated Taylor expansion of traveltime squared around zero offset. The fourth-order Taylor expansion involves NMO velocities and quartic coefficients. We derive general expressions for layer-stripping both second- and fourth-order parameters in horizontally-layered anisotropic strata and specify them for two important cases: horizontally stacked aligned orthorhombic layers and azimuthally rotated orthorhombic layers. In the first of these cases, the formula involving the out-of-symmetry-plane quartic coefficients has a simple functional form and possesses some similarity to the previously known formulas corresponding to the 2D in-symmetry-plane counterparts in VTI media. The error of approximating effective parameters by using approximate VTI formulas can be significant in comparison with the exact formulas derived in this paper. We propose a framework for deriving Dix-type inversion formulas for interval parameter estimation from traveltime expansion coefficients both in the general case and in the specific case of aligned orthorhombic layers. The averaging formulas for calculation of effective parameters and the layer-stripping formulas for interval parameter estimation are readily applicable to 3D seismic reflection processing in layered anisotropic media.