Month: October 2015

Velocity-dependent seislet transform

October 25, 2015 Documentation No comments

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.

Program of the month: sfisolr2

October 15, 2015 Programs No comments

sfisolr2 performs low-rank decomposition for wave propagation in a 2-D isotropic medium using lowrank approximation method.

The output of sfisolr2 can be used by other programs, such as sffftwave2 or sffftexp0 to perform wave modeling or reverse-time migration.

The following example from tccs/lowrank/impres shows a wave snapshot from a point source in an isotropic medium with a variable velocity.

sfisolr2 takes two inputs: the velocity model as standard input and the file given by fft= to specify the dimensions of the Fourier-transformed grid (the values in this file are not used). The program produces two outputs: the right decomposition matrix in the standard output, and the left decomposion matrix specified by left=. To make the results reproducible despite the randomization algorithm, set seed= for pseudorandom number generation.

The rank of the lowrank approximation is controlled by several parameters. The most important of those is the time step size dt=. The other controlling parameters are the approximation tolerance eps= and the number of random probes (maximum rank) npk=.

The related programs are sfanisolr2 for the anisotropic (TTI) case, and sfisolr3 for the 3-D case. The following example from tccs/lowrank/threed shows a 3-D wavefield snapshot computed with sfisolr3:

10 previous programs of the month: