## Streaming PF for random noise attenuation

May 6, 2019 Documentation No comments

In seismic exploration there are many sources of random noise, for example, scattering from a complex surface. Prediction filters (PFs) have been widely used for random noise attenuation, but these typically assume that the seismic signal is stationary. Seismic signals are fundamentally nonstationary. Stationary PFs fail in the presence of nonstationary events, even if the data are cut into overlapping windows (“patching”). We propose an adaptive PF method based on streaming and orthogonalization for random noise attenuation in the $t$-$x$ domain. Instead of using patching or regularization, the streaming orthogonal prediction filter (SOPF) takes full advantage of the streaming method, which generates the signal value as each new noisy data value arrives. The streaming signal-and-noise orthogonalization further improves the signal recovery ability of the SOPF. The streaming characteristic makes the proposed method faster than iterative approaches. In comparison with $f$-$x$ deconvolution and $f$-$x$ regularized nonstationary autoregression (RNA), we tested the feasibility of the proposed method in attenuating random noise on two synthetic datasets. Field data examples confirmed that the $t$-$x$ SOPF had a reasonable denoising ability in practice.

## Least-squares diffraction imaging

May 6, 2019 Documentation No comments

A new paper is added to the collection of reproducible documents: Least-squares path-summation diffraction imaging using sparsity constraints

Diffraction imaging aims to emphasize small-scale subsurface heterogeneities such as faults, pinch-outs, fracture swarms, channels, etc. and can help seismic reservoir characterization. The key step in diffraction imaging workflows is based on the separation procedure suppressing higher-energy reflections and emphasizing diffractions, after which diffractions can be imaged independently. Separation results often contain crosstalk between reflections and diffractions and are prone to noise. We propose an inversion scheme to reduce the crosstalk and denoise diffractions. The scheme decomposes an input full wavefield into three components: reflections, diffractions and noise. We construct the inverted forward modeling operator as the chain of three operators: Kirchhoff modeling, plane wave destruction and path-summation integral filter. Both reflections and diffractions have the same modeling operator. Separation of the components is done by shaping regularization. We impose sparsity constraints to extract diffractions, enforce smoothing along dominant local event slopes to restore reflections and suppress the crosstalk between the components by local signal-and-noise orthogonalization. Synthetic and field data examples confirm the effectivness of the proposed method.

## Program of the month: sfzomig3

May 6, 2019 Programs No comments

sfzomig3 performs 3-D zero-offset modeling or migration using one-way wave extrapolation and the exploding reflector concept.

The following example from rsf/su/rsflab10 shows the result of migrating the benchmark Viking Graben dataset.

The algorithm used by sfzomig3 is known as extended split-step or phase-shift plus interpolation (PSPI). It works in the frequency domain and mixed space-wavenumber domain.

• Gazdag, J., and Sguazzero, P., 1984, Migration of seismic data by phase shift plus interpolation: Geophysics, 49, 124-131.
• Kessinger, W., 1992, Extended split-step Fourier migration: 62nd Ann.
Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, 917-920.

Depending on inv= flag, sfzomig3 performs modeling or migration (if mode=m) or datuming (upward or downward) wavefield continuation (if mode=d). The default is migration (mode=m inv=n).

The algorithm efficiency depends on the number of reference velocities, which corresponds to the number of spatial Fourier transforms. By default, the algorithm is trying to estimate this number automatically at each depth step. The maximum number can be set by nrmax=.

The pmx=, pmy=, and tmx=, tmy= parameters control padding and tapering in space, needed to avoid boundary reflections and Fourier wrap-around artifacts.