A new paper is added to the collection of reproducible documents: Seismic data interpolation using generalised velocity-dependent seislet transform
Data interpolation is an important step for seismic data analysis because many processing tasks, such as multiple attenuation and migration, are based on regularly sampled seismic data. Failed interpolations may introduce artifacts and eventually lead to inaccurate final processing results. In this paper, we generalize seismic data interpolation as a basis pursuit problem and propose an iteration framework for recovering missing data. The method is based on nonlinear iteration and sparse transform. A modified Bregman iteration is used for solving the constrained minimization problem based on compressed sensing. The new iterative strategy guarantees fast convergence by using a fixed threshold value. We also propose a generalized velocity-dependent (VD) formulation of the seislet transform as an effective sparse transform, in which the nonhyperbolic normal moveout equation serves as a bridge between local slope patterns and moveout parameters in the common-midpoint domain. It can also be reduced to the traditional VD-seislet if special heterogeneity parameter is selected. The generalized VD-seislet transform predicts prestack reflection data in offset coordinates, which provides a high compression of reflection events. The method was applied to synthetic and field data examples and the results show that the generalized VD-seislet transform can reconstruct missing data with the help of the modified Bregman iteration even for nonhyperbolic reflections under complex conditions, such as VTI media or aliasing.
A new paper is added to the collection of reproducible documents: Predictive painting across faults
Predictive painting can effectively spread information in 3D volumes following the local structures (dips) of seismic events. However, it has troubles spreading information across faults with significant displacement. To address this problem, we propose to incorporate fault slip information into predictive painting to correctly spread information across faults. The fault slip is obtained by using a local similarity scan to measure local shifts of the different sides of a fault. We propose three different methods to utilize the fault slip information: 1) area partition method, which uses fault slip to correct the painting result after predictive painting in each divided area; 2) fault-zone replacement method, which replaces fault zones with smooth transitions calculated with the fault slip information to avoid sharp jumps; and 3) unfaulting method, where we use the fault slip information to unfault the volume, perform predictive painting in the unfaulted domain, and then map the painting result back to the original space. The proposed methods are tested in application of predictive painting to horizon picking. Numerical examples demonstrate that predictive painting after incorporating fault slip information can correctly spread information across faults, which makes the proposed three approaches of utilizing fault slip information effective and applicable.
A new paper is added to the collection of reproducible documents: Streaming orthogonal prediction filter in $t$ -$x$ domain for random noise attenuation
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.
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.
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.
10 previous programs of the month:
A new paper is added to the collection of reproducible documents: $Q$-compensated least-squares reverse time migration using lowrank one-step wave extrapolation
Attenuation of seismic waves needs to be taken into account in order to improve the accuracy of seismic imaging. In viscoacoustic media, reverse time migration (RTM) can be performed with $Q$-compensation, which is also known as $Q$-RTM. Least-squares RTM (LSRTM) has also been shown to be able to compensate for attenuation through linearized inversion. However, seismic attenuation may significantly slow down the convergence rate of the least-squares iterative inversion process without proper preconditioning. We show that incorporating attenuation compensation into LSRTM can improve the speed of convergence in attenuating media, obtaining high-quality images within the first few iterations. Based on the lowrank one-step seismic modeling operator in viscoacoustic media, we derive its adjoint operator using non-stationary filtering theory. The proposed forward and adjoint operators can be efficiently applied to propagate viscoacoustic waves and to implement attenuation compensation. Recognizing that, in viscoacoustic media, the wave equation Hessian may become ill-conditioned, we propose to precondition LSRTM with $Q$-compensated RTM. Numerical examples show that the resulting $Q$-LSRTM method has a significantly faster convergence rate than LSRTM, and thus is preferable for practical applications.
A new paper is added to the collection of reproducible documents: EMD-seislet transform
The seislet transform uses a prediction operator which is connected to the local slope or frequency of seismic events. In this paper, we propose combining the 1D non-stationary seislet transform with empirical mode decomposition (EMD) in the $f-x$ domain. We use the EMD to decompose data into smoothly variable frequency components for the following 1D seislet transform. The resultant representation shows remarkable sparsity. We introduce the detailed algorithm and use a field example to demonstrate the application of the new seislet transform for sparsity-promoting seismic data processing.
The example in rsf/tutorials/wavelet reproduces the tutorial from Evan Bianco on wavelet estimation for well ties.
The tutorial was published in the June 2016 issue of The Leading Edge.
Madagascar users are encouraged to try improving the results.
A new paper is added to the collection of reproducible documents: 2D modeling and basic processing with Madagascar
This reproducible document was created during the 2017 Working Workshop in Houston.
This document demonstrates finite difference modeling and simple processing using the Madagascar software package. The paper uses this simple processing sequence to teach the basics of Madagascar.
The SEGY file of the Marmousi2 model is downloaded from the Internet and used to create a few synthetic shots. Geometry is computed and loaded in the trace headers. Simple processing including amplitude correction, CMP sorting, velocity conversions, NMO correction, stack, Kirchhoff migration, and least squares Kirchhoff migration are applied. Displays of each processing stage are created. The full processing sequence takes less that 6 minutes on a 2013 MacBook Pro computer.
Working Workshops as opposed to “talking workshops” are meetings where the participants collaborate in small groups to develop new software code or to conduct computational experiments addressing a particular problem.
The 2018 Working Workshop took place in Houston on August 8-11. It was hosted by the University of Houston and organized by Karl Schleicher. The topic of the workshop was Python and Julia programming languages, as well as their interfaces to Madagascar.
The workshop attracted 16 participants (students, academic staff, and industry professionals) from 12 different organizations. Software projects included such topics as machine learning, 3D plotting, parallel processing, wave equation modeling, and well log analysis.