## Missing log data interpolation and semiautomatic seismic well ties

May 7, 2019 Documentation No comments

Relating well log data, measured in depth, to seismic data, measured in time, typically requires estimating well log impedance and a time-to-depth relationship using available sonic and density logs. When sonic and density logs are not available, it is challenging to incorporate wells into integrated reservoir studies as the wells cannot be tied to seismic. We propose a workflow to estimate missing well log information, automatically tie wells to seismic data and generate a global well-log property volume using data matching techniques. We first use local similarity scan to align all logs to constant geologic time and interpolate missing well log information. Local similarity is then used to tie available wells with seismic data. Finally, log data from each well is interpolated along local seismic structures to generate global log property volumes. We use blind well tests to verify the accuracy of well-log interpolation and seismic-well ties. Applying the proposed workflow to a 3D seismic dataset with 26 wells achieves consistent and verifiably accurate results.

## Seismic data interpolation using seislet transform

May 7, 2019 Documentation No comments

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.

## Predictive painting across faults

May 7, 2019 Documentation No comments

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.

## 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.

## $Q$-compensated Least Squares RTM

May 3, 2019 Documentation No comments

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.