A new paper is added to the collection of reproducible documents:
Seismic dip estimation based on the two-dimensional Hilbert transform and its application in random noise attenuation

In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional (2D) derivatives and the 2D Hilbert transform (Riesz transform). Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.

A new paper is added to the collection of reproducible documents:
Structure-constrained relative acoustic impedance using stratigraphic coordinates

Acoustic impedance inversion involves conversion of seismic traces to a reflection coefficient time series, and then into acoustic impedance. The usual assumption for the transformation of post-stack seismic data into impedance , is that seismic traces can be modeled using the simple convolutional model. According to the convolutional model, a seismic trace is a normal-incidence record, which is an assumption that is strictly true only if the earth structure is composed of horizontal layers. In the presence of dipping layers, such an assumption is violated, which introduces bias in the result of impedance inversion. I propose to implement impedance inversion in the stratigraphic coordinate system, where the vertical direction is normal to reflectors and seismic traces represent normal-incidence seismograms. Tests on field data produce more accurate and detailed impedance results from inversion in the stratigraphic coordinate system, compared to impedance results using the conventional Cartesian coordinate system.

A new paper is added to the collection of reproducible documents:
Seislet-based morphological component analysis using scale-dependent exponential shrinkage

Morphological component analysis (MCA) is a powerful tool used in image processing to separate different geometrical components (cartoons and textures, curves and points etc). MCA is based on the observation that many complex signals may not be sparsely represented using only one dictionary/transform, however can have sparse representation by combining several over-complete dictionaries/transforms. In this paper we propose seislet-based MCA for seismic data processing. MCA algorithm is reformulated in the shaping-regularization framework. Successful seislet-based MCA depends on reliable slope estimation of seismic events, which is done by plane-wave destruction (PWD) filters. An exponential shrinkage operator unifies many existing thresholding operators and is adopted in scale-dependent shaping regularization to promote sparsity. Numerical examples demonstrate a superior performance of the proposed exponential shrinkage operator and the potential of seislet-based MCA in application to trace interpolation and multiple removal.

A new paper is added to the collection of reproducible documents:
A fast algorithm for 3D azimuthally anisotropic velocity scan

Conventional velocity scan can be computationally expensive for large-size seismic data, particularly when the presence of anisotropy requires multiparameter estimation. We introduce a fast algorithm for 3D azimuthally anisotropic velocity scan, which is a generalization of the previously proposed 2D butterfly algorithm for hyperbolic Radon transform. To compute the semblance in a two-parameter residual moveout domain, the numerical complexity of our algorithm is roughly as opposed to of the straightforward velocity scan, with being representative of the number of points in either dimension of data space or parameter space. We provide both synthetic and field-data examples to illustrate the efficiency and accuracy of the algorithm.

Another old paper is added to the collection of reproducible documents:
Multiple suppression using prediction-error filter

I present an approach to multiple suppression, that is based on the moveout between primary and multiple events in the CMP gather. After normal moveout correction, primary events will be horizontal, whereas multiple events will not be. For each NMOed CMP gather, I reorder the offset in random order. Ideally, this process has little influence on the primaries, but it destroys the shape of the multiples. In other words, after randomization of the offset order, the multiples appear as random noise. This “man-made” random noise can be removed using prediction-error filter (PEF). The randomization of the offset order can be regarded as a random process, so we can apply it to the CMP gather many times and get many different samples. All the samples can be arranged into a 3-D cube, which is further divided into many small subcubes. A 3-D PEF can then be estimated from each subcube and re-applied to it to remove the multiple energy. After that, all the samples are averaged back into one CMP gather, which is supposed to be free of multiple events. In order to improve the efficiency of the algorithm of estimating the PEF for each subcube, except for the first subcube which starts with a zero-valued initial guess, all the subsequent subcubes take the last estimated PEF as an initial guess. Therefore, the iteration count can be reduced to one step for all the subsequent subcubes with little loss of accuracy. Three examples demonstrate the performance of this new approach, especially in removing the near-offset multiples.

A new paper is added to the collection of reproducible documents:
A graphics processing unit implementation of time-domain full-waveform inversion

The graphics processing unit (GPU) has become a popular device for seismic imaging and inversion due to its superior speedup performance. In this paper we implement GPU-based full waveform inversion (FWI) using the wavefield reconstruction strategy. Because the computation on GPU is much faster than CPU-GPU data communication, in our implementation the boundaries of the forward modeling are saved on the device to avert the issue of data transfer between host and device. The Clayton-Enquist absorbing boundary is adopted to maintain the efficiency of GPU computation. A hybrid nonlinear conjugate gradient algorithm combined with the parallel reduction scheme is utilized to do computation in GPU blocks. The numerical results confirm the validity of our implementation.

Another old paper is added to the collection of reproducible documents:
When is anti-aliasing needed in Kirchhoff migration?

We present criteria to determine when numerical integration of seismic data will incur operator aliasing. Although there are many ways to handle operator aliasing, they add expense to the computational task. This is especially true in three dimensions. A two-dimensional Kirchhoff migration example illustrates that the image zone of interest may not always require anti-aliasing and that considerable cost may be spared by not incorporating it.

A new paper is added to the collection of reproducible documents:
Stratigraphic coordinates, a coordinate system tailored to seismic interpretation

In certain seismic data processing and interpretation tasks, such as spiking deconvolution, tuning analysis, impedance inversion, spectral decomposition, etc., it is commonly assumed that the vertical direction is normal to reflectors. This assumption is false in the case of dipping layers and may therefore lead to inaccurate results. To overcome this limitation, we propose a coordinate system in which geometry follows the shape of each reflector and the vertical direction corresponds to normal reflectivity. We call this coordinate system stratigraphic coordinates. We develop a constructive algorithm that transfers seismic images into the stratigraphic coordinate system. The algorithm consists of two steps. First, local slopes of seismic events are estimated by plane-wave destruction; then structural information is spread along the estimated local slopes, and horizons are picked everywhere in the seismic volume by the predictive-painting algorithm. These picked horizons represent level sets of the first axis of the stratigraphic coordinate system. Next, an upwind finite-difference scheme is used to find the two other axes, which are perpendicular to the first axis, by solving the appropriate gradient equations. After seismic data are transformed into stratigraphic coordinates, seismic horizons should appear flat, and seismic traces should represent the direction normal to the reflectors. Immediate applications of the stratigraphic coordinate system are in seismic image flattening and spectral decomposition. Synthetic and real data examples demonstrate the effectiveness of stratigraphic coordinates.

A new paper is added to the collection of reproducible documents:
Carbonate reservoir characterization using seismic diffraction imaging

Although extremely prolific worldwide, carbonate reservoirs are challenging to characterize using traditional seismic reflection imaging techniques. We use computational experiments with synthetic models to demonstrate the possibility seismic diffraction imaging has of overcoming common obstacles associated with seismic reflection imaging and aiding interpreters of carbonate systems. Diffraction imaging improves the horizontal resolution of individual voids in a karst reservoir model and identification of heterogeneous regions below the resolution of reflections in a reservoir scale model.

A new paper is added to the collection of reproducible documents:
Random noise attenuation using local signal-and-noise orthogonalization

We propose a novel approach to attenuate random noise based on local signal-and-noise orthogonalization. In this approach, we first remove noise using one of the conventional denoising operators, and then apply a weighting operator to the initially denoised section in order to predict the signal-leakage energy and retrieve it from the initial noise section. The weighting operator is obtained by solving a least-squares minimization problem via shaping regularization with a smoothness constraint. Next, the initially denoised section and the retrieved signal are combined to form the final denoised section. The proposed denoising approach corresponds to orthogonalizing the initially denoised signal and noise in a local manner. We evaluate denoising performance by using local similarity. In order to test the orthogonalization property of the estimated signal and noise, we calculate the local similarity map between the denoised signal section and removed noise section. Low values of local similarity indicate a good orthogonalization and thus a good denoising performance. Synthetic and field data examples demonstrate the effectiveness of the proposed approach in applications to noise attenuation for both conventional and simultaneous-source seismic data.