On robust estimation of the location parameter

Application of supervised machine learning paradigms in the prediction of petroleum reservoir properties: Comparative analysis of ANN and SVM models

The scalar images (PP, PS, SP, and SS) of elastic reverse time migration (ERTM) can be generated by applying an imaging condition as crosscorrelation of pure wave modes. In conventional ERTM, Helmholtz decomposition is commonly applied in wavefield separation, which leads to a polarity reversal problem in converted-wave images because of the opposite polarity distributions of the S-wavefields. Polarity reversal of the converted-wave image will cause destructive interference when stacking over multiple shots. Besides, in the 3D case, the curl calculation generates a vector S-wave, which makes it impossible to produce scalar PS, SP, and SS images with the crosscorrelation imaging condition. We evaluate a vector-based ERTM (VB-ERTM) method to address these problems. In VB-ERTM, an amplitude-preserved wavefield separation method based on decoupled elastic wave equation is exploited to obtain the pure wave modes. The output separated wavefields are both vectorial. To obtain the scalar images, the scala...

Vector-based elastic reverse time migration based on scalar imaging condition

We use elastic least-squares reverse time migration (LSRTM) to invert for the reflectivity images of P- and S-wave impedances. Elastic LSRTM solves the linearized elastic-wave equations for forward modeling and the adjoint equations for backpropagating the residual wavefield at each iteration. Numerical tests on synthetic data and field data reveal the advantages of elastic LSRTM over elastic reverse time migration (RTM) and acoustic LSRTM. For our examples, the elastic LSRTM images have better resolution and amplitude balancing, fewer artifacts, and less crosstalk compared with the elastic RTM images. The images are also better focused and have better reflector continuity for steeply dipping events compared to the acoustic LSRTM images. Similar to conventional least-squares migration, elastic LSRTM also requires an accurate estimation of the P- and S-wave migration velocity models. However, the problem remains that, when there are moderate errors in the velocity model and strong multiples, LSRTM ...

/pdf/elastic-least-squares-reverse-time-migration-1a12egarwe.pdf

Elastic least-squares reverse time migration

Polarity changes in converted-wave images constructed by elastic reverse time migration cause destructive interference after stacking over the experiments of a seismic survey. This polarity reversal is due to PS and SP reflectivities reversing sign at certain incidence angles, e.g., at normal incidence in isotropic media. Many of the available polarity correction methods are complex and require costly transformations, e.g., to the angle domain. We derive a simple imaging condition for converted waves to correct the image polarity and reveal the conversion strength from one wave mode to another. Our imaging condition exploits pure P- and S-modes obtained by Helmholtz decomposition. Instead of correlating Cartesian components of the vector S-mode with the P-mode, we exploit all three components of the S wavefield at once to produce a unique image. We generate PS and SP images using geometric relationships among the propagation directions for the P- and S-wavefields, the reflector orientation, and th...

Scalar imaging condition for elastic reverse time migration

Polarity reversals in PS and SP images of elastic reverse time migration will cause destructive interference in the final stacked results, which may lead to an erroneous interpretation. We derive a polarity reversal correction based on an analysis of the polarity distribution of PS and SP images. The key aspect for a polarity reversal correction is the polarity distribution of the S-wave component. Polarity reversal correction methods can be performed according to the actual patterns of the polarity distribution in gathers. For the 2D isotropic case, a sign factor is introduced to represent the polarity distribution of the S-wave component; this sign factor can be computed using the energy flux density vector. We present a procedure to correct the polarity reversal for elastic reverse time migration in the common-shot domain. First, the sign factor is computed during the wavefield reconstruction for every imaging point. Then, the polarity reversal is corrected by multiplying the PS and SP images with the sign factor at every time step when an elastic imaging condition is applied. We also design a filter algorithm for the sign factor to improve its consistency along an event and thereby to diminish the impact of the inaccuracy of the energy flux density vector and to improve the imaging results. Numerical examples have shown that the polarity reversal correction procedure works and that the sign filter algorithm successfully eliminates the consequences of the inaccuracy of the energy flux density vector. The quality of the migration events is effectively improved.

Polarity reversal correction for elastic reverse time migration

One of the important features of elastic reverse-time migration is that it is a depth domain prestack migration method based on a vectorial wavefield. PP- and PS-wave images can be easily generated by implementing an imaging condition to pure wave modes separated with divergence and curl operators in isotropic media. In the 3D case, however, the curl calculation will generate a 3C vector S-wave, which makes it impossible to generate a scalar PS image with the crosscorrelation imaging condition. Therefore, we first analyzed the polarity distribution of a 3D S-wave and concluded that the separated S-wave keeps perpendicular to a plane determined by the particle motion direction and the propagation direction of the S-wave. This specific plane is the raypath plane when the S-wave is excited by an incident P-wave. The normal direction of the raypath plane can be calculated by computing the vector product of the propagation directions of source and receiver wavefields. Then, we used this normal directio...

3D PS-wave imaging with elastic reverse-time migration

Sparse domain thresholding filters operating in a sparse domain are highly effective in removing Gaussian random noise under Gaussian distribution assumption. Erratic noise, which designates non-Gaussian noise that consists of large isolated events with known or unknown distribution, also needs to be explicitly taken into account. However, conventional sparse domain thresholding filters based on the least-squares (LS) criterion are severely sensitive to data with high-amplitude and non-Gaussian noise, i.e., the erratic noise, which makes the suppression of this type of noise extremely challenging. In this paper, we present a robust sparsity-promoting denoising model, in which the LS criterion is replaced by the Huber criterion to weaken the effects of erratic noise. The random and erratic noise is distinguished by using a data-adaptive parameter in the presented method, where random noise is described by mean square, while the erratic noise is downweighted through a damped weight. Different from conventional sparse domain thresholding filters, definition of the misfit between noisy data and recovered signal via the Huber criterion results in a nonlinear optimization problem. With the help of theoretical pseudoseismic data, an iterative robust sparsity-promoting filter is proposed to transform the nonlinear optimization problem into a linear LS problem through an iterative procedure. The main advantage of this transformation is that the nonlinear denoising filter can be solved by conventional LS solvers. Tests with several data sets demonstrate that the proposed denoising filter can successfully attenuate the erratic noise without damaging useful signal when compared with conventional denoising approaches based on the LS criterion.

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

We evaluated a new spectral method and a new finite-difference (FD) method for seismic-wave extrapolation in time. Using staggered temporal and spatial grids, we derived a wave-extrapolation operator using a lowrank decomposition for a first-order system of wave equations and designed the corresponding FD scheme. The proposed methods extend previously proposed lowrank and lowrank FD wave extrapolation methods from the cases of constant density to those of variable density. Dispersion analysis demonstrated that the proposed methods have high accuracy for a wide wavenumber range and significantly reduce the numerical dispersion. The method of manufactured solutions coupled with mesh refinement was used to verify each method and to compare numerical errors. Tests on 2D synthetic examples demonstrated that the proposed method is highly accurate and stable. The proposed methods can be used for seismic modeling or reverse-time migration.

https://www.ahay.org/RSF/book/tccs/sglowrank/paper.pdf

Qizhen Du

Papers

Polarity reversal correction for elastic reverse time migration

Vector-based elastic reverse time migration based on scalar imaging condition

3D PS-wave imaging with elastic reverse-time migration

Signal-Preserving Erratic Noise Attenuation via Iterative Robust Sparsity-Promoting Filter

Lowrank seismic-wave extrapolation on a staggered grid