Estimation of the conversion point position in elastic orthorhombic media

Shibo Xu; Alexey Stovas

doi:10.1190/geo2018-0375.1

Estimation of the conversion point position in elastic orthorhombic media

Geophysics ◽

10.1190/geo2018-0375.1 ◽

2019 ◽

Vol 84 (1) ◽

pp. C15-C25 ◽

Cited By ~ 2

Author(s):

Shibo Xu ◽

Alexey Stovas

Keyword(s):

Real Data ◽

Processing Parameters ◽

Position Estimation ◽

Point Estimation ◽

Radial Coordinate ◽

Converted Wave ◽

Rational Form ◽

Point Position ◽

Conversion Point ◽

Wave Modes

Determination of the conversion point position is very important to carry out seismic processing in the common conversion point gather of converted wave data. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from real data. To estimate the conversion point in an elastic orthorhombic (ORT) medium, we have defined an explicit rational form approximation for the radial coordinate of the conversion point for converted [Formula: see text], [Formula: see text], and [Formula: see text] waves. To obtain the approximation coefficients, the Taylor series approximation in the corresponding vertical slowness for three pure wave modes is applied. The coefficients in our proposed approximation are computed within two vertical symmetry planes. The difference between the acquisition azimuth and the azimuth of the conversion point position is analyzed for different combinations of the wave modes. The accuracy of the conversion point position estimation for three ORT models is illustrated in the numerical examples. One can see from the results that for converted [Formula: see text] and [Formula: see text] waves, our approximation is very accurate in estimating the conversion point position regardless of the tested ORT model. For a converted [Formula: see text] wave, due to the existence of cusps, triplications, and shear singularities, the error in conversion point estimation is relatively larger compared with PS-waves in the vicinity of the singularity point.

Download Full-text

Traveltime approximation for converted waves in elastic orthorhombic media

Geophysics ◽

10.1190/geo2018-0828.1 ◽

2019 ◽

Vol 84 (5) ◽

pp. C229-C237 ◽

Cited By ~ 2

Author(s):

Shibo Xu ◽

Alexey Stovas

Keyword(s):

Seismic Data ◽

Real Data ◽

Processing Parameters ◽

Model Parameters ◽

Seismic Data Processing ◽

Converted Wave ◽

Rational Form ◽

Time Migration ◽

Taylor Series Approximation ◽

Anisotropy Parameters

The moveout approximations are commonly used in seismic data processing such as velocity analysis, modeling, and time migration. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from the real data. To approximate the traveltime in an elastic orthorhombic (ORT) medium, we defined an explicit rational-form approximation for the traveltime of the converted [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves. To obtain the expression of the coefficients, the Taylor-series approximation is applied in the corresponding vertical slowness for three pure-wave modes. By using the effective model parameters for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves, the coefficients in the converted-wave traveltime approximation can be represented by the anisotropy parameters defined in the elastic ORT model. The accuracy in the converted-wave traveltime for three ORT models is illustrated in numerical examples. One can see from the results that, for converted [Formula: see text]- and [Formula: see text]-waves, our rational-form approximation is very accurate regardless of the tested ORT model. For a converted [Formula: see text]-wave, due to the existence of cusps, triplications, and shear singularities, the error is relatively larger compared with PS-waves.

Download Full-text

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

Geophysics ◽

10.1190/geo2016-0146.1 ◽

2017 ◽

Vol 82 (2) ◽

pp. S111-S127 ◽

Cited By ~ 52

Author(s):

Qizhen Du ◽

ChengFeng Guo ◽

Qiang Zhao ◽

Xufei Gong ◽

Chengxiang Wang ◽

...

Keyword(s):

Alternative Methods ◽

Polarity Reversal ◽

Reverse Time ◽

Reverse Time Migration ◽

S Wave ◽

Converted Wave ◽

Imaging Condition ◽

Time Migration ◽

Wavefield Separation ◽

Wave Modes

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 scalar imaging condition in which the scalar product of two vector wavefields with source-normalized illumination is exploited to produce scalar images instead of correlating Cartesian components or magnitude of the vector P- and S-wave modes. Compared with alternative methods for correcting the polarity reversal of PS and SP images, our ERTM solution is more stable and simple. Besides these four scalar images, the VB-ERTM method generates another PP-mode image by using the auxiliary stress wavefields. Several 2D and 3D numerical examples are evaluated to demonstrate the potential of our ERTM method.

Download Full-text

Survival estimation for singly type one censored sample based on generalized Rayleigh distribution

Baghdad Science Journal ◽

10.21123/bsj.11.2.193-201 ◽

2014 ◽

Vol 11 (2) ◽

pp. 193-201

Author(s):

Baghdad Science Journal

Keyword(s):

Current Model ◽

Survival Function ◽

Information Matrix ◽

Interval Estimation ◽

Real Data ◽

Rayleigh Distribution ◽

Point Estimation ◽

Distribution Model ◽

Unknown Parameters ◽

Generalized Rayleigh Distribution

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

Download Full-text

P–S converted wave: conversion point and zero-offset energy in anisotropic media

Journal of Applied Geophysics ◽

10.1016/j.jappgeo.2004.04.007 ◽

2004 ◽

Vol 56 (3) ◽

pp. 155-163 ◽

Cited By ~ 2

Author(s):

Fredy A.V. Artola ◽

Ricardo Leiderman ◽

Sergio A.B. Fontoura ◽

Mércia B.C. Silva

Keyword(s):

Anisotropic Media ◽

Converted Wave ◽

Conversion Point ◽

Zero Offset ◽

Wave Conversion

Download Full-text

Wave-equation angle-domain common-image gathers for converted waves

Geophysics ◽

10.1190/1.2821193 ◽

2008 ◽

Vol 73 (1) ◽

pp. S17-S26 ◽

Cited By ~ 36

Author(s):

Daniel A. Rosales ◽

Sergey Fomel ◽

Biondo L. Biondi ◽

Paul C. Sava

Keyword(s):

Seismic Data ◽

Incidence Angle ◽

Velocity Ratio ◽

Real Data ◽

Single Mode ◽

Practical Application ◽

Converted Wave ◽

Reflection Angle ◽

Wavefield Extrapolation ◽

Local Image

Wavefield-extrapolation methods can produce angle-domain common-image gathers (ADCIGs). To obtain ADCIGs for converted-wave seismic data, information about the image dip and the P-to-S velocity ratio must be included in the computation of angle gathers. These ADCIGs are a function of the half-aperture angle, i.e., the average between the incidence angle and the reflection angle. We have developed a method that exploits the robustness of computing 2D isotropic single-mode ADCIGs and incorporates both the converted-wave velocity ratio [Formula: see text] and the local image dip field. It also maps the final converted-wave ADCIGs into two ADCIGs, one a function of the P-incidence angle and the other a function of the S-reflection angle. Results with both synthetic and real data show the practical application for converted-wave ADCIGs. The proposed approach is valid in any situation as long as the migration algorithm is based on wavefield downward continuation and the final prestack image is a function of the horizontal subsurface offset.

Download Full-text

RGBD Based Gaze Estimation via Multi-Task CNN

Proceedings of the AAAI Conference on Artificial Intelligence ◽

10.1609/aaai.v33i01.33012488 ◽

2019 ◽

Vol 33 ◽

pp. 2488-2495 ◽

Cited By ~ 1

Author(s):

Dongze Lian ◽

Ziheng Zhang ◽

Weixin Luo ◽

Lina Hu ◽

Minye Wu ◽

...

Keyword(s):

Large Scale ◽

Image Synthesis ◽

Position Estimation ◽

Point Estimation ◽

Head Pose Estimation ◽

Depth Image ◽

Eye Position ◽

Gaze Estimation ◽

Head Pose ◽

Gaze Tracking

This paper tackles RGBD based gaze estimation with Convolutional Neural Networks (CNNs). Specifically, we propose to decompose gaze point estimation into eyeball pose, head pose, and 3D eye position estimation. Compared with RGB image-based gaze tracking, having depth modality helps to facilitate head pose estimation and 3D eye position estimation. The captured depth image, however, usually contains noise and black holes which noticeably hamper gaze tracking. Thus we propose a CNN-based multi-task learning framework to simultaneously refine depth images and predict gaze points. We utilize a generator network for depth image generation with a Generative Neural Network (GAN), where the generator network is partially shared by both the gaze tracking network and GAN-based depth synthesizing. By optimizing the whole network simultaneously, depth image synthesis improves gaze point estimation and vice versa. Since the only existing RGBD dataset (EYEDIAP) is too small, we build a large-scale RGBD gaze tracking dataset for performance evaluation. As far as we know, it is the largest RGBD gaze dataset in terms of the number of participants. Comprehensive experiments demonstrate that our method outperforms existing methods by a large margin on both our dataset and the EYEDIAP dataset.

Download Full-text

Traveltime and relative geometric spreading approximation in elastic orthorhombic medium

Geophysics ◽

10.1190/geo2019-0811.1 ◽

2020 ◽

Vol 85 (5) ◽

pp. C153-C162 ◽

Cited By ~ 1

Author(s):

Shibo Xu ◽

Alexey Stovas ◽

Hitoshi Mikada

Keyword(s):

Seismic Data ◽

Real Data ◽

P Wave ◽

Form Expression ◽

Amplitude Variation ◽

Rational Form ◽

Amplitude Variation With Offset ◽

Practical Applications ◽

Numerical Tests ◽

Geometric Spreading

Wavefield properties such as traveltime and relative geometric spreading (traveltime derivatives) are highly essential in seismic data processing and can be used in stacking, time-domain migration, and amplitude variation with offset analysis. Due to the complexity of an elastic orthorhombic (ORT) medium, analysis of these properties becomes reasonably difficult, where accurate explicit-form approximations are highly recommended. We have defined the shifted hyperbola form, Taylor series (TS), and the rational form (RF) approximations for P-wave traveltime and relative geometric spreading in an elastic ORT model. Because the parametric form expression for the P-wave vertical slowness in the derivation is too complicated, TS (expansion in offset) is applied to facilitate the derivation of approximate coefficients. The same approximation forms computed in the acoustic ORT model also are derived for comparison. In the numerical tests, three ORT models with parameters obtained from real data are used to test the accuracy of each approximation. The numerical examples yield results in which, apart from the error along the y-axis in ORT model 2 for the relative geometric spreading, the RF approximations all are very accurate for all of the tested models in practical applications.

Download Full-text