Gaussian beam velocity tomography based on azimuth-opening angle domain common imaging gathers

Abstract Ray-based tomography in the imaging domain, implemented with seismic migration, is currently widely used in industrial applications. However, conventional ray-based tomography has some inherent problems, such as shadow area, multi-path problem and so on, which limit the inversion accuracy. To alleviate these problems, we proposed Gaussian beam velocity tomography (GBT) based on azimuth-opening angle domain common imaging gathers (ADCIGs). According to the first-order Born and Rytov approximations, we derived a linear relationship between travel-time perturbation and velocity perturbation in the imaging domain, by which we construct the explicit expression of the sensitivity kernel function and use a Gaussian beam operator to compute the kernel. Furthermore, by introducing the preconditioned model regularization, a method of GBT under the constraint of a structure-guided filter is derived. Iterative applications of migration and tomography, both based on a Gaussian beam propagator, embody the idea of integrating velocity inversion and imaging. Numerical tests on both synthetic data and field data demonstrate that Gaussian beam propagator-based travel-time tomography in the imaging domain is effective.

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Stacking-velocity tomography for tilted orthorhombic media

Geophysics ◽

10.1190/geo2018-0300.1 ◽

2019 ◽

Vol 84 (3) ◽

pp. C171-C180 ◽

Cited By ~ 1

Author(s):

Qifan Liu ◽

Ilya Tsvankin

Keyword(s):

Parameter Estimation ◽

Subsurface Layer ◽

Synthetic Data ◽

Transversely Isotropic ◽

P Waves ◽

Additional Information ◽

Reflection Data ◽

Anisotropic Layers ◽

Zero Offset ◽

Velocity Tomography

Tilted orthorhombic (TOR) models are typical for dipping anisotropic layers, such as fractured shales, and can also be due to nonhydrostatic stress fields. Velocity analysis for TOR media, however, is complicated by the large number of independent parameters. Using multicomponent wide-azimuth reflection data, we develop stacking-velocity tomography to estimate the interval parameters of TOR media composed of homogeneous layers separated by plane dipping interfaces. The normal-moveout (NMO) ellipses, zero-offset traveltimes, and reflection time slopes of P-waves and split S-waves ([Formula: see text] and [Formula: see text]) are used to invert for the interval TOR parameters including the orientation of the symmetry planes. We show that the inversion can be facilitated by assuming that the reflector coincides with one of the symmetry planes, which is a common geologic constraint often employed for tilted transversely isotropic media. This constraint makes the inversion for a single TOR layer feasible even when the initial model is purely isotropic. If the dip plane is also aligned with one of the symmetry planes, we show that the inverse problem for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves can be solved analytically. When only [Formula: see text]-wave data are available, parameter estimation requires combining NMO ellipses from a horizontal and dipping interface. Because of the increase in the number of independent measurements for layered TOR media, constraining the reflector orientation is required only for the subsurface layer. However, the inversion results generally deteriorate with depth because of error accumulation. Using tests on synthetic data, we demonstrate that additional information such as knowledge of the vertical velocities (which may be available from check shots or well logs) and the constraint on the reflector orientation can significantly improve the accuracy and stability of interval parameter estimation.

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Azimuth–opening angle domain imaging in 3D Gaussian beam depth migration

Journal of Geophysics and Engineering ◽

10.1088/1742-2132/10/2/025013 ◽

2013 ◽

Vol 10 (2) ◽

pp. 025013 ◽

Cited By ~ 5

Author(s):

Jiexiong Cai ◽

Wubao Fang ◽

Huazhong Wang

Keyword(s):

Gaussian Beam ◽

Opening Angle ◽

Depth Migration ◽

Beam Depth

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A Quantitative Ultrasonic Travel-Time Tomography to Investigate Liquid Elaborations in Industrial Processes

Sensors ◽

10.3390/s19235117 ◽

2019 ◽

Vol 19 (23) ◽

pp. 5117 ◽

Cited By ~ 3

Author(s):

Panagiotis Koulountzios ◽

Tomasz Rymarczyk ◽

Manuchehr Soleimani

Keyword(s):

Sound Velocity ◽

Travel Time ◽

Spatial Information ◽

Industrial Applications ◽

Industrial Processes ◽

Liquid Density ◽

Ultrasound Tomography ◽

Imaging Device ◽

Fluid Mass ◽

Travel Time Tomography

This work presents an ultrasound tomography imaging system and method for quantitative mapping of the sound speed in liquid masses. It is highly desirable to be able to inspect vessel fluid mass distribution, notably in the chemical and food industrial operations. Optimization of industrial reactors has been crucial to the improvement of industrial processes. There is a great need to investigate how and if tomographic imaging sensors could aid the automatic control of these process tanks. Single-measurement ultrasound techniques and especially spectrometric methods have been a subject of study of industrial applications. Tomographic systems provide key multi-dimensional and spatial information when compared to the well-established single-channel measurement system. Recently, ultrasound tomography has attracted a great deal of interest in a wide spectrum of industrial applications. The system has been designed as 32 piezoelectric ring-array positioned in a 30 cm tank, with an excitation frequency of 40 kHz. Two-dimensional transmission travel-time tomography was developed to reconstruct the fluid mass distributions. Prior experiments are mainly based on inclusions of a few centimetres and on a liquid solution of different concentrations. They have been conducted to test the spatial and quantitative resolution of the ultrasound imaging device. Analysing the reconstructed images, it is possible to provide accurate spatial resolution with low position errors. The system also demonstrated inclusion movement with a temporal resolution of 4 frames per second (fps) in dynamical imaging sense. Sound velocity quantitative imaging was developed for the investigation of ultrasonic propagation in different liquids. This work, for the first time, shows how quantitative sound velocity imaging using transmission mode time of flight data could be used to characterize liquid density distribution of industrial reactors. The results suggest that ultrasound tomography can be used to quantitatively monitor important process parameters.

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Stereological Estimation of Orientation Distribution of Generalized Cylinders from a Unique 2D Slice

Microscopy and Microanalysis ◽

10.1017/s1431927613013548 ◽

2013 ◽

Vol 19 (6) ◽

pp. 1678-1687 ◽

Cited By ~ 1

Author(s):

Jean-Pierre Da Costa ◽

Stefan Oprean ◽

Pierre Baylou ◽

Christian Germain

Keyword(s):

Cross Sections ◽

Composite Structures ◽

Large Scale ◽

Fibrous Composite ◽

Three Dimensional ◽

Synthetic Data ◽

Inequality Constraints ◽

Orientation Distribution ◽

Industrial Applications ◽

Cost Constraints

AbstractThough three-dimensional (3D) imaging gives deep insight into the inner structure of complex materials, the stereological analysis of 2D snapshots of material sections is still necessary for large-scale industrial applications for reasons related to time and cost constraints. In this paper, we propose an original framework to estimate the orientation distribution of generalized cylindrical structures from a single 2D section. Contrary to existing approaches, knowledge of the cylinder cross-section shape is not necessary. The only requirement is to know the area distribution of the cross-sections. The approach relies on minimization of a least squares criterion under linear equality and inequality constraints that can be solved with standard optimization solvers. It is evaluated on synthetic data, including simulated images, and is applied to experimental microscopy images of fibrous composite structures. The results show the relevance and capabilities of the approach though some limitations have been identified regarding sensitivity to deviations from the assumed model.

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Fast acoustic velocity tomography of focusing operators

Geophysics ◽

10.1190/geo2013-0389.1 ◽

2014 ◽

Vol 79 (4) ◽

pp. R121-R131 ◽

Cited By ~ 2

Author(s):

Hu Jin ◽

George A. McMechan

Keyword(s):

Constant Velocity ◽

Null Space ◽

Focal Point ◽

Grid Point ◽

Synthetic Data ◽

Velocity Model ◽

The Stability ◽

Starting Model ◽

Velocity Tomography ◽

Focus Point

A 2D velocity model was estimated by tomographic imaging of overlapping focusing operators that contain one-way traveltimes, from common-focus points to receivers in an aperture along the earth’s surface. The stability and efficiency of convergence and the quality of the resulting models were improved by a sequence of ideas. We used a hybrid parameterization that has an underlying grid, upon which is superimposed a flexible, pseudolayer model. We first solved for the low-wavenumber parts of the model (approximating it as constant-velocity pseudo layers), then we allowed intermediate wavenumbers (allowing the layers to have linear velocity gradients), and finally did unconstrained iterations to add the highest wavenumber details. Layer boundaries were implicitly defined by focus points that align along virtual marker (reflector) horizons. Each focus point sampled an area bounded by the first and last rays in the data aperture at the surface; this reduced the amount of computation and the size of the effective null space of the solution. Model updates were performed simultaneously for the velocities and the local focus point positions in two steps; local estimates were performed independently by amplitude semblance for each focusing operator within its area of dependence, followed by a tomographic weighting of the local estimates into a global solution for each grid point, subject to the constraints of the parameterization used at that iteration. The system of tomographic equations was solved by simultaneous iterative reconstruction, which is equivalent to a least-squares solution, but it does not involve a matrix inversion. The algorithm was successfully applied to synthetic data for a salt dome model using a constant-velocity starting model; after a total of 25 iterations, the velocity error was [Formula: see text] and the final mean focal point position error was [Formula: see text] wavelength.

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Computational and asymptotic aspects of velocity inversion

Geophysics ◽

10.1190/1.1441996 ◽

1985 ◽

Vol 50 (8) ◽

pp. 1253-1265 ◽

Cited By ~ 21

Author(s):

Norman Bleistein ◽

Jack K. Cohen ◽

Frank G. Hagin

Keyword(s):

Asymptotic Analysis ◽

Synthetic Data ◽

Small Variation ◽

Computer Time ◽

Velocity Variation ◽

Inversion Method ◽

Singular Function ◽

Velocity Inversion ◽

Dirac Delta ◽

Peak Value

We discuss computational and asymptotic aspects of the Born inversion method and show how asymptotic analysis is exploited to reduce the number of integrations in an f-k like solution formula for the velocity variation. The output of this alternative algorithm produces the reflectivity function of the surface. This is an array of singular functions—Dirac delta functions which peak on the reflecting surfaces—each scaled by the normal reflection strength at the surface. Thus, imaging of a reflector is achieved by construction of its singular function and estimation of the reflection strength is deduced from the peak value of that function. By asymptotic analysis of the application of the algorithm to the Kirchhoff representation of the backscattered field, we show that the peak value of the output estimates the reflection strength even when the condition of small variation in velocity (an assumption of the original derivation) is violated. Furthermore, this analysis demonstrates that the method provides a migration algorithm when the amplitude has not been preserved in the data. The design of the computer algorithm is discussed, including such aspects as constraints due to causality and spatial aliasing. We also provide O‐estimates of computer time. This algorithm has been successfully implemented on both synthetic data and common‐midpoint stacked field data.

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Prestack Gaussian-beam depth migration in anisotropic media

Geophysics ◽

10.1190/1.2711423 ◽

2007 ◽

Vol 72 (3) ◽

pp. S133-S138 ◽

Cited By ~ 48

Author(s):

Tianfei Zhu ◽

Samuel H. Gray ◽

Daoliu Wang

Keyword(s):

Gaussian Beam ◽

Ray Tracing ◽

Synthetic Data ◽

Transversely Isotropic ◽

Anisotropic Media ◽

Elastic Parameters ◽

Depth Migration ◽

Kirchhoff Migration ◽

Beam Depth ◽

Dynamic Ray Tracing

Gaussian-beam depth migration is a useful alternative to Kirchhoff and wave-equation migrations. It overcomes the limitations of Kirchhoff migration in imaging multipathing arrivals, while retaining its efficiency and its capability of imaging steep dips with turning waves. Extension of this migration method to anisotropic media has, however, been hampered by the difficulties in traditional kinematic and dynamic ray-tracing systems in inhomogeneous, anisotropic media. Formulated in terms of elastic parameters, the traditional anisotropic ray-tracing systems aredifficult to implement and inefficient for computation, especially for the dynamic ray-tracing system. They may also result inambiguity in specifying elastic parameters for a given medium.To overcome these difficulties, we have reformulated the ray-tracing systems in terms of phase velocity.These reformulated systems are simple and especially useful for general transversely isotropic and weak orthorhombic media, because the phase velocities for these two types of media can be computed with simple analytic expressions. These two types of media also represent the majority of anisotropy observed in sedimentary rocks. Based on these newly developed ray-tracing systems, we have extended prestack Gaussian-beam depth migration to general transversely isotropic media. Test results with synthetic data show that our anisotropic, prestack Gaussian-beam migration is accurate and efficient. It produces images superior to those generated by anisotropic, prestack Kirchhoff migration.

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Hard and Soft EM in Bayesian Network Learning from Incomplete Data

Algorithms ◽

10.3390/a13120329 ◽

2020 ◽

Vol 13 (12) ◽

pp. 329

Author(s):

Andrea Ruggieri ◽

Francesco Stranieri ◽

Fabio Stella ◽

Marco Scutari

Keyword(s):

Incomplete Data ◽

Belief Propagation ◽

Structure Learning ◽

Synthetic Data ◽

Industrial Applications ◽

Sufficient Statistics ◽

Computational Speed ◽

The Em Algorithm ◽

Expectation Maximisation ◽

The Impact

Incomplete data are a common feature in many domains, from clinical trials to industrial applications. Bayesian networks (BNs) are often used in these domains because of their graphical and causal interpretations. BN parameter learning from incomplete data is usually implemented with the Expectation-Maximisation algorithm (EM), which computes the relevant sufficient statistics (“soft EM”) using belief propagation. Similarly, the Structural Expectation-Maximisation algorithm (Structural EM) learns the network structure of the BN from those sufficient statistics using algorithms designed for complete data. However, practical implementations of parameter and structure learning often impute missing data (“hard EM”) to compute sufficient statistics instead of using belief propagation, for both ease of implementation and computational speed. In this paper, we investigate the question: what is the impact of using imputation instead of belief propagation on the quality of the resulting BNs? From a simulation study using synthetic data and reference BNs, we find that it is possible to recommend one approach over the other in several scenarios based on the characteristics of the data. We then use this information to build a simple decision tree to guide practitioners in choosing the EM algorithm best suited to their problem.

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Seismic full-waveform inversion using minimization of virtual scattering sources

Geophysics ◽

10.1190/geo2019-0533.1 ◽

2020 ◽

Vol 85 (3) ◽

pp. R299-R311

Author(s):

Donguk Lee ◽

Sukjoon Pyun

Keyword(s):

Newton Method ◽

Scattering Problem ◽

Waveform Inversion ◽

Synthetic Data ◽

Inverse Scattering Problem ◽

Simulated Data ◽

Model Space ◽

Full Waveform Inversion ◽

Velocity Inversion ◽

Full Waveform

Full-waveform inversion (FWI) is a powerful tool for imaging underground structures with high resolution; however, this approach commonly suffers from the cycle-skipping issue. Recently, various FWI methods have been suggested to address this problem. Such methods are mainly classified into either data-space manipulation or model-space extension. We developed an alternative FWI method that belongs to the latter class. First, we define the virtual scattering source based on perturbation theory. The virtual scattering source is estimated by minimizing the differences between observed and simulated data with a regularization term penalizing the weighted virtual scattering source. The inverse problem for obtaining the virtual scattering source can be solved by the linear conjugate gradient method. The inverted virtual scattering source is used to update the wavefields; thus, it helps FWI to better approximate the nonlinearity of the inverse scattering problem. As the second step, the virtual scattering source is minimized to invert the velocity model. By assuming that the variation of the reconstructed wavefield is negligible, we can apply an approximated full Newton method to the velocity inversion with reasonable cost comparable to the Gauss-Newton method. From the numerical examples using synthetic data, we confirm that the proposed method performs better and more robust than the simple gradient-based FWI method. In addition, we show that our objective function has fewer local minima, which helps to mitigate the cycle-skipping problem.

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Least-squares Gaussian beam migration

Geophysics ◽

10.1190/geo2015-0328.1 ◽

2016 ◽

Vol 81 (3) ◽

pp. S87-S100 ◽

Cited By ~ 22

Author(s):

Hao Hu ◽

Yike Liu ◽

Yingcai Zheng ◽

Xuejian Liu ◽

Huiyi Lu

Keyword(s):

Least Squares ◽

Gaussian Beam ◽

Spatial Resolution ◽

Field Data ◽

Synthetic Data ◽

Data Sets ◽

Data Set ◽

Seismic Acquisition ◽

Gaussian Beam Migration ◽

Least Squares Migration

Least-squares migration (LSM) can be effective to mitigate the limitation of finite-seismic acquisition, balance the subsurface illumination, and improve the spatial resolution of the image, but it requires iterations of migration and demigration to obtain the desired subsurface reflectivity model. The computational efficiency and accuracy of migration and demigration operators are crucial for applying the algorithm. We have developed a test of the feasibility of using the Gaussian beam as the wavefield extrapolating operator for the LSM, denoted as least-squares Gaussian beam migration. Our method combines the advantages of the LSM and the efficiency of the Gaussian beam propagator. Our numerical evaluations, including two synthetic data sets and one marine field data set, illustrate that the proposed approach could be used to obtain amplitude-balanced images and to broaden the bandwidth of the migrated images in particular for the low-wavenumber components.

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