Least-squares Gaussian beam migration in viscoacoustic media

Geophysics ◽  
2020 ◽  
Vol 86 (1) ◽  
pp. S17-S28
Author(s):  
Yubo Yue ◽  
Yujin Liu ◽  
Yaonan Li ◽  
Yunyan Shi
Keyword(s):  
Green’S Function ◽  
Least Squares ◽  
Gaussian Beam ◽  
Green's Function ◽  
Seismic Waves ◽  
Image Resolution ◽  
Data Sets ◽  
Phase Dispersion ◽  
Using Data ◽  
Gaussian Beam Migration

Because of amplitude decay and phase dispersion of seismic waves, conventional migrations are insufficient to produce satisfactory images using data observed in highly attenuative geologic environments. We have developed a least-squares Gaussian beam migration method for viscoacoustic data imaging, which can not only compensate for amplitude decay and phase dispersion caused by attenuation, but it can also improve image resolution and amplitude fidelity through linearized least-squares inversion. We represent the viscoacoustic Green’s function by a summation of Gaussian beams, in which an attenuation traveltime is incorporated to simulate or compensate for attenuation effects. Based on the beam representation of the Green’s function, we construct the viscoacoustic Born forward modeling and adjoint migration operators, which can be effectively evaluated by a time-domain approach based on a filter-bank technique. With the constructed operators, we formulate a least-squares migration scheme to iteratively solve for the optimal image. Numerical tests on synthetic and field data sets demonstrate that our method can effectively compensate for the attenuation effects and produce images with higher resolution and more balanced amplitudes than images from acoustic least-squares Gaussian beam migration.

Least-squares Gaussian beam migration

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. S87-S100 ◽  
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.

Least-squares Gaussian beam migration in elastic media

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. S329-S340 ◽  
Author(s):  
Yubo Yue ◽  
Paul Sava ◽  
Zhongping Qian ◽  
Jidong Yang ◽  
Zhen Zou
Keyword(s):  
Least Squares ◽  
Gaussian Beam ◽  
Computational Cost ◽  
Synthetic Data ◽  
Preconditioned Conjugate Gradient ◽  
Imaging Method ◽  
Data Sets ◽  
Isotropic Media ◽  
Gaussian Beam Migration ◽  
Multicomponent Data

Gaussian beam migration (GBM) is an effective imaging method that has the ability to image multiple arrivals while preserving the advantages of ray-based methods. We have extended this method to linearized least-squares imaging for elastic waves in isotropic media. We have dynamically transformed the multicomponent data to the principal components of different wave modes using the polarization information available in the beam migration process, and then we use Gaussian beams as wavefield propagator to construct the forward modeling and adjoint migration operators. Based on the constructed operators, we formulate a least-squares migration scheme that is iteratively solved using a preconditioned conjugate gradient method. With this method, we can obtain crosstalk-attenuated multiwave images with better subsurface illumination and higher resolution than those of the conventional elastic Gaussian beam migration. This method also allows us to achieve a good balance between computational cost and imaging accuracy, which are both important requirements for iterative least-squares migrations. Numerical tests on two synthetic data sets demonstrate the validity and effectiveness of our proposed method.

The Search of Diffusive Properties in Ambient Seismic Noise

2021 ◽  
Author(s):  
José Piña-Flores ◽  
Martín Cárdenas-Soto ◽  
Antonio García-Jerez ◽  
Michel Campillo ◽  
Francisco J. Sánchez-Sesma
Keyword(s):  
Green’S Function ◽  
Surface Waves ◽  
Green's Function ◽  
Seismic Noise ◽  
Elastic Field ◽  
Spectral Ratio ◽  
Ambient Seismic Noise ◽  
Data Sets ◽  
Original Experiment ◽  
Imaging Theory

ABSTRACT Ambient seismic noise (ASN) is becoming of interest for geophysical exploration and engineering seismology, because it is possible to exploit its potential for imaging. Theory asserts that the Green’s function can be retrieved from correlations within a diffuse field. Surface waves are the most conspicuous part of Green’s function in layered media. Thus, the velocities of surface waves can be obtained from ASN if the wavefield is diffuse. There is widespread interest in the conditions of emergence and properties of diffuse fields. In the applications, useful approximations of the Green’s function can be obtained from cross correlations of recorded motions of ASN. An elastic field is diffuse if the background illumination is azimuthally uniform and equipartitioned. It happens with the coda waves in earthquakes and has been verified in carefully planned experiments. For one of these data sets, the 1999 Chilpancingo (Mexico) experiment, there are some records of earthquake pre-events that undoubtedly are composed of ASN, so that the processing for coda can be tested on them. We decompose the ASN energies and study their equilibration. The scheme is inspired by the original experiment and uses the ASN recorded in an L-shaped array that allows the computation of spatial derivatives. It requires care in establishing the appropriate ranges for measuring parameters. In this search for robust indicators of diffusivity, we are led to establish that under certain circumstances, the S and P energy equilibration is a process that anticipates the diffusion regime (not necessarily isotropy), which justifies the use of horizontal-to-vertical spectral ratio in the context of diffuse-field theory.

Least-squares Gaussian beam migration in viscoacoustic media

2019 ◽  
Author(s):  
Yubo Yue ◽  
Pengyuan Sun ◽  
Jianlei Zhang ◽  
Shihu Wang ◽  
Jun Liao ◽  
...  
Keyword(s):  
Least Squares ◽  
Gaussian Beam ◽  
Gaussian Beam Migration

New objective functions for waveform inversion

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 213-222 ◽  
Author(s):  
L. Neil Frazer ◽  
Xinhua Sun
Keyword(s):  
Green’S Function ◽  
Objective Function ◽  
Impulse Response ◽  
Green's Function ◽  
Waveform Inversion ◽  
Data Sets ◽  
Minimum Phase ◽  
Objective Functions ◽  
Data Set ◽  
Parameter Values

Inversion is an organized search for parameter values that maximize or minimize an objective function, referred to here as a processor. This note derives three new seismic processors that require neither prior deconvolution nor knowledge of the source‐receiver wavelet. The most powerful of these is the fourwise processor, as it is applicable to data sets from multiple shots and receivers even when each shot has a different unknown signature and each receiver has a different unknown impulse response. Somewhat less powerful than the fourwise processor is the pairwise processor, which is applicable to a data set consisting of two or more traces with the same unknown wavelet but possibly different gains. When only one seismogram exists the partition processor can be used. The partition processor is also applicable when there is only one shot (receiver) and each receiver (shot) has a different signature. In fourwise and pairwise inversions the unknown wavelets may be arbitrarily long in time and need not be minimum phase. In partition inversion the wavelet is assumed to be shorter in time than the data trace itself but is not otherwise restricted. None of the methods requires assumptions about the Green’s function.

scholarly journals Least-squares Gaussian beam migration

2017 ◽  
Vol 14 (1) ◽  
pp. 184-196 ◽  
Author(s):  
Maolin Yuan ◽  
Jianping Huang ◽  
Wenyuan Liao ◽  
Fuyou Jiang
Keyword(s):  
Least Squares ◽  
Gaussian Beam ◽  
Gaussian Beam Migration

Gaussian beam imaging of fractures near the wellbore using sonic logging tools after removing dispersive borehole waves

Geophysics ◽  
2020 ◽  
Vol 85 (4) ◽  
pp. D133-D143
Author(s):  
David Li ◽  
Xiao Tian ◽  
Hao Hu ◽  
Xiao-Ming Tang ◽  
Xinding Fang ◽  
...  
Keyword(s):  
Gaussian Beam ◽  
Field Data ◽  
Gas Production ◽  
Dipole Source ◽  
Data Sets ◽  
Data Set ◽  
Receiver Array ◽  
Gaussian Beam Migration ◽  
Sonic Logging ◽  
Borehole Waves

The ability to image near-wellbore fractures is critical for wellbore integrity monitoring as well as for energy production and waste disposal. Single-well imaging uses a sonic logging instrument consisting of a source and a receiver array to image geologic structures around a wellbore. We use cross-dipole sources because they can excite waves that can be used to image structures farther away from the wellbore than traditional monopole sources. However, the cross-dipole source also will excite large-amplitude, slowly propagating dispersive waves along the surface of the borehole. These waves will interfere with the formation reflection events. We have adopted a new fracture imaging procedure using sonic data. We first remove the strong amplitude borehole waves using a new nonlinear signal comparison method. We then apply Gaussian beam migration to obtain high-resolution images of the fractures. To verify our method, we first test our method on synthetic data sets modeled using a finite-difference approach. We then validate our method on a field data set collected from a fractured natural gas production well. We are able to obtain high-quality images of the fractures using Gaussian beam migration compared with Kirchhoff migration for the synthetic and field data sets. We also found that a low-frequency source (around 1 kHz) is needed to obtain a sharp image of the fracture because high-frequency wavefields can interact strongly with the fluid-filled borehole.

Green's Function Approach to Global Parameter Estimation in Information Processing

2003 ◽  
Vol 17 (18) ◽  
pp. 949-953
Author(s):  
K. Y. Michael Wong ◽  
Fuli Li
Keyword(s):  
Information Processing ◽  
Green’S Function ◽  
Green's Function ◽  
Training Data ◽  
Data Sets ◽  
Global Parameter ◽  
Novel Approach ◽  
Prior Expectation ◽  
Validation Procedure ◽  
Global Parameters

In information processing systems for classification and regression tasks, global parameters are often introduced to balance the prior expectation about the processed data and the emphasis on reproducing the training data. Since over-emphasizing either of them leads to poor generalization, optimal global parameters are needed. Conventionally, a time-consuming cross-validation procedure is used. Here we introduce a novel approach to this problem, based on the Green's function. All estimations can be made empirically and hence can be easily extended to more complex systems. The method is fast since it does not require the validation step. Its performances on benchmark data sets are very satisfactory.

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