scholarly journals Analytical approximations of diving-wave imaging in constant-gradient medium

Geophysics ◽  
2014 ◽  
Vol 79 (4) ◽  
pp. S131-S140 ◽  
Author(s):  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Image Point ◽  
Practical Applications ◽  
Analytical Approximations ◽  
Wave Imaging ◽  
Analytical Formulas ◽  
Constant Gradient ◽  
Gradient Medium

Full-waveform inversion (FWI) in practical applications is currently used to invert the direct arrivals (diving waves, no reflections) using relatively long offsets. This is driven mainly by the high nonlinearity introduced to the inversion problem when reflection data are included, which in some cases require extremely low frequency for convergence. However, analytical insights into diving waves have lagged behind this sudden interest. We use analytical formulas that describe the diving wave’s behavior and traveltime in a constant-gradient medium to develop insights into the traveltime moveout of diving waves and the image (model) point dispersal (residual) when the wrong velocity is used. The explicit formulations that describe these phenomena reveal the high dependence of diving-wave imaging on the gradient and the initial velocity. The analytical image point residual equation can be further used to scan for the best-fit linear velocity model, which is now becoming a common sight as an initial velocity model for FWI. We determined the accuracy and versatility of these analytical formulas through numerical tests.

scholarly journals Full-Waveform Inversion for Imaging Faulted Structures: A Case Study from the Japan Trench Forearc Slope

2021 ◽  
Author(s):  
Ehsan Jamali Hondori ◽  
Chen Guo ◽  
Hitoshi Mikada ◽  
Jin-Oh Park
Keyword(s):  
Seismic Data ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Control Measures ◽  
Japan Trench ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Time Migration ◽  
Shallow Sediments

AbstractFull-waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model in a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to ensure that the observed and simulated waveforms kinematically fit within an error of less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer-stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM), to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data are acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model that could improve the depth images down to almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature that could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

Full waveform inversion: early start of model building process to resolve the complex near surface model in the Exmouth sub-basin, North West Shelf Australia

2018 ◽  
Vol 58 (2) ◽  
pp. 884
Author(s):  
Lianping Zhang ◽  
Haryo Trihutomo ◽  
Yuelian Gong ◽  
Bee Jik Lim ◽  
Alexander Karvelas
Keyword(s):  
Model Building ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Image Point ◽  
Surface Model ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
North West ◽  
Full Waveform

The Schlumberger Multiclient Exmouth 3D survey was acquired over the Exmouth sub-basin, North West Shelf Australia and covers 12 600 km2. One of the primary objectives of this survey was to produce a wide coverage of high quality imaging with advanced processing technology within an agreed turnaround time. The complexity of the overburden was one of the imaging challenges that impacted the structuration and image quality at the reservoir level. Unlike traditional full-waveform inversion (FWI) workflow, here, FWI was introduced early in the workflow in parallel with acquisition and preprocessing to produce a reliable near surface velocity model from a smooth starting model. FWI derived an accurate and detailed near surface model, which subsequently benefitted the common image point (CIP) tomography model updates through to the deeper intervals. The objective was to complete the FWI model update for the overburden concurrently with the demultiple stages hence reflection time CIP tomography could start with a reasonably good velocity model upon completion of the demultiple process.

scholarly journals Estimation of the anisotropy parameters from imaging moveout of diving wave in a factorized anisotropic medium

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. C139-C150 ◽  
Author(s):  
Shibo Xu ◽  
Alexey Stovas ◽  
Tariq Alkhalifah
Keyword(s):  
Anisotropic Medium ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Parameters Estimation ◽  
Model Parameters ◽  
Full Waveform ◽  
Vertical Heterogeneity ◽  
Analytical Formulas ◽  
Anisotropy Parameters ◽  
The One

The importance of diving waves is being realized because they provide long-wavelength model information, which can be used to help invert for the reflection information in full-waveform inversion. The factorized model is defined here as a combination of vertical heterogeneity and constant anisotropy, and it admits closed-form description of the traveltime. We have used these resulting analytical formulas to describe the behavior of diving waves in a factorized anisotropic medium, and we used an approximate imaging moveout formulation (residual moveout after imaging) to update the velocity model when the wrong model parameters (isotropic assumption) were used for imaging. We then used these analytical representations of the image moveout to establish a semblance analysis framework to search for the optimal anisotropic parameters. We have also discussed different parameterizations of the factorized medium to find the one that gave the best accuracy in anisotropy parameters estimation.

scholarly journals From tomography to full-waveform inversion with a single objective function

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. R55-R61 ◽  
Author(s):  
Tariq Alkhalifah ◽  
Yunseok Choi
Keyword(s):  
Objective Function ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Half Cycle ◽  
Velocity Models ◽  
Full Waveform ◽  
Single Objective

In full-waveform inversion (FWI), a gradient-based update of the velocity model requires an initial velocity that produces synthetic data that are within a half-cycle, everywhere, from the field data. Such initial velocity models are usually extracted from migration velocity analysis or traveltime tomography, among other means, and are not guaranteed to adhere to the FWI requirements for an initial velocity model. As such, we evaluated an objective function based on the misfit in the instantaneous traveltime between the observed and modeled data. This phase-based attribute of the wavefield, along with its phase unwrapping characteristics, provided a frequency-dependent traveltime function that was easy to use and quantify, especially compared to conventional phase representation. With a strong Laplace damping of the modeled, potentially low-frequency, data along the time axis, this attribute admitted a first-arrival traveltime that could be compared with picked ones from the observed data, such as in wave equation tomography (WET). As we relax the damping on the synthetic and observed data, the objective function measures the misfit in the phase, however unwrapped. It, thus, provided a single objective function for a natural transition from WET to FWI. A Marmousi example demonstrated the effectiveness of the approach.

Green’s function for migration: Continuous recording geometry

Geophysics ◽  
2000 ◽  
Vol 65 (1) ◽  
pp. 167-175 ◽  
Author(s):  
Gerard T. Schuster ◽  
Jianxing Hu
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Continuous Distribution ◽  
Velocity Model ◽  
Field Approximation ◽  
Image Point ◽  
Point Scatterer ◽  
Fundamental Understanding ◽  
Analytical Formulas ◽  
Zero Offset

Analytical formulas are derived to give the point scatterer responses for the zero‐offset and nonzero‐offset migration operators. These formulas are derived under the far‐field approximation for a continuous distribution of sources and receivers, and are denoted as migration Green’s functions. By specifying a homogeneous velocity model with irregular layers, these Green’s functions can be used to quickly compute the synthetic migrated sections without having to compute the modeled data. Thus, these formulas provide a fundamental understanding of migration artifacts and their relationship to the image point location and source‐receiver configuration. This understanding lays the foundation for the next step, elimination of these artifacts by migration deconvolution.

Parametric convolutional neural network-domain full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (6) ◽  
pp. R881-R896 ◽  
Author(s):  
Yulang Wu ◽  
George A. McMechan
Keyword(s):  
Neural Network ◽  
Convolutional Neural Network ◽  
Initial Velocity ◽  
Prior Information ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Model Errors ◽  
Initial Model ◽  
Full Waveform

Most current full-waveform inversion (FWI) algorithms minimize the data residuals to estimate a velocity model based on the assumption that the updated model is the sum of a background model and an estimated model perturbation. We have performed reparameterization of the initial velocity model, by the weights in a convolutional neural network (CNN), to automatically capture the salient features in the initial model, as a priori information. The prior information in CNN weights is iteratively updated as regularization to constrain the CNN-domain inversion to refine the features captured in CNN pretraining by reducing the data misfit. Synthetic examples using a 1D increasing velocity function v(z) and a 2D smoothed version of the correct Marmousi2 model as initial models indicate that the performance of the CNN-domain FWI depends on the existence and accuracy of the prior information in the initial velocity model (i.e., whether features whose positions, shapes, and values are present in the correct model are approximately included in the initial model). Forty different sets of randomly initialized CNN weights are used to parameterize and test CNN-domain FWI, using a 2D smoothed Sigsbee model as the initial velocity model. All 40 sets invert for the Sigsbee salt body more accurately (with a smaller standard deviation of the final rms model errors), by CNN-domain FWI, than FWI does. Features that are not represented within the CNN hidden layers in the initial velocity model, and so cannot be recovered by CNN-domain FWI, can be recovered using the final CNN-domain FWI velocity model as the starting model in a subsequent conventional FWI.

scholarly journals A reflection-based efficient wavefield inversion

Geophysics ◽  
2021 ◽  
pp. 1-53
Author(s):  
Chao Song ◽  
Tariq Alkhalifah
Keyword(s):  
High Resolution ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Background Model ◽  
Ocean Bottom ◽  
Velocity Inversion ◽  
Velocity Models ◽  
Wavefield Inversion

Full-waveform inversion (FWI) is popularly used to obtain a high-resolution subsurface velocity model. However, it requires either a good initial velocity model or low-frequency data to mitigate the cycle-skipping issue. Reflection-waveform inversion (RWI) uses a migration/demigration process to retrieve a background model that can be used as a good initial velocity in FWI. The drawback of the conventional RWI is that it requires the use of a least-squares migration, which is often computationally expensive, and is still prone to cycle skipping at far offsets. To improve the computational efficiency and overcome the cycle skipping in the original RWI, we incorporate it into a recently introduced method called efficient wavefield inversion (EWI) by inverting for the Born scattered wavefield instead of the wavefield itself. In this case, we use perturbation-related secondary sources in the modified source function. Unlike conventional RWI, the perturbations are calculated naturally as part of the calculation of the scattered wavefield in an efficient way. As the sources in the reflection-based EWI (REWI) are located in the subsurface, we are able to update the background model along the reflection wave path. In the background velocity inversion, we calculate the background perturbation by a deconvolution process at each frequency. After obtaining the REWI inverted velocity model, a sequential FWI or EWI is needed to obtain a high-resolution model. We demonstrate the validity of the proposed approach using synthetic data generated from a section of the Sigsbee2A model. To further demonstrate the effectiveness of the proposed approach, we test it on an ocean bottom cable (OBC) dataset from the North Sea. We find that the proposed methodology leads to improved velocity models as evidenced by flatter angle gathers.

scholarly journals Full Waveform Inversion for Imaging Faulted Structures; a Case Study from Japan Trench Forearc Slope

2021 ◽  
Author(s):  
Ehsan Jamali Hondori ◽  
Chen Guo ◽  
Hitoshi Mikada ◽  
Jin-Oh Park
Keyword(s):  
Seismic Data ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Control Measures ◽  
Japan Trench ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
Time Migration ◽  
Shallow Sediments

Abstract Full waveform inversion (FWI) of limited-offset marine seismic data is a challenging task due to the lack of refracted energy and diving waves from the shallow sediments, which are fundamentally required to update the long-wavelength background velocity model through a tomographic fashion. When these events are absent, a reliable initial velocity model is necessary to assure that the observed and simulated waveforms kinematically fit within an error less than half a wavelength to protect the FWI iterative local optimization scheme from cycle skipping. We use a migration-based velocity analysis (MVA) method, including a combination of the layer stripping approach and iterations of Kirchhoff prestack depth migration (KPSDM) to build an accurate initial velocity model for the FWI application on 2D seismic data with a maximum offset of 5.8 km. The data is acquired in the Japan Trench subduction zone, and we focus on the area where the shallow sediments overlying a highly reflective basement on top of the Cretaceous erosional unconformity are severely faulted and deformed. Despite the limited offsets available in the seismic data, our carefully designed workflow for data preconditioning, initial model building, and waveform inversion provides a velocity model which could improve the depth images down to a depth of almost 3.5 km. We present several quality control measures to assess the reliability of the resulting FWI model, including ray path illuminations, sensitivity kernels, reverse time migration (RTM) images, and KPSDM common image gathers. A direct comparison between the FWI and MVA velocity profiles reveals a sharp boundary at the Cretaceous basement interface, a feature which could not be observed in the MVA velocity model. The normal faults caused by the basal erosion of the upper plate in the study area reach the seafloor with evident subsidence of the shallow strata, implying that the faults are active.

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