Fast 2D full-waveform modeling and inversion using the Schur complement approach

Geophysics ◽  
2019 ◽  
Vol 84 (5) ◽  
pp. R783-R792 ◽  
Author(s):  
Debanjan Datta ◽  
Piyoosh Jaysaval ◽  
Mrinal Sen ◽  
Adrien F. Arnulf
Keyword(s):  
Water Column ◽  
Linear Equations ◽  
Waveform Inversion ◽  
Schur Complement ◽  
Simple Algebra ◽  
Velocity Model ◽  
Near Surface ◽  
Full Waveform ◽  
Anomalous Zone ◽  
And Inversion

In most full-waveform inversion (FWI) problems, sufficient prior information is available to constrain the velocity of certain parts of the model, e.g., the water column or, in some cases, near-surface velocities. We take advantage of this situation and develop a fast Schur-complement-based forward modeling and inversion approach by partitioning the velocity model into two parts. The first part consists of the constrained zone that does not change during the inversion, whereas the second part is the anomalous zone to be updated during the inversion. For this decomposition, we partially factorize the governing system of linear equations by computing a Schur complement for the anomalous zone. The Schur complement system is then solved to compute the fields in the anomalous zone, which are then back substituted to compute the fields in the constrained region. For each successive modeling steps with new anomalous zone velocities, the corresponding Schur complement is easily computed using simple algebra. Because the anomalous part of the model is comparatively smaller than the whole model, considerable computational savings can be achieved using our Schur approach. Additionally, we showed that the Schur complement method maintains the accuracy of standard frequency-domain finite difference formulations, but this comes at a slightly higher peak memory requirement. Our FWI workflow shows reduced runtime by 15%–57% depending upon the depth of the water column without losing any accuracy compared to the standard method.

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.

An application of full-waveform inversion to land data using the pseudo-Hessian matrix

2016 ◽  
Vol 4 (4) ◽  
pp. T627-T635
Author(s):  
Yikang Zheng ◽  
Wei Zhang ◽  
Yibo Wang ◽  
Qingfeng Xue ◽  
Xu Chang
Keyword(s):  
Hessian Matrix ◽  
Waveform Inversion ◽  
Computational Cost ◽  
Velocity Model ◽  
Surface Velocity ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Near Surface ◽  
Full Waveform ◽  
The Time Domain

Full-waveform inversion (FWI) is used to estimate the near-surface velocity field by minimizing the difference between synthetic and observed data iteratively. We apply this method to a data set collected on land. A multiscale strategy is used to overcome the local minima problem and the cycle-skipping phenomenon. Another obstacle in this application is the slow convergence rate. The inverse Hessian can enhance the poorly blurred gradient in FWI, but obtaining the full Hessian matrix needs intensive computation cost; thus, we have developed an efficient method aimed at the pseudo-Hessian in the time domain. The gradient in our FWI workflow is preconditioned with the obtained pseudo-Hessian and a synthetic example verifies its effectiveness in reducing computational cost. We then apply the workflow on the land data set, and the inverted velocity model is better resolved compared with traveltime tomography. The image and angle gathers we get from the inversion result indicate more detailed information of subsurface structures, which will contribute to the subsequent seismic interpretation.

scholarly journals Interferometric full-waveform inversion

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. R45-R60
Author(s):  
Mrinal Sinha ◽  
Gerard T. Schuster
Keyword(s):  
Field Data ◽  
Waveform Inversion ◽  
Time Lapse ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
Target Region ◽  
Data Space ◽  
Full Waveform ◽  
Shallow Part

Velocity errors in the shallow part of the velocity model can lead to erroneous estimates of the full-waveform inversion (FWI) tomogram. If the location and topography of a reflector are known, then such a reflector can be used as a reference reflector to update the underlying velocity model. Reflections corresponding to this reference reflector are windowed in the data space. Windowed reference reflections are then crosscorrelated with reflections from deeper interfaces, which leads to partial cancellation of static errors caused by the overburden above the reference interface. Interferometric FWI (IFWI) is then used to invert the tomogram in the target region, by minimizing the normalized waveform misfit between the observed and predicted crosscorrelograms. Results with synthetic and field data with static errors above the reference interface indicate that an accurate tomogram can be inverted in areas lying within several wavelengths of the reference interface. IFWI can also be applied to synthetic time-lapse data to mitigate the nonrepeatability errors caused by time-varying overburden variations. The synthetic- and field-data examples demonstrate that IFWI can provide accurate tomograms when the near surface is ridden with velocity errors.

Waveform tomography of field vibroseis data using an approximate 2D geometry leads to improved velocity models

Geophysics ◽  
2012 ◽  
Vol 77 (1) ◽  
pp. R33-R43 ◽  
Author(s):  
Brendan R. Smithyman ◽  
Ronald M. Clowes
Keyword(s):  
Waveform Inversion ◽  
Velocity Model ◽  
Surface Velocity ◽  
Time Shift ◽  
Full Waveform Inversion ◽  
Near Surface ◽  
Traveltime Tomography ◽  
Full Waveform ◽  
First Arrival ◽  
Waveform Tomography

Waveform tomography, a combination of traveltime tomography (or inversion) and waveform inversion, is applied to vibroseis first-arrival data to generate an interpretable model of P-wave velocity for a site in the Nechako Basin, south-central British Columbia, Canada. We use constrained 3D traveltime inversion followed by 2D full-waveform inversion to process long-offset (14.4 km) first-arrival refraction waveforms, resulting in a velocity model of significantly higher detail than a conventional refraction-statics model generated for a processing workflow. The crooked-line acquisition of the data set makes 2D full-waveform inversion difficult. Thus, a procedure that improves the tractability of waveform tomography processing of vibroseis data recorded on crooked roads is developed to generate a near-surface ([Formula: see text]) velocity model for the study area. The data waveforms are first static corrected using a time shift determined by 3D raytracing, which accounts for the crossline offsets produced by the crooked-line acquisition. The velocity model generated from waveform tomography exhibits substantial improvement when compared with a conventional refraction-statics model. It also shows improved resolution of sharp discontinuities and low-velocity regions when compared to the model from traveltime tomography alone, especially in regions where the geometry errors are moderate. Interpretation of the near-surface velocity model indicates possible subbasins in the Nechako Basin and delineates the Eocene volcanic rocks of the study area. This approach limits the ability of the full-waveform inversion to fit some propagation modes; however, the tractability of the inversion in the near-surface region is improved. This new development is especially useful in studies that do not warrant 3D seismic acquisition and processing.

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.

Target-oriented inversion using the Patched Green′s function method

Geophysics ◽  
2021 ◽  
pp. 1-77
Author(s):  
Danyelle da Silva ◽  
Edwin Fagua Duarte ◽  
Wagner Almeida ◽  
Mauro Ferreira ◽  
Francisco Alirio Moura ◽  
...  
Keyword(s):  
Condensed Matter ◽  
Waveform Inversion ◽  
Time Lapse ◽  
Velocity Model ◽  
Dyson Equation ◽  
Computational Time ◽  
Green Functions ◽  
Target Area ◽  
Computational Domain ◽  
Full Waveform

We have designed a target-oriented methodology to perform Full Waveform Inversion using a frequency-domain wave propagator based on the so-called Patched Green’s Function (PGF) technique. Originally developed in condensed matter physics to describe electronic waves in materials, the PGF technique is easily adaptable to the case of wave propagation in a spatially variable media in general. By dividing the entire computational domain into two sections, namely the target area and the outside target area, we calculate the Green Functions related to each section separately. The calculations related to the section outside the target are performed only once at the beginning of inversion, whereas the calculations in the target area are performed repeatedly for each iteration of the inversion process. With the Green Functions of the separate areas, we calculate the Green Functions of the two systems patched together through the application of a Recursive Dyson equation. By performing 2D and time-lapse experiments on the Marmousi model and a Brazilian Pre-salt velocity model, we demonstrate that the target-oriented PGF reduces the computational time of the inversion without compromising accuracy. In fact, when compared with conventional FWI results, the PGF-based calculations are identical but done in a fraction of the time.

FULL-WAVEFORM INVERSION WITH SOURCE AND RECEIVER COUPLING EFFECTS CORRECTION

Geophysics ◽  
2021 ◽  
pp. 1-37
Author(s):  
Xinhai Hu ◽  
Wei Guoqi ◽  
Jianyong Song ◽  
Zhifang Yang ◽  
Minghui Lu ◽  
...  
Keyword(s):  
Waveform Inversion ◽  
Nonlinear Least Squares ◽  
Real Data ◽  
Model Parameters ◽  
Full Waveform Inversion ◽  
Linear Inversion ◽  
Near Surface ◽  
Model Parameter ◽  
Full Waveform ◽  
Coupling Factors

Coupling factors of sources and receivers vary dramatically due to the strong heterogeneity of near surface, which are as important as the model parameters for the inversion success. We propose a full waveform inversion (FWI) scheme that corrects for variable coupling factors while updating the model parameter. A linear inversion is embedded into the scheme to estimate the source and receiver factors and compute the amplitude weights according to the acquisition geometry. After the weights are introduced in the objective function, the inversion falls into the category of separable nonlinear least-squares problems. Hence, we could use the variable projection technique widely used in source estimation problem to invert the model parameter without the knowledge of source and receiver factors. The efficacy of the inversion scheme is demonstrated with two synthetic examples and one real data test.

Tunnel detection at Yuma Proving Ground, Arizona, USA — Part 1: 2D full-waveform inversion experiment

Geophysics ◽  
2019 ◽  
Vol 84 (1) ◽  
pp. B95-B105 ◽  
Author(s):  
Yao Wang ◽  
Richard D. Miller ◽  
Shelby L. Peterie ◽  
Steven D. Sloan ◽  
Mark L. Moran ◽  
...  
Keyword(s):  
Surface Wave ◽  
Waveform Inversion ◽  
Velocity Profiles ◽  
Infinite Length ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Near Surface ◽  
Tunnel Detection ◽  
Full Waveform ◽  
Wave Methods

We have applied time domain 2D full-waveform inversion (FWI) to detect a known 10 m deep wood-framed tunnel at Yuma Proving Ground, Arizona. The acquired seismic data consist of a series of 2D survey lines that are perpendicular to the long axis of the tunnel. With the use of an initial model estimated from surface wave methods, a void-detection-oriented FWI workflow was applied. A straightforward [Formula: see text] quotient masking method was used to reduce the inversion artifacts and improve confidence in identifying anomalies that possess a high [Formula: see text] ratio. Using near-surface FWI, [Formula: see text] and [Formula: see text] velocity profiles were obtained with void anomalies that are easily interpreted. The inverted velocity profiles depict the tunnel as a low-velocity anomaly at the correct location and depth. A comparison of the observed and simulated waveforms demonstrates the reliability of inverted models. Because the known tunnel has a uniform shape and for our purposes an infinite length, we apply 1D interpolation to the inverted [Formula: see text] profiles to generate a pseudo 3D (2.5D) volume. Based on this research, we conclude the following: (1) FWI is effective in near-surface tunnel detection when high resolution is necessary. (2) Surface-wave methods can provide accurate initial S-wave velocity [Formula: see text] models for near-surface 2D FWI.

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