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 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.

scholarly journals Machine Learning as a Seismic Prior Velocity Model Building Method for Full-Waveform Inversion: A Case Study from Colombia

2021 ◽  
Vol 178 (2) ◽  
pp. 423-448
Author(s):  
Ursula Iturrarán-Viveros ◽  
Andrés M. Muñoz-García ◽  
Octavio Castillo-Reyes ◽  
Khemraj Shukla
Keyword(s):  
Machine Learning ◽  
Initial Velocity ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Velocity Model ◽  
Wave Impedance ◽  
P Wave ◽  
Well Log ◽  
Velocity Models ◽  
Full Waveform

AbstractWe use machine learning algorithms (artificial neural networks, ANNs) to estimate petrophysical models at seismic scale combining well-log information, seismic data and seismic attributes. The resulting petrophysical images are the prior inputs in the process of full-waveform inversion (FWI). We calculate seismic attributes from a stacked reflected 2-D seismic section and then train ANNs to approximate the following petrophysical parameters: P-wave velocity ($$V_\mathrm{{p}}$$ V p ), density ($$\rho $$ ρ ) and volume of clay ($$V_\mathrm{{clay}}$$ V clay ). We extend the use of the $$V_\mathrm{{clay}}$$ V clay by constraining it with the well lithology and we establish two classes: sands and shales. Consequently, machine learning allows us to build an initial estimate of the earth property model ($$V_\mathrm{{p}}$$ V p ), which is iteratively refined to produce a synthetic seismogram that matches the observed seismic data. We apply the 1-D Kennett method as a forward modeling tool to create synthetic data with the images of $$V_\mathrm{{p}}$$ V p , $$\rho $$ ρ and the thickness of layers (sands or shales) obtained with the ANNs. A nonlinear least-squares inversion algorithm minimizes the residual (or misfit) between observed and synthetic full-waveform data, which improves the $$V_\mathrm{{p}}$$ V p resolution. In order to show the advantage of using the ANN velocity model as the initial velocity model for the inversion, we compare the results obtained with the ANNs and two other initial velocity models. One of these alternative initial velocity models is computed via P-wave impedance, and the other is achieved by velocity semblance analysis: root-mean-square velocity (RMS). The results are in good agreement when we use $$\rho $$ ρ and $$V_\mathrm{{p}}$$ V p obtained by ANNs. However, the results are poor and the synthetic data do not match the real acquired data when using the semblance velocity model and the $$\rho $$ ρ from the well log (constant for the entire 2-D section). Nevertheless, the results improve when including $$\rho $$ ρ , the layered structure driven by the $$V_\mathrm{{clay}}$$ V clay (both obtained with ANNs) and the semblance velocity model. When doing inversion starting with the initial $$V_\mathrm{{p}}$$ V p model estimated using the P-wave impedance, there is some gain of the final $$V_\mathrm{{p}}$$ V p with respect to the RMS initial $$V_\mathrm{{p}}$$ V p . To assess the quality of the inversion of $$V_\mathrm{{p}}$$ V p , we use the information for two available wells and compare the final $$V_\mathrm{{p}}$$ V p obtained with ANNs and the final $$V_\mathrm{{p}}$$ V p computed with the P-wave impedance. This shows the benefit of employing ANNs estimations as prior models during the inversion process to obtain a final $$V_\mathrm{{p}}$$ V p that is in agreement with the geology and with the seismic and well-log data. To illustrate the computation of the final velocity model via FWI, we provide an algorithm with the detailed steps and its corresponding GitHub code.

Azimuthally dependent anisotropic velocity model update

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. C27-C53 ◽  
Author(s):  
Zvi Koren ◽  
Igor Ravve
Keyword(s):  
High Resolution ◽  
Velocity Field ◽  
Phase Angle ◽  
Velocity Model ◽  
Background Model ◽  
Physical Parameters ◽  
Model Parameters ◽  
Effective Parameters ◽  
Velocity Models

We consider a case where a 3D depth migration has been performed in the local angle domain (LAD) using rich-azimuth seismic data (e.g., conventional land surveys). The subsurface geologic model is characterized by considerable azimuthally anisotropic velocity variations. The background velocity field used for the migration can consist of azimuthally independent, e.g., vertical transverse isotropy, and/or azimuthally dependent (e.g., orthorhombic), velocity layers. The resulting 3D full-azimuth reflection angle gathers generated by the LAD migration represent in situ high-resolution amplitude preserved reflectivities associated with opening angles between incident and reflected slowness vectors in the specular directions. Residual moveouts (RMOs) automatically picked on these 3D image gathers along major horizons can indicate considerable residual periodic azimuthal variations. This situation is typical in depth imaging applied to unconventional shale plays, where the background velocity model doesn’t yet account for the aligned stress/fracture systems that exist in some of the target layers. We use the azimuthally dependent, phase-angle RMOs to update the interval parameters of the background model, accounting for the azimuthal anisotropy effect. Until now, this problem was mainly treated in the unmigrated time-offset domain, which is limited in describing the actual in situ changes of the velocity field with azimuths. The subsurface full-azimuth phase-angle domain RMOs provide better physical parameters to analyze the in situ azimuthal variations of the anisotropic media. Our method is grounded in a newly derived generalized Dix-based theory, where locally the background and updated models are assumed to be 1D anisotropic velocity models. At each lateral location, the orthorhombic axis [Formula: see text] points in the vertical direction across all layers, but the azimuthal orientations of the orthorhombic layers change from layer to layer. An effective model for such a layered structure (background or updated) is represented by a single layer with a vertical time identical to that of the whole package, effective fast and slow normal moveout (NMO) velocities, and an effective azimuthal orientation of the slow NMO velocity. Our approach begins with computation of these effective parameters for the background model and conversion of the high-resolution RMOs into a dense set of updated, effective, azimuthally dependent NMO velocities, which are then converted into three effective parameters of the updated model. Next, we apply a generalized Dix-based inversion approach to estimate the local NMO parameters for each updated layer. Finally, we convert the local parameters into interval azimuthally varying anisotropic model parameters (e.g., TTI, orthorhombic, or tilted orthorhombic) within each layer. The 1D Dix-based approach presented in this work should not be considered an alternative to more accurate 3D global inversion approaches, such as global anisotropic tomography. However, the proposed method can be effectively used for moderately laterally varying models, and some of the principal physical rules derived for the 1D model can be further used to improve the formulation and geophysical constraints applied to 3D global inversion methods.

Elastic reflection waveform inversion based on the decomposition of sensitivity kernels

Geophysics ◽  
2019 ◽  
Vol 84 (2) ◽  
pp. R235-R250 ◽  
Author(s):  
Zhiming Ren ◽  
Zhenchun Li ◽  
Bingluo Gu
Keyword(s):  
Wave Velocity ◽  
Waveform Inversion ◽  
Velocity Model ◽  
P Wave ◽  
Background Model ◽  
Reverse Time ◽  
S Wave ◽  
Velocity Models ◽  
Time Migration ◽  
Starting Model

Full-waveform inversion (FWI) has the potential to obtain an accurate velocity model. Nevertheless, it depends strongly on the low-frequency data and the initial model. When the starting model is far from the real model, FWI tends to converge to a local minimum. Based on a scale separation of the model (into the background model and reflectivity model), reflection waveform inversion (RWI) can separate out the tomography term in the conventional FWI kernel and invert for the long-wavelength components of the velocity model by smearing the reflected wave residuals along the transmission (or “rabbit-ear”) paths. We have developed a new elastic RWI method to build the P- and S-wave velocity macromodels. Our method exploits a traveltime-based misfit function to highlight the contribution of tomography terms in the sensitivity kernels and a sensitivity kernel decomposition scheme based on the P- and S-wave separation to suppress the high-wavenumber artifacts caused by the crosstalk of different wave modes. Numerical examples reveal that the gradients of the background models become sufficiently smooth owing to the decomposition of sensitivity kernels and the traveltime-based misfit function. We implement our elastic RWI in an alternating way. At each loop, the reflectivity model is generated by elastic least-squares reverse time migration, and then the background model is updated using the separated traveltime kernels. Our RWI method has been successfully applied in synthetic and real reflection seismic data. Inversion results demonstrate that the proposed method can retrieve preferable low-wavenumber components of the P- and S-wave velocity models, which are reliable to serve as a starting model for conventional elastic FWI. Also, our method with a two-stage inversion workflow, first updating the P-wave velocity using the PP kernels and then updating the S-wave velocity using the PS kernels, is feasible and robust even when P- and S-wave velocities have different structures.

2-D velocity inversion/imaging of large offset seismic data via the tau‐p domain

Geophysics ◽  
1993 ◽  
Vol 58 (7) ◽  
pp. 1002-1016 ◽  
Author(s):  
Edmund C. Reiter ◽  
G. Michael Purdy ◽  
M. Nafi Toksöz
Keyword(s):  
Velocity Field ◽  
Three Dimensional ◽  
Synthetic Data ◽  
Velocity Model ◽  
Intermediate Step ◽  
Ocean Bottom ◽  
Velocity Inversion ◽  
Best Fitting ◽  
Ray Parameter ◽  
Refraction Data

We describe a method for determining a two‐dimensional (2-D) velocity field from refraction data that has been decomposed into some function of slowness. The most common decomposition, intercept time‐slowness or [Formula: see text], is used as an intermediate step in an iterative wave field continuation procedure previously applied to one‐dimensional (1-D) velocity inversions. We extend the 1-D approach to 2-D by performing the downward continuation along numerically computed raypaths. This allows a correction to be made for the change in ray parameter induced by 2-D velocity fields. A best fitting velocity model is chosen as a surface defined by critically reflected and refracted energy that has been downward continued into a three dimensional (3-D) space of velocity, offset, and depth. Synthetic data are used to demonstrate how this approach can compensate for the effects of known lateral inhomogeneities while determining an underlying 1-D velocity field. We also use synthetic data to show how multiple refraction lines may be used to determine a general 2-D velocity model. Large offset field data collected with an Ocean Bottom Hydrophone are used to illustrate this technique in an area of significant lateral heterogeneity caused by a sloping seafloor.

Imaging the Deep Galicia margin using three-dimensional full waveform inversion

2020 ◽  
Author(s):  
Bhargav Boddupalli ◽  
Tim Minshull ◽  
Joanna Morgan ◽  
Gaye Bayrakci
Keyword(s):  
High Resolution ◽  
Travel Time ◽  
Waveform Inversion ◽  
Three Dimensional ◽  
Velocity Model ◽  
Normal Faults ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
Time Model ◽  
Full Waveform

<p>Imaging of hyperextended zone and exhumed continental mantle rocks can improve our understanding of the tectonics of the final stages of rifting. In the Deep Galicia margin, the upper and lower crust are coupled allowing the normal faults to cut through the brittle crust and penetrate to the mantle leading to serpentinization of the mantle. Localized extensional forces caused extreme thinning and elongation of crystalline continental crust causing the continental blocks to slip over a lithospheric-scale detachment fault called the S-reflector.  </p><p>A high-resolution velocity model obtained using seismic full waveform inversion gives us deeper insights into the rifting process. In this study, we present results from three dimensional acoustic full waveform inversion performed using wide-angle seismic data acquired in the deep water environments of the Deep Galicia margin using ocean bottom seismometers. We performed full waveform inversion in the time domain, starting with a velocity model obtained using travel-time tomography, of dimensions 78.5 km x 22.1 km and depth 12 km. The high-resolution modelling shows short-wavelength variations in the velocity, adding details to the travel-time model. We superimposed our final model, converted to two-way time, on pre-stack time-migrated three-dimensional reflection data from the same survey. Compared to the starting model, our model shows improved alignment of the velocity variations along the steeply dipping normal faults and a sharp velocity contrast across the S-reflector. We validated our result using checkerboard tests, by tracking changes in phases of the first arrivals during the inversion and by comparing the observed and the synthetic waveforms. We observe a clear evidence for preferential serpentinization (45 %) of the mantle with lower velocities in the mantle correlating with the fault intersections with the S-reflector.</p>

Full-waveform inversion for imaging and geologic interpretation: A deepwater Gulf of Mexico case study

2019 ◽  
Vol 7 (2) ◽  
pp. SB11-SB21
Author(s):  
Yannick Cobo ◽  
Carlos Calderón-Macías ◽  
Shihong Chi
Keyword(s):  
Gulf Of Mexico ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Full Waveform Inversion ◽  
Depth Range ◽  
Frequency Model ◽  
Amplitude Inversion ◽  
Velocity Models ◽  
Full Waveform ◽  
Wavefield Inversion

Full-waveform inversion (FWI) is commonly used in model-building workflows to improve the resolution of the shallow velocity model and thus has a potentially positive impact on the imaging of deeper targets. This type of inversion commonly makes use of first arrivals from the longest offsets. However, signal from smaller offsets and later times can extend the depth range of the FWI-derived velocity model. Waveform inversion methods that use reflections have been shown to provide greater details and accuracy when deriving velocity models for deepwater exploration and production. The derived velocity sometimes provides an improved migrated image useful for interpretation in complex geology and enhances geologic features such as subsalt sediments, faults, and channels. We have used combination of FWI and a wavefield inversion approach known as reconstructed wavefield inversion (RWI) that makes use of diving waves and reflections to derive a velocity model for a deepwater survey off the coast of Veracruz in the Gulf of Mexico. The velocity model we derived from this approach produces an improved image of the target reservoir, and furthermore contains enough geologic details for direct interpretation. We enhanced the resolution of the velocity model further by performing a poststack amplitude inversion with the FWI + RWI derived velocity used as the input low-frequency model. The resulting high-resolution velocity provides an excellent product for detecting shallow gas anomalies, delineating a gas reservoir in an anticline structure as well as a system of deep, sand-filled channels. The inverted velocity also indicates a better correlation with sonic velocity measured from two blind wells than the initial tomography velocity, indicating the benefits of FWI approaches for quantitative reservoir characterization in deepwater environments.

Full-waveform inversion for salt: A coming of age

2019 ◽  
Vol 38 (3) ◽  
pp. 204-213 ◽  
Author(s):  
Ping Wang ◽  
Zhigang Zhang ◽  
Jiawei Mei ◽  
Feng Lin ◽  
Rongxin Huang
Keyword(s):  
Waveform Inversion ◽  
Synthetic Data ◽  
Complex Salt ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
Very High Frequency ◽  
Velocity Models ◽  
Full Waveform ◽  
Streamer Data ◽  
Subsalt Imaging

Full-waveform inversion (FWI), proposed by Lailly and Tarantola in the 1980s, is considered to be the most promising data-driven tool for automatically building velocity models. Many successful examples have been reported using FWI to update shallow sediments, gas pockets, and mud volcanoes. However, successful applications of FWI to update salt structures had almost only been seen on synthetic data until recent progress at the Atlantis Field in the Gulf of Mexico. We revisited some aspects of FWI algorithms to minimize cycle-skipping and amplitude discrepancy issues and derived an FWI algorithm that is able to build complex salt velocity models. We applied this algorithm to a variety of data sets, including wide-azimuth and full-azimuth (FAZ) streamer data as well as ocean-bottom-node data, with different geologic settings in order to demonstrate the effectiveness of the method for salt velocity updates and to examine some fundamentals of the salt problem. We observed that, in multiple cases, salt velocity models from this FWI algorithm produced subsalt images of superior quality. We demonstrate with one FAZ streamer data example in Keathley Canyon that we do not necessarily need very high frequency in FWI for subsalt imaging purposes. Based on this observation, we envision that sparse node for velocity acquisition may provide appropriate data to handle large and complex salt bodies with FWI. We believe the combination of advanced FWI algorithms and appropriate data acquisition will bring a step change to subsalt imaging.

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