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.

scholarly journals Accelerating full-waveform inversion with attenuation compensation

Geophysics ◽  
2018 ◽  
Vol 83 (1) ◽  
pp. A13-A20 ◽  
Author(s):  
Zhiguang Xue ◽  
Junzhe Sun ◽  
Sergey Fomel ◽  
Tieyuan Zhu
Keyword(s):  
Wave Equation ◽  
Convergence Rate ◽  
Waveform Inversion ◽  
Adjoint Operator ◽  
Synthetic Data ◽  
Low Rank ◽  
Full Waveform Inversion ◽  
Time Step ◽  
Velocity Models ◽  
Full Waveform

The calculation of the gradient in full-waveform inversion (FWI) usually involves crosscorrelating the forward-propagated source wavefield and the back-propagated data residual wavefield at each time step. In the real earth, propagating waves are typically attenuated due to the viscoelasticity, which results in an attenuated gradient for FWI. Replacing the attenuated true gradient with a [Formula: see text]-compensated gradient can accelerate the convergence rate of the inversion process. We have used a phase-dispersion and an amplitude-loss decoupled constant-[Formula: see text] wave equation to formulate a viscoacoustic FWI. We used this wave equation to generate a [Formula: see text]-compensated gradient, which recovers amplitudes while preserving the correct kinematics. We construct an exact adjoint operator in a discretized form using the low-rank wave extrapolation technique, and we implement the gradient compensation by reversing the sign of the amplitude-loss term in the forward and adjoint operators. This leads to a [Formula: see text]-dependent gradient preconditioning method. Using numerical tests with synthetic data, we demonstrate that the proposed viscoacoustic FWI using a constant-[Formula: see text] wave equation is capable of producing high-quality velocity models, and our [Formula: see text]-compensated gradient accelerates its convergence rate.

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 A parameterization study for elastic VTI full-waveform inversion of hydrophone components: Synthetic and North Sea field data examples

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. R299-R308 ◽  
Author(s):  
Antoine Guitton ◽  
Tariq Alkhalifah
Keyword(s):  
North Sea ◽  
Waveform Inversion ◽  
Transversely Isotropic ◽  
Horizontal Velocity ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
S Wave ◽  
Data Set ◽  
Full Waveform ◽  
Streamer Data

Choosing the right parameterization to describe a transversely isotropic medium with a vertical symmetry axis (VTI) allows us to match the scattering potential of these parameters to the available data in a way that avoids a potential tradeoff and focuses on the parameters to which the data are sensitive. For 2D elastic full-waveform inversion in VTI media of pressure components and for data with a reasonable range of offsets (as with those found in conventional streamer data acquisition systems), assuming that we have a kinematically accurate normal moveout velocity ([Formula: see text]) and anellipticity parameter [Formula: see text] (or horizontal velocity [Formula: see text]) obtained from tomographic methods, a parameterization in terms of horizontal velocity [Formula: see text], [Formula: see text], and [Formula: see text] is preferred to the more conventional parameterization in terms of [Formula: see text], [Formula: see text], and [Formula: see text]. In the [Formula: see text], [Formula: see text], and [Formula: see text] parameterization and for reasonable scattering angles (<[Formula: see text]), [Formula: see text] acts as a “garbage collector” and absorbs most of the amplitude discrepancies between the modeled and observed data, more so when density [Formula: see text] and S-wave velocity [Formula: see text] are not inverted for (a standard practice with streamer data). On the contrary, in the [Formula: see text], [Formula: see text], and [Formula: see text] parameterization, [Formula: see text] is mostly sensitive to large scattering angles, leaving [Formula: see text] exposed to strong leakages from [Formula: see text] mainly. These assertions will be demonstrated on the synthetic Marmousi II as well as a North Sea ocean bottom cable data set, in which inverting for the horizontal velocity rather than the vertical velocity yields more accurate models and migrated images.

High frequency full waveform inversion as an interpretation solution

2019 ◽  
Vol 59 (2) ◽  
pp. 904
Author(s):  
Laurence Letki ◽  
Matt Lamont ◽  
Troy Thompson
Keyword(s):  
High Frequency ◽  
Waveform Inversion ◽  
Earth Model ◽  
Full Waveform Inversion ◽  
Ocean Bottom ◽  
Very High Frequency ◽  
Computing Power ◽  
Seismic Surveys ◽  
Full Waveform ◽  
Direct Interpretation

The amount of available data to help us characterise the subsurface is ever increasing. Large seismic surveys, long offsets, multi- and full-azimuth datasets, including 3D and 4D, marine, ocean-bottom nodes and extremely high fold land surveys, are now common. In parallel, computing power is also increasing and, in combination with better data, this enables us to develop better tools and to use better physics to build models of the subsurface. Wave-equation based techniques, such as full waveform inversion (FWI), have therefore become a lot more practical. FWI uses the entire wavefield, including refractions and reflections, primaries and multiples, to generate a refined, high resolution Earth model. This technique is now commonly used at lower frequencies (up to 12 Hz) to derive more accurate models for improved seismic imaging and reduced depth conversion uncertainty. By including higher frequencies in FWI, we can attempt to resolve for finer and finer details. FWI models using the entire bandwidth of the seismic data constitute an interpretation product in itself, with applications in both structural interpretation and reservoir characterisation. Incorporating more physics within the FWI implementation, combined with modern supercomputer facilities, promises to increase the focus on very high frequency FWI in the coming years. In this paper, through a series of field examples, we illustrate the applications and rewards of high frequency FWI: from improved imaging, improved quantitative interpretation and depth conversion to a direct interpretation of the FWI models.

scholarly journals Adding Prior Information in FWI through Relative Entropy

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 599
Author(s):  
Danilo Cruz ◽  
João de Araújo ◽  
Carlos da Costa ◽  
Carlos da Silva
Keyword(s):  
Inverse Problem ◽  
Relative Entropy ◽  
Global Minimum ◽  
Prior Information ◽  
Waveform Inversion ◽  
Petroleum Industry ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Full Waveform

Full waveform inversion is an advantageous technique for obtaining high-resolution subsurface information. In the petroleum industry, mainly in reservoir characterisation, it is common to use information from wells as previous information to decrease the ambiguity of the obtained results. For this, we propose adding a relative entropy term to the formalism of the full waveform inversion. In this context, entropy will be just a nomenclature for regularisation and will have the role of helping the converge to the global minimum. The application of entropy in inverse problems usually involves formulating the problem, so that it is possible to use statistical concepts. To avoid this step, we propose a deterministic application to the full waveform inversion. We will discuss some aspects of relative entropy and show three different ways of using them to add prior information through entropy in the inverse problem. We use a dynamic weighting scheme to add prior information through entropy. The idea is that the prior information can help to find the path of the global minimum at the beginning of the inversion process. In all cases, the prior information can be incorporated very quickly into the full waveform inversion and lead the inversion to the desired solution. When we include the logarithmic weighting that constitutes entropy to the inverse problem, we will suppress the low-intensity ripples and sharpen the point events. Thus, the addition of entropy relative to full waveform inversion can provide a result with better resolution. In regions where salt is present in the BP 2004 model, we obtained a significant improvement by adding prior information through the relative entropy for synthetic data. We will show that the prior information added through entropy in full-waveform inversion formalism will prove to be a way to avoid local minimums.

scholarly journals Velocity model building by 3D frequency-domain, full-waveform inversion of wide-aperture seismic data

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE101-VE117 ◽  
Author(s):  
Hafedh Ben-Hadj-Ali ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
High Resolution ◽  
Frequency Domain ◽  
Distributed Memory ◽  
Waveform Inversion ◽  
Steepest Descent Method ◽  
Frequency Domain Method ◽  
Full Waveform Inversion ◽  
Direct Solver ◽  
Velocity Models ◽  
Full Waveform

We assessed 3D frequency-domain (FD) acoustic full-waveform inversion (FWI) data as a tool to develop high-resolution velocity models from low-frequency global-offset data. The inverse problem was posed as a classic least-squares optimization problem solved with a steepest-descent method. Inversion was applied to a few discrete frequencies, allowing management of a limited subset of the 3D data volume. The forward problem was solved with a finite-difference frequency-domain method based on a massively parallel direct solver, allowing efficient multiple-shot simulations. The inversion code was fully parallelized for distributed-memory platforms, taking advantage of a domain decomposition of the modeled wavefields performed by the direct solver. After validation on simple synthetic tests, FWI was applied to two targets (channel and thrust system) of the 3D SEG/EAGE overthrust model, corresponding to 3D domains of [Formula: see text] and [Formula: see text], respectively. The maximum inverted frequencies are 15 and [Formula: see text] for the two applications. A maximum of 30 dual-core biprocessor nodes with [Formula: see text] of shared memory per node were used for the second target. The main structures were imaged successfully at a resolution scale consistent with the inverted frequencies. Our study confirms the feasibility of 3D frequency-domain FWI of global-offset data on large distributed-memory platforms to develop high-resolution velocity models. These high-velocity models may provide accurate macromodels for wave-equation prestack depth migration.

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