Application of a new 2D time-domain full-waveform inversion scheme to crosshole radar data

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. J53-J64 ◽  
Author(s):  
Jacques R. Ernst ◽  
Alan G. Green ◽  
Hansruedi Maurer ◽  
Klaus Holliger
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Radar Data ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
Arrival Times ◽  
Full Waveform ◽  
First Arrival ◽  
Radar Wave

Crosshole radar tomography is a useful tool in diverse investigations in geology, hydrogeology, and engineering. Conventional tomograms provided by standard ray-based techniques have limited resolution, primarily because only a fraction of the information contained in the radar data (i.e., the first-arrival times and maximum first-cycle amplitudes) is included in the inversion. To increase the resolution of radar tomograms, we have developed a versatile full-waveform inversion scheme that is based on a finite-difference time-domain solution of Maxwell’s equations. This scheme largely accounts for the 3D nature of radar-wave propagation and includes an efficient method for extracting the source wavelet from the radar data. After demonstrating the potential of the new scheme on two realistic synthetic data sets, we apply it to two crosshole field data sets acquired in very different geologic/hydrogeologic environments. These are the first applications of full-waveform tomography to observed crosshole radar data. The resolution of all full-waveform tomograms is shown to be markedly superior to that of the associated ray tomograms. Small subsurface features a fraction of the dominant radar wavelength and boundaries between distinct geological/hydrological units are sharply imaged in the full-waveform tomograms.

scholarly journals Application of Time-Domain Full Waveform Inversion to Cross-Hole Radar Data Measured at Xiuyan Jade Mine, China

Sensors ◽  
2018 ◽  
Vol 18 (9) ◽  
pp. 3114 ◽  
Author(s):  
Sixin Liu ◽  
Xintong Liu ◽  
Xu Meng ◽  
Lei Fu ◽  
Qi Lu ◽  
...  
Keyword(s):  
High Resolution ◽  
Ray Tracing ◽  
Time Domain ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Radar Data ◽  
Liaoning Province ◽  
Full Waveform Inversion ◽  
Full Waveform ◽  
The Time Domain

Xiuyan Jade, produced in Xiuyan County, Liaoning Province, China is one of the four famous jade in China. King Jade, which is deemed the largest jade body of the world, was broken out from a hill. The local government planned to build a tourism site based on the jade culture there. The purpose of the investigation was to evaluate the stability of subsurface foundation, and the possible positions of mined-out zones to prevent the further rolling of the jade body. Cross-hole radar tomography is the key technique in the investigation. Conventional travel time and attenuation tomography based on ray tracing theory cannot provide high-resolution images because only a fraction of the measured information is used in the inversion. Full-waveform inversion (FWI) can provide high-resolution permittivity and conductivity images because it utilizes all the information provided by the radar signals. We deduce the gradient expression of the time-domain FWI with respect to the permittivity and conductivity using a method that is different from that of the previous work and realize the FWI algorithm that can simultaneously update the permittivity and conductivity by using the conjugate gradient method. Inverted results from synthetic data show that time-domain FWI can significantly improve the resolution compared with the ray-based tomogram methods. FWI can distinguish targets that are as small as one-half to one-third wavelength and the inverted physical values are closer to the real ones than those provided by the ray tracing method. We use the FWI algorithm to the field data measured at Xiuyan jade mine. Both the inverted permittivity and conductivity can comparably delineate four mined-out zones, which exhibit low-permittivity and low-conductivity characteristics. Furthermore, the locations of the interpreted mined-out zones are in good agreement with the existing mining channels recorded by geological data.

3D prestack plane-wave, full-waveform inversion

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE135-VE144 ◽  
Author(s):  
Denes Vigh ◽  
E. William Starr
Keyword(s):  
Plane Wave ◽  
Data Acquisition ◽  
Time Domain ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Full Waveform ◽  
The Time Domain

Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers are an attractive input to waveform inversion with dramatically reduced computer run times compared to traditional shot-gather approaches. The study was conducted on two synthetic data sets — Marmousi2 and SMAART Pluto 1.5 — and a field data set. The results showed that a velocity field can be reconstructed well using a multiscale time-domain implementation of waveform inversion. Although the time-domain solution does not take advantage of wavenumber redundancy, the method is feasible on current computer architectures for 3D surveys. The inverted velocity volume produces a quality image for exploration geologists by using numerous iterations of waveform inversion.

Which data residual norm for robust elastic frequency-domain full waveform inversion?

Geophysics ◽  
2010 ◽  
Vol 75 (3) ◽  
pp. R37-R46 ◽  
Author(s):  
Romain Brossier ◽  
Stéphane Operto ◽  
Jean Virieux
Keyword(s):  
Frequency Domain ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Sampling Interval ◽  
Data Sets ◽  
Full Waveform Inversion ◽  
S Wave ◽  
Fitting Procedure ◽  
Full Waveform ◽  
Threshold Criterion

Elastic full-waveform inversion is an ill-posed data-fitting procedure that is sensitive to noise, inaccuracies of the starting model, definition of multiparameter classes, and inaccurate modeling of wavefield amplitudes. We have investigated the performance of different minimization functionals as the least-squares norm [Formula: see text], the least-absolute-values norm [Formula: see text], and combinations of both (the Huber and so-called hybrid criteria) with reference to two noisy offshore (Valhall model) and onshore (overthrust model) synthetic data sets. The four minimization functionals were implemented in 2D elastic frequency-domain full-waveform inversion (FWI), where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies. For the offshore and onshore case studies, the [Formula: see text]-norm provided the most reliable models for P- and S-wave velocities ([Formula: see text] and[Formula: see text]), even when strongly decimated data sets that correspond to few frequencies were used in the inversion and when outliers polluted the data. The [Formula: see text]-norm can provide reliable results in the presence of uniform white noise for [Formula: see text] and [Formula: see text] if the data redundancy is increased by refining the frequency sampling interval in the inversion at the expense of computational efficiency. The [Formula: see text]-norm and the Huber and hybrid criteria, unlike the [Formula: see text]-norm, allow for successful imaging of the [Formula: see text] model from noisy data in a soft-seabed environment, where the P-to-S-waves have a small footprint in the data. However, the Huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial-and-error investigations for reliable estimation. The [Formula: see text]-norm provides a robust alternative to the [Formula: see text]-norm for inverting decimated data sets in the framework of efficient frequency-domain FWI.

2D frequency-domain elastic full-waveform inversion using time-domain modeling and a multistep-length gradient approach

Geophysics ◽  
2014 ◽  
Vol 79 (2) ◽  
pp. R41-R53 ◽  
Author(s):  
Kun Xu ◽  
George A. McMechan
Keyword(s):  
Fourier Transform ◽  
Frequency Domain ◽  
Time Domain ◽  
Grid Point ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Domain Modeling ◽  
Full Waveform ◽  
Gradient Approach

To decouple the parameters in elastic full-waveform inversion (FWI), we evaluated a new multistep-length gradient approach to assign individual weights separately for each parameter gradient and search for an optimal step length along the composite gradient direction. To perform wavefield extrapolations for the inversion, we used parallelized high-precision finite-element (FE) modeling in the time domain. The inversion was implemented in the frequency domain; the data were obtained at every subsurface grid point using the discrete Fourier transform at each time-domain extrapolation step. We also used frequency selection to reduce cycle skipping, time windowing to remove the artifacts associated with different source spatial patterns between the test and predicted data, and source wavelet estimation at the receivers over the full frequency spectrum by using a fast Fourier transform. In the inversion, the velocity and density reconstructions behaved differently; as a low-wavenumber tomography (for velocities) and as a high-wavenumber migration (for density). Because velocities and density were coupled to some extent, variations were usually underestimated (smoothed) for [Formula: see text] and [Formula: see text] and correspondingly overestimated (sharpened) for [Formula: see text]. The impedances [Formula: see text] and [Formula: see text] from the products of the velocity and density results compensated for the under- or overestimations of their variations, so the recovered impedances were closer to the correct ones than [Formula: see text], [Formula: see text], and [Formula: see text] were separately. Simultaneous reconstruction of [Formula: see text], [Formula: see text], and [Formula: see text] was robust on the FE and finite-difference synthetic data (without surface waves) from the elastic Marmousi-2 model; satisfactory results are obtained for [Formula: see text], [Formula: see text], [Formula: see text], and the recovered [Formula: see text] and [Formula: see text] from their products. Convergence is fast, needing only a few tens of iterations, rather than a few hundreds of iterations that are typical in most other elastic FWI algorithms.

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 Time domain viscoelastic full waveform inversion

2017 ◽  
Vol 209 (3) ◽  
pp. 1718-1734 ◽  
Author(s):  
Gabriel Fabien-Ouellet ◽  
Erwan Gloaguen ◽  
Bernard Giroux
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Full Waveform Inversion ◽  
Full Waveform
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