Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

A B S T R A C TFull waveform inversion aims to use all information provided by seismic data to deliver high-resolution models of subsurface parameters. However, multiparameter full waveform inversion suffers from an inherent trade-off between parameters and from ill-posedness due to the highly non-linear nature of full waveform inversion. Also, the models recovered using elastic full waveform inversion are subject to local minima if the initial models are far from the optimal solution. In addition, an objective function purely based on the misfit between recorded and modelled data may honour the seismic data, but disregard the geological context. Hence, the inverted models may be geologically inconsistent, and not represent feasible lithological units. We propose that all the aforementioned difficulties can be alleviated by explicitly incorporating petrophysical information into the inversion through a penalty function based on multiple probability density functions, where each probability density function represents a different lithology with distinct properties. We treat lithological units as clusters and use unsupervised K-means clustering to separate the petrophysical information into different units of distinct lithologies that are not easily distinguishable. Through several synthetic examples, we demonstrate that the proposed framework leads full waveform inversion to elastic models that are superior to models obtained either without incorporating petrophysical information, or with a probabilistic penalty function based on a single probability density function. [Correction added on 24 January 2020, after first online publication: the word "wavefield" in the title has been replaced with "waveform" in this version.]

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“…An alternative regularization approach uses total variation by adding another term

{scriptJ}_{M}^{TV} false(λ, μ false)

to the objective function in order to preserve sharp interfaces in the recovered models (Guitton ; Zhang et al . ),

{scriptJ}_{M}^{TV} false(λ, μ false) = \int_{normalΩ} \sqrt{{false∥ \nabla λ (x) false∥}^{2}} d x + \int_{normalΩ} \sqrt{{false∥ \nabla μ (x) false∥}^{2}} d x,

where Ω represents the subsurface spatial domain.…”

Section: Elastic Wavefield Tomographymentioning

confidence: 99%

Elastic full waveform inversion with probabilistic petrophysical clustering

Aragao

Sava

2020

Geophysical Prospecting

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“…The gradient (for a source and receiver pair) of the misfit (objective) function in equation 3 can be calculated from the adjoint-state method (Plessix, 2006;Zhang et al, 2018a),…”

Section: Theorymentioning

confidence: 99%

“…The L 2 norm objective function requires that the maximum mismatch of the predicted and observed data should not exceed a half-cycle for all arrivals; otherwise, the adjoint source is cycle-skipped. The correlationbased objective function (Van Leeuwen andMulder, 2008, 2010;Routh et al, 2011;Choi and Alkhalifah, 2012;Chi et al, 2015;Zhang et al, 2018a;Wu et al, 2019) or adaptive full waveform inversion (AWI) (Warner and Guasch, 2014) can compare the arrivals globally within a time window and in some cases are free of cycle-skipping. Third, find a simplified representation of the complex data.…”

Section: Introductionmentioning

confidence: 99%

“…Crosscorrelation-type objective functions emphasize matching the phases of the predicted and the observed data, and thus, are insensitive to amplitude errors caused by the simplified physics we use to represent the medium (Choi and Alkhalifah, 2012). The non-zero lag crosscorrelation based FWI (Van Leeuwen andMulder, 2008, 2010;Zhang et al, 2018a) have an additional degree of freedom when comparing two data sets, which breaks the half-cycle difference criterion of the point-wise waveform comparison. However, the global crosscorrelation is often biased towards strong arrivals and is vulnerable to crosstalks between neighboring arrivals when using a large time lag.…”

Section: Introductionmentioning

confidence: 99%

“…However, the sensitivity kernels of the proposed method as shown inFigures 6e and 6fhave the right updating directions. A larger stretching/squeezing range allows a larger search area when comparing the observed and predicted data Zhang et al (2018a). suggest using the auto-correlation…”

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confidence: 99%

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Local-crosscorrelation elastic full-waveform inversion

Zhang

Alkhalifah

2019

GEOPHYSICS

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Full-waveform inversion (FWI) in its classic form is a method based on minimizing the [Formula: see text] norm of the difference between the observed and simulated seismic waveforms at the receiver locations. The objective is to find a subsurface model that reproduces the full waveform including the traveltimes and amplitudes of the observed seismic data. However, the widely used [Formula: see text]-norm-based FWI faces many issues in practice. The point-wise comparison of waveforms fails when the phase difference between the compared waveforms of the predicted and observed data is larger than a half-cycle. In addition, amplitude matching is impractical considering the simplified physics that we often use to describe the medium. To avoid these known problems, we have developed a novel elastic FWI algorithm using the local-similarity attribute. It compares two traces within a predefined local time extension; thus, is not limited by the half-cycle criterion. The algorithm strives to maximize the local similarities of the predicted and observed data by stretching/squeezing the observed data. Phases instead of amplitudes of the seismic data are used in the comparison. The algorithm compares two data sets locally; thus, it performs better than the global correlation in matching multiple arrivals. Instead of picking/calculating one stationary stretching/squeezing curve, we used a weighted integral to find all possible stationary curves. We also introduced a polynomial-type weighting function, which is determined only by the predefined maximum stretching/squeezing and is guaranteed to be smoothly varying within the extension range. Compared with the previously used Gaussian or linear weighting functions, our polynomial one has fewer parameters to play around with. A modified synthetic elastic Marmousi model and the North Sea field data are used to verify the effectiveness of the developed approach and also reveal some of its limitations.

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Full waveform inversion based on a local traveltime correction and zero-mean cross-correlation-based misfit function

Dong

Han

et al. 2019

Acta Geophys.

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Normalized nonzero-lag crosscorrelation elastic full-waveform inversion

Cited by 25 publications

References 44 publications

Elastic full waveform inversion with probabilistic petrophysical clustering

Elastic full waveform inversion with probabilistic petrophysical clustering

Local-crosscorrelation elastic full-waveform inversion

Full waveform inversion based on a local traveltime correction and zero-mean cross-correlation-based misfit function

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