A deconvolution‐based objective function for wave‐equation inversion

Luo, Simon; Sava, Paul

doi:10.1190/1.3627773

Cited by 104 publications

(86 citation statements)

References 12 publications

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“…In the forward version of AWI, its omission will lead the algorithm to tend to increase the amplitudes of the predicted data without limit, so that all the Wiener coefficients become small. And in the reverse version of AWI that is directly analogous to Luo and Sava's (2011) formulation, omission of some form of normalization will tend to drive the predicted data toward zero. The best-fitting model, for the un-normalized reverse method for surface data, will then tend to evolve toward one that contains no reflectors and that includes a strong negative vertical velocity gradient, such that no energy reaches the receivers; appropriately normalized AWI does not suffer from this problem.…”

Section: Crosscorrelationmentioning

confidence: 99%

“…Although the genesis of our approach originally lay elsewhere, AWI is mathematically more closely related to the approaches of van Leeuwen and Mulder (2010) and Luo and Sava (2011); we discuss the relationship of AWI with these and other methods later in the paper.…”

Section: Introductionmentioning

confidence: 99%

“…These methods currently appear to fall into one of two groups: either the methods are efficient and affordable on commercial data sets in three dimensions, but fail to converge when the data and/or the model are realistically complicated, or the methods work well on realistic data, but have not so far been proven to be affordably achievable on 3D field data. Methods in the first group include those of van Mulder (2008, 2010), Luo and Sava (2011), and perhaps Ma and Hale (2013), and methods in the second group include those of van Leeuwen and Herrmann (2013) and Almomin (2012, 2015). Mathematically, our approach is most closely related to the first two methods, but it takes two important concepts from the other methods, and it is these concepts that seem to be central to the success of AWI on realistic data sets.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive waveform inversion: Theory

2016

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Conventional full-waveform seismic inversion attempts to find a model of the subsurface that is able to predict observed seismic waveforms exactly; it proceeds by minimizing the difference between the observed and predicted data directly, iterating in a series of linearized steps from an assumed starting model. If this starting model is too far removed from the true model, then this approach leads to a spurious model in which the predicted data are cycle skipped with respect to the observed data. Adaptive waveform inversion (AWI) provides a new form of full-waveform inversion (FWI) that appears to be immune to the problems otherwise generated by cycle skipping. In this method, least-squares convolutional filters are designed that transform the predicted data into the observed data. The inversion problem is formulated such that the subsurface model is iteratively updated to force these Wiener filters toward zero-lag delta functions. As that is achieved, the predicted data evolve toward the observed data and the assumed model evolves toward the true model. This new method is able to invert synthetic data successfully, beginning from starting models and under conditions for which conventional FWI fails entirely. AWI has a similar computational cost to conventional FWI per iteration, and it appears to converge at a similar rate. The principal advantages of this new method are that it allows waveform inversion to begin from less-accurate starting models, does not require the presence of low frequencies in the field data, and appears to provide a better balance between the influence of refracted and reflected arrivals upon the final-velocity model. The AWI is also able to invert successfully when the assumed source wavelet is severely in error.

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Section: Crosscorrelationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive waveform inversion: Theory

2016

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“…Since the deconvolution filter includes the normalization process between the modeled and observed data, it can properly address the unbalanced energy of traces in the damped wavefields. Luo and Sava (2011) proposed a deconvolution-based objective function for the frequencydomain FWI. They calculated the deconvolution between the modeled and observed data at each frequency with an additional axis of time-lag (or phase).…”

Section: Introductionmentioning

confidence: 99%

Time-domain full-waveform inversion of exponentially damped wavefield using the deconvolution-based objective function

Choi

Alkhalifah

2018

GEOPHYSICS

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CitationChoi Y, Alkhalifah T (2017) Time-domain full waveform inversion of exponentially damped wavefield using the deconvolution-based objective function ABSTRACTFull waveform inversion (FWI) suffers from the cycle-skipping problem when the available frequency-band of data is not low enough. We apply an exponential damping to the data to generate artificial low frequencies, which helps FWI avoid cycle skipping. In this case, the leastsquare misfit function does not properly deal with the exponentially damped wavefield in FWI, because the amplitude of traces decays almost exponentially with increasing offset in a dampedwavefield. Thus, we use a deconvolution-based objective function for FWI of the exponentially damped wavefield. The deconvolution filter includes inherently a normalization between the modeled and observed data, thus it can address the unbalanced amplitude of a damped wavefield.We, specifically, normalize the modeled data with the observed data in the frequency-domain to estimate the deconvolution filter and selectively choose a frequency-band for normalization that mainly includes the artificial low frequencies. We calculate the gradient of the objective function using the adjoint-state method. The synthetic and benchmark data examples show that our FWI algorithm generates a convergent long wavelength structure without low frequency information in the recorded data.

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“…As a natural generalization, Luo and Sava (2011) proposed a deconvolution-based misfit function. For attenuation tomography, Plessix (2006) used a misfit function based on the centroid frequency shift method (Quan and Harris, 1997), which requires a source wavelet.…”

Section: Introductionmentioning

confidence: 99%

Methods for source-independent Q estimation from microseismic and crosswell perforation shot data in a layered, isotropic viscoelastic medium

Shigapov

Kashtan

Droujinine

et al. 2013

SEG Technical Program Expanded Abstracts 2013

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SUMMARYWe consider the problem of anelastic full waveform inversion in a multi-layered, isotropic viscoelastic medium from microseismic and cross-hole perforation shots. Usually, the source wavelet is not well known, so we focus on Q estimation techniques that can handle this problem. We revisit the spectral ratio method (SRM) and discuss its domain of applicability. We conclude that SRM can be used for interval Q estimation if the sources and receivers are contained in the same homogeneous layer. To overcome the restrictions of SRM, we consider the more sophisticated source-independent full waveform inversion (SIFWI). We compare three different source-independent misfit functions on synthetic data and show that they can be used for Q estimation in a viscoelastic medium. We use 3-D complex ray theory to implement SIFWI in a layered viscoelastic medium.

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A deconvolution‐based objective function for wave‐equation inversion

Cited by 104 publications

References 12 publications

Adaptive waveform inversion: Theory

Adaptive waveform inversion: Theory

Time-domain full-waveform inversion of exponentially damped wavefield using the deconvolution-based objective function

Methods for source-independent Q estimation from microseismic and crosswell perforation shot data in a layered, isotropic viscoelastic medium

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