Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

Dutta, Gaurav; Lü, Kai; Wang, Xin; Schuster, Gerard T.

doi:10.1190/segam2013-1131.1

Cited by 8 publications

(6 citation statements)

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“…These problems are severe when there is strong attenuation that leads to strong phase delays in the arrivals (Tarantola, 1988; Aki and Richards, 2002;Zhu and Harris, 2015;Komatitsch et al, 2016). To solve these problems, it is necessary to take the attenuation factor into account when applying WT to near-surface data (Dutta and Schuster, 2014). With the stronger computational ability, to understand the attenuation in both theory and practice becomes more feasible to exploration seismologists.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

“…Based on this approximation, the velocity c is a function of ratio between the frequency ω and the reference frequency ω0. As a result, higher frequency components of seismic waves are attenuated more than low frequency components during the propagation (Dutta and Schuster, 2014). If Q >> 100, the attenuation can almost be neglected and c ≈ c0 holds except for very low or very high frequencies according to equation 17.…”

Section: Sensitivity Of the Velocity With Respect To Qmentioning

confidence: 99%

“…In this study, homogeneous Q models are used for simplification and comparison. The first reason is a relatively local change of Q may not raise enough variations in the migration image or inverted tomograms (Dutta and Schuster, 2014). Therefore, a constant Q model is setup as our strategy for the numerical tests to show the impact of the overall change of Q on the inversion.…”

Section: Numerical Testsmentioning

confidence: 99%

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Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

Han

Chen

Hanafy

et al. 2018

Journal of Applied Geophysics

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Section: Accepted Manuscriptmentioning

confidence: 99%

Section: Sensitivity Of the Velocity With Respect To Qmentioning

confidence: 99%

Section: Numerical Testsmentioning

confidence: 99%

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Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

Han

Chen

Hanafy

et al. 2018

Journal of Applied Geophysics

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“…Figures 1(a) and 1(c) show the true velocity and Q p models, respectively, used for generating the observed data with attenuation. The migration velocity model is shown in Figure 1(b) and the migration Q p model used for Q p -LSRTM (Dutta et al, 2013) is shown in Figure 1 The Q p -LSRTM image, shown in Figure 2(c), shows significant improvements in the image quality in the shallow and deeper parts. However, Q p -LSRTM is computationally expensive and it requires an estimate of the smoothly varying Q p distribution in the subsurface.…”

Section: Numerical Examplesmentioning

confidence: 99%

A cross-correlation objective function for least-squares migration and visco-acoustic imaging

Dutta

Sinha

Schuster

2014

SEG Technical Program Expanded Abstracts 2014

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SUMMARYConventional acoustic least-squares migration inverts for a reflectivity image that best matches the amplitudes of the observed data. However, for field data applications, it is not easy to match the recorded amplitudes because of the viscoelastic nature of the earth and inaccuracies in the estimation of source signature and strength at different shot locations. To relax the requirement for strong amplitude matching of least-squares migration, we use a normalized cross-correlation objective function that is only sensitive to the similarity between the predicted and the observed data. Such a normalized cross-correlation objective function is also equivalent to a time-domain phase inversion method where the main emphasis is only on matching the phase of the data rather than the amplitude. Numerical tests on synthetic and field data show that such an objective function can be used as an alternative to visco-acoustic least-squares reverse time migration (Q p -LSRTM) when there is strong attenuation in the subsurface and the estimation of the attenuation parameter Q p is insufficiently accurate.

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“…However, a LSM method can be formulated that can partly account for attenuation loss if the Q-distribution is known (Dutta et al, 2013). If the modeling operator L accounts for attenuation, then the Hessian inverse [L T L] −1 estimated by iterative LSM partly compensates for the effects of attenuation suffered by the observed data d. This requires an accurate estimate of the attenuation model as well as modeling and adjoint operators that account for anelastic effects (Blanch and Symes, 1995;Dutta et al, 2013). Figure 3 shows the migration images for the Marmousi model with attenuation.…”

Section: Benefits Of Lsmmentioning

confidence: 99%

Making the most out of least-squares migration

et al. 2014

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SUMMARYStandard migration images can suffer from migration artifacts due to 1) poor source-receiver sampling, 2) weak amplitudes caused by geometric spreading, 3) attenuation, 4) defocusing, 5) poor resolution due to limited source-receiver aperture, and 6) ringiness caused by a ringy source wavelet. To partly remedy these problems, least-squares migration (LSM), also known as linearized seismic inversion or migration deconvolution (MD), proposes to linearly invert seismic data for the reflectivity distribution. If the migration velocity model is sufficiently accurate, then LSM can mitigate many of the above problems and lead to a more resolved migration image, sometimes with twice the spatial resolution. However, there are two problems with LSM: the cost can be an order of magnitude more than standard migration and the quality of the LSM image is no better than the standard image for velocity errors of 5% or more. We now show how to get the most from leastsquares migration by reducing the cost and velocity sensitivity of LSM. LEAST-SQUARES MIGRATION THEORYThe theory for least-squares migration is described in Nemeth et al. (1999) and Duquet et al. (2000), where the smooth background does not change with iteration number. Only the reflectivity distribution is updated at each iteration. This algorithm is equivalent to linearized waveform inversion (Lailly, 1984), and can be described as iteratively updating the reflectivity vector m bywhere α is the step length, P is the preconditioning matrix that approximates the inverse to the Hessian matrix, d is the recorded reflection data, k represents the iteration index, and L represents the linearized forward modeling operator that uses the smooth background velocity model 1 . If the preconditioner is inadequate, a conjugate gradient or quasi-Newton method is used to iteratively update the solution. In practice, the algorithm is often implemented in the time-space domain.The implementation of LSM is described in Nemeth et al. (1999) and Duquet et al. (2000) for diffraction stack migration and in Plessix and Mulder (2004) for reverse time migration. Typically, diffraction stack migration provides images with fewer artifacts because it only smears reflections along the migration ellipses. In contrast, RTM automatically generates upgoing reflections from reflectors, so residuals are also smeared between 1 A smooth velocity model is typically used so as to avoid smearing residuals along the rabbit-ear wavepaths. The smearing of residuals should only be along the migration ellipses that are tangent to the reflector boundaries (Zhan et al., 2014). reflecting interfaces (Guitton, 2006; Liu et al., 2011;Zhan et al., 2014) to give rise to unwanted migration artifacts. To avoid such updates, we smooth the migration velocity model (McMechan, 1983;Loewenthal et al., 1987;Fletcher et al., 2005). To mitigate problems with an inaccurate migration velocity model, regularization terms or constraints (Sacchi et al., 2006;Guitton, 2006; Wang et al., 2011;Dong et al., 2012;Dai, 2013;Dai an...

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Attenuation compensation in least-squares reverse time migration using the visco-acoustic wave equation

Cited by 8 publications

References 30 publications

Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

Visco-acoustic wave-equation traveltime inversion and its sensitivity to attenuation errors

A cross-correlation objective function for least-squares migration and visco-acoustic imaging

Making the most out of least-squares migration

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