Elastic frequency-domain finite-difference contrast source inversion method

He, Qinglong; Chen, Yong; Han, Bo; Li, Yang

doi:10.1088/0266-5611/32/3/035009

Cited by 5 publications

(7 citation statements)

References 43 publications

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“…; He et al . ). The objective function is defined as

E ({boldR}_{ρ}, {boldR}_{I_{P}}, {boldR}_{I_{S}}, {boldU}_{ρ}, {boldU}_{I_{P}}, {boldU}_{I_{S}}) = (J + J_{normalTK}) J_{normalMR},

where

\begin{matrix} true \\ right J_{normalMR} & = & left \frac{1}{3} \sum_{Ω} ([γ_{ρ} ({(||, \nabla U_{ρ})}^{2} + δ_{ρ}) + γ_{I_{P}} ({(||, \nabla U_{I_{P}})}^{2} + δ_{I_{P}})) \\ left + (], γ_{I_{S}}, ({(||, \nabla U_{I_{S}})}^{2} + δ_{I_{S}})) \end{matrix}

is the MR term,

γ_{ρ}

γ_{I_{P}}

and

γ_{I_{S}}

are the normalized factors, and

δ_{ρ}

δ_{I_{P}}

and

δ_{I_{S}}

are the smoothing parameters.…”

Section: Theory and Methodologymentioning

confidence: 97%

“…; Li, Semerci and Abubakar ; He et al . ). L1‐norm and L2‐norm regularizers generally favour piecewise constant contrasts and smooth profiles, respectively.…”

Section: Introductionmentioning

confidence: 97%

“…, ; He et al . ). It is also worth noting that the minimization of the multiplicative cost functional can be performed analytically in CSI with the weighted L2‐norm MR.…”

Section: Introductionmentioning

confidence: 97%

“…To solve this problem, researchers developed the multiplicative regularization (MR) scheme, which utilizes a multiplicative factor as a regularization term to constrain the inversion and thus eliminates the requirement of a weighting parameter. MR was first proposed in contrast-source inversion (CSI) (van den Berg, Abubakar and Fokkema 2003;Abubakar et al 2008;Li, Semerci and Abubakar 2013;He et al 2016). L1-norm and L2-norm regularizers generally favour piecewise constant contrasts and smooth profiles, respectively.…”

mentioning

confidence: 99%

“…L1-norm and L2-norm regularizers generally favour piecewise constant contrasts and smooth profiles, respectively. The weighted L2-norm regularizer favours flat parts and non-flat parts of the model equally and has become increasingly more popular in finite-difference CSI (Abubakar et al 2008(Abubakar et al , 2009He et al 2016). It is also worth noting that the minimization of the multiplicative cost functional can be performed analytically in CSI with the weighted L2-norm MR.…”

mentioning

confidence: 99%

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Imaging of elastic seismic data by least‐squares reverse time migration with weighted L2‐norm multiplicative and modified total‐variation regularizations

Ren

2019

Geophysical Prospecting

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Least‐squares reverse time migration has the potential to yield high‐quality images of the Earth. Compared with acoustic methods, elastic least‐squares reverse time migration can effectively address mode conversion and provide velocity/impendence and density perturbation models. However, elastic least‐squares reverse time migration is an ill‐posed problem and suffers from a lack of uniqueness; further, its solution is not stable. We develop two new elastic least‐squares reverse time migration methods based on weighted L2‐norm multiplicative and modified total‐variation regularizations. In the proposed methods, the original minimization problem is divided into two subproblems, and the images and auxiliary variables are updated alternatively. The method with modified total‐variation regularization solves the two subproblems, a Tikhonov regularization problem and an L2‐total‐variation regularization problem, via an efficient inversion workflow and the split‐Bregman iterative method, respectively. The method with multiplicative regularization updates the images and auxiliary variables by the efficient inversion workflow and nonlinear conjugate gradient methods in a nested fashion. We validate the proposed methods using synthetic and field seismic data. Numerical results demonstrate that the proposed methods with regularization improve the resolution and fidelity of the migration profiles and exhibit superior anti‐noise ability compared with the conventional method. Moreover, the modified‐total‐variation‐based method has marginally higher accuracy than the multiplicative‐regularization‐based method for noisy data. The computational cost of the proposed two methods is approximately the same as that of the conventional least‐squares reverse time migration method because no additional forward computation is required in the inversion of auxiliary variables.

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“…; He et al . ). The objective function is defined as

E ({boldR}_{ρ}, {boldR}_{I_{P}}, {boldR}_{I_{S}}, {boldU}_{ρ}, {boldU}_{I_{P}}, {boldU}_{I_{S}}) = (J + J_{normalTK}) J_{normalMR},

where

\begin{matrix} true \\ right J_{normalMR} & = & left \frac{1}{3} \sum_{Ω} ([γ_{ρ} ({(||, \nabla U_{ρ})}^{2} + δ_{ρ}) + γ_{I_{P}} ({(||, \nabla U_{I_{P}})}^{2} + δ_{I_{P}})) \\ left + (], γ_{I_{S}}, ({(||, \nabla U_{I_{S}})}^{2} + δ_{I_{S}})) \end{matrix}

is the MR term,

γ_{ρ}

γ_{I_{P}}

and

γ_{I_{S}}

are the normalized factors, and

δ_{ρ}

δ_{I_{P}}

and

δ_{I_{S}}

are the smoothing parameters.…”

Section: Theory and Methodologymentioning

confidence: 97%

“…; Li, Semerci and Abubakar ; He et al . ). L1‐norm and L2‐norm regularizers generally favour piecewise constant contrasts and smooth profiles, respectively.…”

Section: Introductionmentioning

confidence: 97%

“…, ; He et al . ). It is also worth noting that the minimization of the multiplicative cost functional can be performed analytically in CSI with the weighted L2‐norm MR.…”

Section: Introductionmentioning

confidence: 97%

mentioning

confidence: 99%

mentioning

confidence: 99%

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