Nonlinear multichannel impedance inversion by total-variation regularization

Gholami, Ali

doi:10.1190/geo2015-0004.1

Cited by 136 publications

(25 citation statements)

References 17 publications

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“…When r ( i ) is small, equation can be approximated as (Gholami )

r false(i false) \approx \frac{Δ z (i)}{2 z (i)} \approx \frac{1}{2} ln \frac{z (i + 1)}{z (i)} .

…”

Section: Seismic Inversionmentioning

confidence: 99%

“…The discretization of equation yields

r = By,

where B is the difference operator defined as (Gholami )

B = [\begin{matrix} - 1 & 1 \\ - 1 & 1 \\ ⋱ & ⋱ \\ - 1 & 1 \\ - 1 & 1 \end{matrix}],

and

y_{i} = false(1 / 2 false) ln z_{i}

, which is the i th element of y .…”

Section: Seismic Inversionmentioning

confidence: 99%

“…In addition, it cannot allow spatial regularization (Jamali Hondori et al . ; Gholami ; Hamid and Pidlisecky ). So, we deal with the multi‐trace inversion.…”

Section: Seismic Inversionmentioning

confidence: 99%

“…reflectivity) at sample i, respectively (Berteussen and Ursin 1983;Youzwishen 2001). When r(i) is small, equation (13) can be approximated as (Gholami 2015) r…”

Section: Seismic Impedance Inversionmentioning

confidence: 99%

“…However, the inversion results obtained by these formulas are sensitive to noise in seismic data (Berteussen and Ursin 1983;Hamid and Pidlisecky 2015). In addition, it cannot allow spatial regularization (Jamali Hondori et al 2013;Gholami 2015;Hamid and Pidlisecky 2015). So, we deal with the multi-trace inversion.…”

Section: Seismic Impedance Inversionmentioning

confidence: 99%

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Seismic deconvolution and inversion with erratic data

Dai

Chao

Yang

et al. 2018

Geophysical Prospecting

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If there are some erratic data (e.g. outliers), which may arise from measurement error, or other reasons, in seismic data, the seismic deconvolution and inversion need to be implemented in a way that minimizes their effects. However, the deconvolution and inversion methods based on L2‐norm misfit function are highly sensitive to these erratic seismic observations. As an alternative, L1‐norm misfit functions are more robust and erratic‐resistant. In order to find the solution of the inverse problem constrained by an L1‐norm misfit function, an iteratively re‐weighted least squares algorithm is used frequently. However, it is relatively time consuming. In this paper, we propose a new method based on the sparse signal representation theory. The overcomplete dictionary used for the sparse representation of seismic data with erratic data is composed of two bases: a wavelet basis used for representing the seismic data to implement deconvolution and a Dirac basis used for representing the erratic data. In addition, at the stage of seismic inversion after deconvolution, total variation and a priori model are used as the regularization constraint terms to estimate inversion results with a blocky and laterally continuous structure. The new method is successfully tested on the noisy synthetic seismic data with erratic data. Finally, the proposed method is performed on a real seismic data section, and the inversion results are reasonable, i.e. consistent with the geologic structure of the original seismic data. Compared to the conventional sparse deconvolution and inversion method, the proposed method not only eliminates the effect of outliers, but also has highly improved computational efficiency.

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“…When r ( i ) is small, equation can be approximated as (Gholami )

r false(i false) \approx \frac{Δ z (i)}{2 z (i)} \approx \frac{1}{2} ln \frac{z (i + 1)}{z (i)} .

…”

Section: Seismic Inversionmentioning

confidence: 99%

“…The discretization of equation yields

r = By,

where B is the difference operator defined as (Gholami )

B = [\begin{matrix} - 1 & 1 \\ - 1 & 1 \\ ⋱ & ⋱ \\ - 1 & 1 \\ - 1 & 1 \end{matrix}],

and

y_{i} = false(1 / 2 false) ln z_{i}

, which is the i th element of y .…”

Section: Seismic Inversionmentioning

confidence: 99%

“…In addition, it cannot allow spatial regularization (Jamali Hondori et al . ; Gholami ; Hamid and Pidlisecky ). So, we deal with the multi‐trace inversion.…”

Section: Seismic Inversionmentioning

confidence: 99%

“…reflectivity) at sample i, respectively (Berteussen and Ursin 1983;Youzwishen 2001). When r(i) is small, equation (13) can be approximated as (Gholami 2015) r…”

Section: Seismic Impedance Inversionmentioning

confidence: 99%