Nonlinear inversion of pre-stack seismic data using variable metric method

Zhang, Fanchang; Dai, Ronghuo

doi:10.1016/j.jappgeo.2016.03.035

Cited by 15 publications

(8 citation statements)

References 24 publications

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“…) is used to enhance the inversion stability, to make the low‐frequency information contained in inversion results more consistent with actual work area and to improve the lateral continuity of inversion results. In practical application, a priori model can be obtained by kriging interpolation (Hansen ) with well log data or seismic velocity analysis information under the constraint of a priori geological knowledge (Hamid and Pidlisecky ; Zhang and Dai ). Hence, we combined these two constraints and derived the following objective function for post‐stack seismic inversion

F false(boldY false) = false| false| boldR - {BY | |}_{F}^{2} + α false| false| Y | {false|}_{TV} + μ false| false| {boldY}_{priori} - Y {| |}_{F}^{2},

where Y priori is the a priori model, α is the regularization parameter for TV‐regularization constraint, μ is the regularization parameter for a priori model regularization constraint,

false| false| \cdot false| |_{F}

represents the Frobenius‐norm and

false| false| \cdot false| |_{TV}

represents the so‐called TV‐norm that is defined as (Beck and Teboulle )

\begin{matrix} true \\ right | | boldY false| |_{TV} & = & left \sum_{i = 1}^{n - 1} \sum_{j = 1}^{m - 1} \sqrt{{(Y_{i, j} - Y_{i + 1, j})}^{2} + {(Y_{i, j} - Y_{i, j + 1})}^{2}} \\ left + \sum_{i = 1}^{n - 1} | Y_{i, m} - \end{matrix}

…”

Section: Seismic Inversionmentioning

confidence: 99%

“…Then, equation can be written in a matrix form for q incident angles (Dai et al . ; Dai, Zhang, and Liu ; Zhang and Dai )

[\begin{matrix} R false(θ_{1} false) \\ R false(θ_{2} false) \\ ⋮ \\ R false(θ_{q} false) \end{matrix}] = [\begin{matrix} a false(θ_{1} false) & b false(θ_{1} false) & c false(θ_{1} false) \\ a false(θ_{2} false) & b false(θ_{2} false) & c false(θ_{2} false) \\ ⋮ & ⋮ & ⋮ \\ a false(θ_{q} false) & b false(θ_{q} false) & c false(θ_{q} false) \end{matrix}] [\begin{matrix} R_{p} \\ R_{s} \\ R_{ρ} \end{matrix}],

where

θ_{1}, θ_{2}, \dots θ_{q}

represents q incident angles.…”

Section: Seismic Inversionmentioning

confidence: 99%

“…From the definition of relative variation ratio, we can see that it takes the same form of reflectivity. Hence, the objective function takes the similar form of deconvolution (Zhang and Dai ), i.e.

0true F (p) = | | d - {boldAp false| false|}_{2}^{2} + λ \sum_{i = 1}^{3 n} ln (1 + \frac{p_{i}^{2}}{σ^{2}}),

…”

Section: Seismic Inversionmentioning

confidence: 99%

“…The conventional post-stack inversion process is through the standard recursion formulas to obtain impedance data or other parameters in a single trace (Berteussen and Ursin 1983;Zhang, Dai and Liu 2014b;Zhang and Dai 2016). However, the inversion results obtained by these formulas are sensitive to noise in seismic data (Berteussen and Ursin 1983;Hamid and Pidlisecky 2015).…”

Section: Seismic Impedance Inversionmentioning

confidence: 99%

“…So, a priori model regularization constraint (Dai et al 2014;Zhang, Dai and Liu 2014b;Liu 2015, 2016;Gholami 2016;Yin et al 2016) is used to enhance the inversion stability, to make the low-frequency information contained in inversion results more consistent with actual work area and to improve the lateral continuity of inversion results. In practical application, a priori model can be obtained by kriging interpolation (Hansen 1993) with well log data or seismic velocity analysis information under the constraint of a priori geological knowledge (Hamid and Pidlisecky 2015;Zhang and Dai 2016). Hence, we combined these two constraints and derived the following objective function for post-stack seismic 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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F false(boldY false) = false| false| boldR - {BY | |}_{F}^{2} + α false| false| Y | {false|}_{TV} + μ false| false| {boldY}_{priori} - Y {| |}_{F}^{2},

where Y priori is the a priori model, α is the regularization parameter for TV‐regularization constraint, μ is the regularization parameter for a priori model regularization constraint,