Abstract
The seismic sedimentology is an emerging inter-discipline originating from the seismic stratigraphy and sequence stratigraphy. However, implementation of the seismic sedimentological research is found with high difficulties, due to influences imposed by structural and depositional background data (including strong reflections). In this paper, seismic records are regarded as a combination of the reflection from the depositional background and lithological data volumes, and moreover, the seismogram of the depositional background data is characterized by the low frequency and stable phase. Subsequently, the Kernel Hebbian Algorithm (KHA) has been modified to remove the influence of the depositional background data. The seismic trace data are used as the training set, and an innovative attempt has been made to incorporate the Ricker wavelet kernel function. Finally, a depositional background data volume extraction methodology with respect to input of higher-dimension seismic data has been developed, on the basis of the Modified KHA (MKHA), so as to obtain the lithological data volume. Utilizing the unsupervised online learning capabilities of the MKHA, iterative calculation of Kernel PCA can greatly reduce the computational complexity and can be adapted to big data problems. This paper introduces the Ricker wavelet kernel function to transform the original seismic data into the feature space through the inner-product operation, extract the non-linear features, and solve the problem that the seismic data of the original sample space is linearly inseparable. The seismic sedimentological analysis based on the lithological data volume that is able to reflect hidden sand bodies can achieve elaborate carving of the reservoir. The proposed method has been tested in Working Block A of the East-1 district in the Sulige gas field, the Ordos Basin, China. The case study demonstrates that the presented method is capable of efficiently removing the depositional background data, and making great contributions to improving accuracy of the seismic sedimentological analysis of the effective reservoir, with the help of higher-dimension seismic data.
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Notes
According to the KHA (Kim et al. 2005), in the Reproducing Kernel Hilbert Space (RKHS), \(b(t) = W(t)\phi (S(t))\). W is a weight matrix. \(\phi (S(t))\) is a pattern presented at time t which is randomly selected from the mapped data points \(\left\{ {\phi \left( {S_{1} } \right), \ldots \phi \left( {S_{m} } \right)} \right\}\). For notational convenience, we assume that there is a function \(J(t)\) which maps t to \(i \in \left\{ {1, \ldots ,m} \right\}\) ensuring \(\phi (S(J(t))) = \phi (S_{i} )\)and denote \(\phi (S(J(t)))\) simply by \(\phi (S(t))\). From the direct KPCA solution, it is known that \(W(t)\) can be expanded in the mapped data points \(\phi (S_{i} )\). This restricts the search space to linear combinations of the \(\phi (S_{i} )\) such that \(W(t)\) can be expressed as \(W(t) = A(t)\phi\) with a \(l \times m\) matrix \(A(t) = \left( {a_{1} (t)^{\text{T}} , \ldots a_{l} (t)^{\text{T}} } \right)^{\text{T}}\) of the weight expansion coefficients. The ith row \(a_{i} = \left( {a_{i1} , \ldots a_{im} } \right)\)of\(A(t)\) corresponds to the expansion coefficients of the ith eigenvector of K in the \(\phi (S_{i} )\), i.e., \(w_{i} \left( t \right) = \phi^{\text{T}} a_{i} \left( t \right)\).
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This work was financially supported by the National Science and Technology Major Project (2017ZX05001-003).
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Dou, Y. A method to remove depositional background data based on the Modified Kernel Hebbian Algorithm. Acta Geophys. 68, 701–710 (2020). https://doi.org/10.1007/s11600-020-00415-2
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DOI: https://doi.org/10.1007/s11600-020-00415-2