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- -norm (1)
- Abubakar (2)
- algorithm (2)
- amplitude (1)
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- seismic processing and interpretation (1)
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We present the so-called local contrast-source inversion (CSI-FD) algorithm for inversion of the time-lapse seismic data. Similar to the original contrast-source inversion algorithm using the integral equation (CSI-IE) approach, in the CSI-FD, the unknown contrast source and the unknown contrast are updated alternately to minimize a predefined cost function, and hence, there is no full forward problem solution required in each iterative step of the inversion process. However, the CSI-FD algorithm uses a finitedifference frequency-domain (FDFD) approach equipped with a perfectly matched layer (PML) absorbing boundary condition, which enables this algorithm to reconstruct objects embedded in an unbounded inhomogeneous background medium. This feature makes the CSI-FD more effective than the CSI-IE for time-lapse applications because the latter only uses a homogeneous or a layered background medium. Numerical experiments show that the CSI-FD has significant advantages over the CSI-IE algorithm.

In addition, introducing the finite-difference operator into the algorithm does not reduce the efficiency of this algorithm because the stiffness matrix of the finitedifference operator is only dependent on the background medium, which does not change throughout the inversion process. Therefore, in two-dimensional (2D) configurations, this finite-difference operator only must be inverted once, and the resulting inverted operator can be reused in each iterative step of the inversion process. Furthermore, because a direct matrix inversion technique is employed in our 2D FDFD code, the computational cost to generate the response of an inhomogeneous background medium is limited.

Similar to the CSI-IE, and in order to enhance the quality of the profile reconstruction, an extra weighted L2 norm regularization term is added, which is effective for structures with sharp boundaries, as illustrated in the numerical results. The weighting parameter of this extra regularization term in the cost function is determined automatically by employing the multiplicative regularization technique. This technique is shown to be robust in terms of noise suppression and in handling limited measurement data.

Abubakar, algorithm, baseline model, change, contrast, contrast source, csi-ie method, domain, function, inhomogeneous background, inversion, Inversion Algorithm, inversion process, model, Reservoir Characterization, reservoir description and dynamics, seismic processing and interpretation, source, structure, technique, Upstream Oil & Gas, Van den Berg

SPE Disciplines: Reservoir Description and Dynamics > Reservoir Characterization > Seismic processing and interpretation (1.00)

Zaslavsky, M. (Schlumberger-Doll Research) | Druskin, V. (Schlumberger-Doll Research) | Liu, J. (Schlumberger-Doll Research) | Habashy, T. (Schlumberger-Doll Research) | Abubakar, A. (Schlumberger-Doll Research)

We present three-dimensional inversion algorithms for inversion of cross-well electromagnetic and controlled-source electromagnetic (CSEM) data. The inversion is accomplished with a Gauss-Newton technique where the model parameters are forced to lie within their upper and lower bounds by means of a non-linear transformation procedure. The Jacobian is computed using an adjoint method. A line search method is employed to enforce a reduction of the cost function at each iteration. To improve the conditioning of the inversion problem, we use one of two different regularization schemes. The first is an

Electromagnetic (EM) methods are one of the important tools for appraisal of a reservoir because of their sensitivity to conductivity which is a function of the fluid saturation. One of the commonly used EM techniques is single-well induction logging measurement. This technique is employed both as a wireline measurement and as a measurement while drilling to estimate near wellbore conductivity. This induction logging measurement has a sensitivity of up to a few meters from the well and is a function of the separation between the transmitter and receiver, the frequency of operation and the resistivity distribution.

To reach deeper into the reservoir, a cross-well EM technology was developed; see Wilt

-norm, Abubakar, algorithm, amplitude, Artificial Intelligence, conductivity, conductivity distribution, CSEM, formation evaluation, function, grid, inversion, log analysis, model, multiplicative cost function, nonlinear, problem, receiver, regularization, Reservoir Characterization, reservoir description and dynamics, solution, transmitter, Upstream Oil & Gas, vector, well logging

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