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Maximum likelihood estimation of reflection coefficients from seismic data, a case study
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Also an 1-D algorithm, in which any numbers of layers can be included and in which an inversion is achieved for any two free layer-parameters, has been developed. Because only two data values are available at one frequency, the method is not directly sufficient to produce a true sounding. Therefore, maximum use should be made of geologic control and subsidiary geophysical information to assume other parameters. The inversion needs an initial model and optimization, because even for a simple two-layer model the only unique solution can be obtained by assuming the upper layer resistivity to be known. In many locations it may be possible to detect two or more VLF stations at different azimuths, indicating possible anisotropy or lateral changes in structure in addition to the desired 1-D geometries. The possibility to rotate surface impedances allows the interpretation of any single anisotropic layer sandwiched in isotropic layers. Some field applications are presented to give an idea of the capabilities of developed programs and numerical results are also compared with 2-D numerical calculations of the transmission surface analogy method.
Maximum Likelihood Estimation of Reflection Coefficients from Seismic Data, a Case Study I. BREVIK and E.W. BERG Reservoir Description Group, Continental Shelf and Petroleum Technology, Research Institute Ltd., IKUA/S, P.O. Box 1883, N-7001 Trondheim (Norway)
This paper concerns an application of a nonlinear inversion algorithm for the estimation of reflection coefficients from real seismic data, using a 1D seismic impulse response model. The algorithm has also been tested with respect to stability and uniqueness using a synthetic seismic section. Due to the occurrence of local minima of the objective function, the estimates of the model parameters showed a dependency on the initial values. This dependency seemed to increase with the level of noise. Using stacked and time-migrated 3D surface seismic sections and well-log data, we have applied this algorithm in order to estimate a high resolution section of reflection coefficients in the vicinity of a well, at a depth of approximately 2400 m. We were able to obtain sets of reflection coefficients at a sample rate of 2 ms using seismic data sampled at 4-ms intervals. This corresponds to a vertical thickness of approximately 2.5 m at this depth. Such a high resolution is needed for detailed reservoir studies.
Also an 1-D algorithm, in which any numbers of layers can be included and in which an inversion is achieved for any two free layer-parameters, has been developed. Because only two data values are available at one frequency, the method is not directly sufficient to produce a true sounding. Therefore, maximum use should be made of geologic control and subsidiary geophysical information to assume other parameters. The inversion needs an initial model and optimization, because even for a simple two-layer model the only unique solution can be obtained by assuming the upper layer resistivity to be known. In many locations it may be possible to detect two or more VLF stations at different azimuths, indicating possible anisotropy or lateral changes in structure in addition to the desired 1-D geometries. The possibility to rotate surface impedances allows the interpretation of any single anisotropic layer sandwiched in isotropic layers. Some field applications are presented to give an idea of the capabilities of developed programs and numerical results are also compared with 2-D numerical calculations of the transmission surface analogy method.
Maximum Likelihood Estimation of Reflection Coefficients from Seismic Data, a Case Study I. BREVIK and E.W. BERG Reservoir Description Group, Continental Shelf and Petroleum Technology, Research Institute Ltd., IKUA/S, P.O. Box 1883, N-7001 Trondheim (Norway)
This paper concerns an application of a nonlinear inversion algorithm for the estimation of reflection coefficients from real seismic data, using a 1D seismic impulse response model. The algorithm has also been tested with respect to stability and uniqueness using a synthetic seismic section. Due to the occurrence of local minima of the objective function, the estimates of the model parameters showed a dependency on the initial values. This dependency seemed to increase with the level of noise. Using stacked and time-migrated 3D surface seismic sections and well-log data, we have applied this algorithm in order to estimate a high resolution section of reflection coefficients in the vicinity of a well, at a depth of approximately 2400 m. We were able to obtain sets of reflection coefficients at a sample rate of 2 ms using seismic data sampled at 4-ms intervals. This corresponds to a vertical thickness of approximately 2.5 m at this depth. Such a high resolution is needed for detailed reservoir studies.