Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak re...Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchy- constrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.展开更多
In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality. From one example the article indicates that the fundamentality of the locally solid Riesz spa...In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality. From one example the article indicates that the fundamentality of the locally solid Riesz space is independent from the Lebesgue property.展开更多
基金supported by the Major Basic Research Development Program of China (973 Program)(No.2013CB228606)the National Science foundation of China (No.41174117)+1 种基金the National Major Science-Technology Project (No.2011ZX05031-001)Innovation Fund of PetroChina (No.2010D-5006-0301)
文摘Sparsity constrained deconvolution can improve the resolution of band-limited seismic data compared to conventional deconvolution. However, such deconvolution methods result in nonunique solutions and suppress weak reflections. The Cauchy function, modified Cauchy function, and Huber function are commonly used constraint criteria in sparse deconvolution. We used numerical experiments to analyze the ability of sparsity constrained deconvolution to restore reflectivity sequences and protect weak reflections under different constraint criteria. The experimental results demonstrate that the performance of sparsity constrained deconvolution depends on the agreement between the constraint criteria and the probability distribution of the reflectivity sequences; furthermore, the modified Cauchy- constrained criterion protects the weak reflections better than the other criteria. Based on the model experiments, the probability distribution of the reflectivity sequences of carbonate and clastic formations is statistically analyzed by using well-logging data and then the modified Cauchy-constrained deconvolution is applied to real seismic data much improving the resolution.
基金the Research Fund for the Doctoral Program of Higher Education(20010055013)
文摘In this paper we focus ourselves on the positive cone of the locally solid Riesz spaces to characterize the fundamentality. From one example the article indicates that the fundamentality of the locally solid Riesz space is independent from the Lebesgue property.
