应用Lie对称法,当弹性能具有三阶非调和修正项时,分析纵向变形的非线性弹性波动方程.通过不同对称下的恒等条件,寻找对称代数,并将它简化为二阶常微分方程.对该简化的常微分方程作进一步分析后,获得若干个显式的精确解.分析Apostol的研究成果(Apostol B F.On anon-linear wave equationin elasticity.Phys Lett A,2003,318(6):545-552)发现,非调和修正项通常导致解在有限时间内具有时间相关奇异性.除了得到时间相关奇异性的解外,还得到无法显示时间相关奇异性的解.
Accurate salt dome detection from 3D seismic data is crucial to different seismic data analysis applications. We present a new edge based approach for salt dome detection in migrated 3D seismic data. The proposed algorithm overcomes the drawbacks of existing edge-based techniques which only consider edges in the x （crossline） and y （inline） directions in 2D data and the x （crossline）, y （inline）, and z （time） directions in 3D data. The algorithm works by combining 3D gradient maps computed along diagonal directions and those computed in x, y, and z directions to accurately detect the boundaries of salt regions. The combination of x, y, and z directions and diagonal edges ensures that the proposed algorithm works well even if the dips along the salt boundary are represented only by weak reflectors. Contrary to other edge and texture based salt dome detection techniques, the proposed algorithm is independent of the amplitude variations in seismic data. We tested the proposed algorithm on the publicly available Netherlands offshore F3 block. The results suggest that the proposed algorithm can detect salt bodies with high accuracy than existing gradient based and texture-based techniques when used separately. More importantly, the proposed approach is shown to be computationally efficient allowing for real time implementation and deployment.
