摘要
传统有限差分方法在处理起伏地表时存在一些困难,而坐标变换法可将起伏地表映射为水平地表以克服此缺点.但同时,地下构造被变换得更加复杂,导致了波传播和成像的不准确.本文提出了一种分层的坐标变换方法,并应用到了弹性波逆时偏移中,此方法既可以克服起伏地表的影响,又可以不破坏地下构造.波场正向延拓、逆时延拓和分离是在辅助坐标系下完成的,而成像是在笛卡尔坐标系下完成的.通过对简单起伏模型和中原起伏模型的试算证明了本文提出方法的准确性.同时,对两种极端起伏地层高程不准确的情况进行测试可以看出:分层坐标变换逆时偏移方法的成像效果远好于传统坐标变换方法.
The traditional Finite Difference（FD）method has some difficulties in calculating synthetic waveforms for the velocity with an irregular surface,while the mapping method is verified to be able to overcome such disadvantage by transforming the irregular surface into horizontal one.However,the interfaces below the surface are also transformed to more complex ones,which are possible to generate the inaccuracy during wave propagation and imaging.To solve these problems from the irregular surface velocity model,we propose a new layered mapping operator for the FD,and then extend it to develop a new elastic wave forward modeling and reverse time migration（RTM）method.The basic idea of the layered mapping method is to discrete each layer into curved grids,and then mapping them to rectangular grids,which can transform the irregular borders to horizontal ones.When the curved grids are transformed to rectangular ones,the differential equations will transform from the physical domain to the calculation domain at the same time.During the process of elastic RTM,the layered mapping method should be used both in the forward propagation and reverse time propagation of the wave field on the source and receiver sides,respectively.The input initial velocity is the one after the same mapping process.Wave field forward continuation,reverse time continuation and separation are implemented in an auxiliary system coordinate while imaging in Cartesian coordinates.A velocity model with four layers with an irregular surface is used to calculate the forward modeling synthetic waveforms.By comparing the snapshots from the traditional mapping method with the layered mapping method proposed in this paper,we can find that our methods can treat the irregular surface well,while the results from the traditional mapping method may generate some artifacts.The snapshots after separating the wave field are displayed,which shows that Pwave and S-wave are separated clearly.Then the elastic RTM using the layered mapping method is tested.The imaging
出处
《地球物理学报》
SCIE
EI
CAS
CSCD
北大核心
2015年第8期2896-2911,共16页
Chinese Journal of Geophysics
基金
国家重点基础研究发展计划(2014CB239006
2011CB202402)
国家自然科学基金(41104069
41274124)
中央高校基本科研业务费专项资金(R1401005A
15CX06005A)联合资助
关键词
分层坐标变换
起伏自由地表
弹性波逆时偏移
波场分离
Layered mapping method
Irregular free-surface
Elastic wave RTM
Wave-field separation
