An Elastic Reverse Time Migration Method For Vector Shear Wave Based On The Decoupled Elastic Wave Equation

The decoupled elastic wave equation is an efficient wave field separation method for obtaining vector elastic wave field.This method can obtain not only the decoupled P-wave and S-wave particle vibration velocity field,but also the single P-wave and S-wave stress tensor.Among them,there is no definite physical meaning when using the single component of the Swave pure stress field.Therefore,this paper focuses on the imaging of the S-wave pure stress wavefield based on the elastic wave decoupled equation.In addition,the polarity reversal problem of pure-wave imaging in the open angle and the problem of extraction and imaging of angle domain common-image gathers are explored in this paper.In order to solve the problem that the pure stress field of S-wave has no clear physical meaning when using single component imaging,this paper introduces the stress invariant tensor into the S-wave pure stress field.And the physical quantities and the physical meaning of the elastic wave are unified.Based on the definition of the second invariant of the stress deviation,the shear wave stress invariants are constructed,and a single scalar field which can completely represent the S-wave pure stress fields is obtained.Finally,for the imaging problem of S-wave pure stress field,the P-wave stress field is regarded as source wave field,while the S-wave stress invariant constructed is regarded as receiver wave field.And the stress PS imaging results are obtained.The feasibility of the method is verified by numerical experiments.In this paper,the reason of polarity reversal at open angle based on decoupled elastic wave equation of pure-wave field imaging is analyzed.Aiming at this problem,a directional derivative imaging method is proposed in this paper,which combines the scalar imaging condition with Laplacian filter.The same terms in the derivative component and the imaging component are selectively selected as the final imaging results.Theoretical deduction and model testing are used to verify the accuracy of this method.For the problem of stacking imaging in reverse time migration,we describe the image from the perspective of extracting common imaging point gathers in angle domain.Then the common image point gathers are extracted based on the calculation of reflection angle by Poynting vector.Based on imaging characteristics of different angle domain gathers,the stacking strategy of the common image point gathers in the angle domain is proposed.Finally,the accuracy of stacking imaging of common imaging point gather in the angle domain is verified by the test of the model.This paper mainly focuses on the study of RTM method for vector shear wave based on the decoupled elastic wave equation,in which wave-field construction,imaging conditions and stacking image are demonstrated.The establishment of shear wave stress field and its reverse time migration,polarity correction in pure-wave imaging,and the extraction of gathers in angle domain for stacking are discussed in detail,and theoretical proofs and model tests verify the accuracy of the proposed methods.