Study On The Computational Method Of The Elastic Wave-field Based On Gaussian Beams

With the increasing exploitation of oil and gas resources, ones need to deal withmany intricate problems in exploration geophysics. Elastic wave field has thecharacteristics of multi-wave and multi-component. If the Multi-wave andmulti-component exploration technology is applied to practical seismic exploration,ones can obtain much more abundant wave field information which is very importantto understand the attributes of elastic medium in the subsurface.Elastodynamic Gaussian beam is a high-frequency approximate solution of theelastodynamic equation. Gaussian beam integral formula is valid even in varioussingular regions where the ray method fails (the vicinity of caustic, critical point, etc.)Gaussian beam method contains both the dynamic and the kinematic properties of thewave field, and avoids two-point ray tracing. So it is fast in the computational speedand produces the results with high precision. At present, the Gaussian beam methodhas been successfully applied to migration imaging in the scalar case, while themulti-wave and multi-component problem has not been well studied.The main research purpose in this thesis is to investigate the computationalmethods of elastic Gaussian beam. We explain the paraxial ray theory and thefundamental principle of Gaussian beam to a certain extent. On this basis, we carryout the discussion for dynamic ray tracing of inhomogeneous medium and layeredstructures, and applies the factor of transverse spreading to the calculation of2.5Dwave field. Furthermore, we also discuss the relationship between beam parameters,and their effects on propagation and diffusion of elastic Gaussian beam.In the second aspect, the application of Gaussian beam in the synthesis of elasticwave field is studied. We use the superposition of vector wave field to probe thedecomposition of elastic Green functions and the synthetic method of elastic Gaussianpackets which is applied in the calculation of seismic snapshots and records.Whereafter, we provide the precision analysis of travel-time, amplitude andpolarization direction of seismic records in homogeneous medium. At last, simple models have been used to demonstrate the validity of elastic Gaussian packet method.