Study On The Computation Method Of 2.5-D Acoustic Ray Wave Field In Simple Media

The technique of seismic wave field numerical modeling is a method of researching on the relationship between the structures, physical properties and lithology under various kinds of geologic conditions and characteristics of seismic wave response, and is of great significance to improve our understandi- ng of seismic wave propagation and to solve the questions we confront in the process of geo-exploration and development. As a approximation of geometric- al optics ,the asymptotic ray theory plays an important role in seismic wave field numerical modeling because of the characteristics such as small computation and visual conciseness. This paper mainly analyze and discuss the computation method of acoustic ray field in 2.5-D medium and how to use Kirchhoff integral to compute seismic wave field.As a special case of 3-D wave propagation, the 2.5-D wave propagation have two fundamental assumptions, one is that the source is a point without direction, the other is the media underground varies only with two dimensions. That is to say, when the 3-D wave exploded by a point source is propagating in the various kinds of media, and when a linear survey is carried out on the surface, the wave field received has a symmetry with the line. In 2.5-D medium,'characteristic equations'can be simplified, the 3×3 Jacobian that determines the 3-D geometric spreading factor and amplitude can be simplified to a product of the 2×2 Jacobian and a factor, that is to say we can make use of the out of–plane geometric spreading factor to rectify 2-D in-plane geometric spreading factor to 3-D in-plane geometric spreading factor. In 2.5-D media, one can approximate 3-D wave propagation with the computation of wave field in 2-D plane.This paper analyzes the computation methods of traveltime and amplitude(geometric spreading factor) in the medium whose velocity only varies with depth and analyze the law of traveltime and in-plane(out of plane) geometric spreading factor versus offset. While the distribution of velocity of medium is known, then we can compute the acoustic Green function of any point .Due to the problems like singularity of wave fields in caustic or the invalidation in shadow zone, this paper improves the ordinary ray method by the theory of Kirchhoff integral. Based on the Huygens-Fresnel principle,we can consider the reflector surface as a series of diffractors and the reflection wave field as the contributions of diffraction responses, and if obtaining the Green functions of every diffractor underground ,then we can accomplish the computation of wave fields of reflection or refraction. This paper firstly discusses the computation in homogeneous medium and testifies that Kirchhoff integral can model the primary reflection, obtain the correct amplitude in caustics and the diffraction wave- field in shadow zone.Then, this paper apply this method to the laterally inhomogeneous and multi-layered media. When the velocity has a lateral variation, the separations of diffractors and the traveltime and geometrical spreading factor corresponding either source or receiver rays of every diffractor is realized by kinematics ray tracing. We determine the geometrical spreading factor by geometrical optics and compute the wave field of receiver rays by linear interpolation, and take the reflection/transmission loss into account, and then complete the computation of integral. This paper computes the synthetic seismograms of several examples whose velocities have laterally variations. When the integral surface we select has a caustic, the integral will soon become singular. We can choose a suitable surface to escape the ray caustic and compute the integral. Finally, based on an example of homogeneous medium, i compare the computation of kirchhoff integral with the computation of ordinary ray theory, analyze the relative errors of traveltime and amplitude, and obtain a ideal result.As to the computation quantity ,the time on computing Kirchhoff integral in frequence domain is longer than in time domain, however, the total computation time has relation to the traced rays. Massive rays must be traced in the complex structures to satisfy the enough sampling of the reflector, so more computation time is needed. That is to say, the computation quantity of Kirchhoff integral is determined by complexity and the number of layers in the model.