The correctness of the finite-difference problems of the time- and wave fields continuation for the migration image of the basement boundary

Abstract

In modern seismic exploration, the migration procedure plays an important role for further interpretation of the observed data. It is the migration that makes it possible to display the deep structure of the geological section based on the dynamic characteristics of the registered wave fields.
 When processing WARRP (wide angle reflection/refraction profiling) seismic data, standard migration methods are ineffective, which is due to the peculiarities of observation systems. All existing migration methods are mainly based on reflected waves, which have a limited registration interval. The wave field on WARRP is observed at distances from sources that reach several hundred kilometers, and the uneven step between receivers is on average 1—3 km. Under such conditions, it is difficult and sometimes impossible to separate the reflected waves.
 The finite-difference reflection/refraction migration developed at the Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine has proven its effectiveness in constructing migration images of the depth structure of the section based on WARRP data observed in various regions of the world. The main difference of this migration method is the use of refracted waves as reference waves registered in the large offsets. At the same time, there is a question of the correctness of the reproduction of the depth structure of the section on the migration image, which depends on the correctness of the calculation methods. The algorithm of finite-difference reflection/refraction migration contains a continuation of the time and wave fields.
 The article presents a proof of the mathematical correctness of the solution of the eikonal differential equations and the scalar wave equation by the finite-difference method, on which are based the continuation of the time and wave fields, respectively.
 The given comparison of the formed migration images and the velocity models, calculated by the ray-tracing method, of the upper crust along the PANCAKE and TTZ-South profiles allows us to assert that the combination of the results of kinematic and dynamic processing of WARRP data allows to increase the informativeness of their further interpretation