The Research Of Least-squares Kirchhoff Migration

Seismic exploration technology is always the research emphasis in the geophysics,as one of the important ways to find oil and gas reservoirs.With the development of seismic exploration technology,the exploration targets have been diverted from tectonic oil and gas reservoirs to lithologic reservoirs,which cause higher requirement of seismic exploration technology.Seismic imaging technology has also made great progress,as an important part of seismic exploration technology.In brief,seismic imaging technology has evolved from superimposed imaging,migration imaging to inversion imaging.In addition,the linear inversion imaging,also known as the least-squares migration imaging,is proposed to adapt to the increasing expectations for image accuracy and amplitude-preserving of seismic exploration.The least-squares migration considers the imaging problem as an inverse problem based on the minimization of a least-squares waveform error functional,which improves the problem of conventional blurred imaging and can meet the requirements of lithologic imaging.For least-squares migration imaging,the most important step is to construct migration and demigration operators based on the Born approximation.In addition,the conventional ray-based,one-way and two-way wave equation migration and demigration operators can be applied to the least-squares imaging framework.In this paper,we use relatively simple Kirchhoff migration and demigration operators,because Kirchhoff migration has the characteristics of strong adaptability and fast calculation speed.For the simple media and structures,the Kirchhoff time migration and demigration operators are deduced by using the double square root equation to calculate the travel time.The least-squares Kirchhoff time migration of the data domain is realized by conjugate gradient method.This method is helpful to improve the formation resolution and restore the true amplitude information,which can provide real and reliable amplitude information for AVO or AVA analysis.For the more complex media and velocity models,the ray tracing is used to calculate the travel time,and the Kirchhoff depth migration and demigration operators are constructed,thus achieving the least-squares Kirchhoff depth migration.This provides a very good solution for dealing with data that contains complex subsurface media and structures.In addition,the correctness,validity and practicability of the least-squares Kirchhoff time and depth migration methods are verified by the trial of several models and a field data.The following conclusions are drawn:(1)For the least-square Kirchhoff time migration,the effect of suppressing the migration noise,balancing amplitude and improving the resolution is well explained.(2)For the least-squares Kirchhoff depth migration,our method can recover the theoretic reflectivity model as the number of iteration increases,and improve both vertical and lateral amplitude preservation,especially for the deeper reflectors.Our method can show more small-scale structures and local structural features,which plays an important role in identifying and determining of the complex oil and gas reservoirs in the oil and gas exploration.