一种基于双调和样条插值的完全非规则地震数据重建

A Completely Irregular Seismic Data Reconstruction Based on Biharmonic Spline Interpolation

在地震勘探过程中,由于地形、环境等影响,采集到的地震数据常常是不规则且不完整的,这会对后续地震数据的处理造成不良影响,因此地震数据重建是一个常用的处理手段。目前已经发展了多种地震数据重建方法,大部分的地震数据的重建工作都是建立在一个规则网格上进行,而对于完全非规则地震数据的重建研究较少。本文基于双调和样条插值的方法提出了一种非规则地震数据重建方法,通过求取一个能够通过n个点的双调和样条函数,将残缺的且非规则的地震数据插值到规则的网格中,从而得到完整的地震数据。本文进一步提出了分块插值的思想,在插值之前将每一时间或频率切片进行分块,对每一块分别进行插值。此方法改善了插值对内存需求过大的弊端,并极大的提高了计算效率。通过合成地震数据进行测试,实验证明了提出的双调和样条插值方法的插值效果。

During seismic exploration,the acquired seismic data are often irregular and incomplete due to topography and environment,which can adversely affect the subsequent processing of seismic data,so seismic data reconstruction is a common processing tool.A variety of seismic data reconstruction methods have been developed and most of them are based on a regular grid,while less research has been conducted on the reconstruction of completely irregular seismic data.In this paper,we propose an irregular seismic data reconstruction method based on the method of biharmonic spline interpolation,which interpolates the incomplete and irregular seismic data into a regular grid by finding a biharmonic function that can pass through n points,so as to obtain the complete seismic data.This paper further proposes the idea of blocking interpolation,where each time or frequency slice is blocked before interpolation,and each block of slice is interpolated separately.This method improves the drawback of large scale memory requirement for interpolation and greatly improves the computational efficiency.The interpolation effectiveness of the proposed biharmonic spline interpolation method is experimentally demonstrated by testing with synthetic seismic data.