地震数据Bregman整形迭代插值方法

Seismic data interpolation based on Bregman shaping iteration

人工地震方法由于受到野外观测系统和经济因素等的限制,采集的数据在空间方向总是不规则分布.但是,许多地震数据处理技术的应用(如:多次波衰减,偏移和时移地震)都基于空间规则分布条件下的地震数据体.因此,数据插值技术是地震数据处理流程中关键环节之一.失败的插值方法往往会引入虚假信息,给后续处理环节带来严重的影响.迭代插值方法是目前广泛应用的地震数据重建思路,但是常规的迭代插值方法往往很难保证插值精度,并且迭代收敛速度较慢,尤其存在随机噪声的情况下,插值地震道与原始地震道之间存在较大的信噪比差异.因此开发快速的、有效的迭代数据插值方法具有重要的工业价值.本文将地震数据插值归纳为数学基追踪问题,在压缩感知理论框架下,提出新的非线性Bregman整形迭代算法来求解约束最小化问题,同时在迭代过程中提出两种匹配的迭代控制准则,通过有效的稀疏变换对缺失数据进行重建.通过理论模型和实际数据测试本文方法,并且与常规迭代插值算法进行比较,结果表明Bregman整形迭代插值方法能够更加有效地恢复含有随机噪声的缺失地震信息.

Due to limitations of observational systems in the field and economic factors,collected data usually display irregular distributions in spatial directions.While many seismic data processing methods,such as multiple attenuation,migration,and time-lapse data analysis,are based on the prerequisite of regular data distribution in spatial directions.Therefore,data interpolation is an important step in seismic data processing.A failed interpolation method may create artifacts,which affect the subsequent processing steps.The iterative interpolation method is widely used in seismic data reconstruction,but traditional iterative interpolations are difficult to ensure accurate interpolation results and fast convergence speed.Especially in the condition of random noise,there will be large differences of the signal-to-noise ratio between interpolated and original traces.Thus,it is necessary to develop fast and effective iterative interpolation methods.In this paper,we treat seismic data interpolation as a basis pursuit problem under the frame of compressed sensing（CS）,and propose a new nonlinear Bregman shaping iteration algorithm to solve the constrained minimization problem.We also propose two new iterative control criterions according to the characteristics of Bregman shaping iteration,which can recover missing data through effective sparse transform.Compared with the conventional iteration method,the examples of synthetic and field data demonstrate that the Bregman shaping iteration interpolation can reconstruct missing seismic data more efficiently even in the case with random noise.