基于改进泊松碟采样的地震数据重构

Seismic Data Reconstruction Based on an Improved Poisson Disk Sampling

测量矩阵是压缩感知中一个重要的因素,不同的测量矩阵在不同的条件下重构出的效果会不一样,而且在整个重构过程中起着重要的作用。地震勘探中由于实际情况的影响使得压缩感知中测量矩阵的使用有所限制。针对地震勘探实际情况,结合jitter采样和泊松碟采样的优点,提出了一种改进的泊松碟采样方法,泊松碟采样并没有受到规则网格的约束,这里改进的泊松碟采样是基于规则网格的条件,结合jitter方式,避免了对空间采样点的浪费和克服了间距过大的缺点,同时提高了采样效率,针对野外的实际情况可以调节检波器的布置位置。目前,在一些领域,如图像重构、信号处理等,高斯随机测量矩阵都得到了广泛应用并且其重构效果都很好,但在地震勘探中,由于受到现有检波器的限制,高斯随机测量矩阵并不符合地震勘探的条件。这里,模拟数据和实验数据都表明改进的泊松碟采样方式能够和广泛应用的高斯随机测量矩阵一样取得较好的重构效果,并且代替高斯随机测量矩阵在地震勘探中取得实际应用。

Measurement matrix is the key element in compressed sensing,and has a direct effect on reconstructioned data. The using of measurement matrix is limited due to physical environment in seismic exploration. Based on physical situation in seismic exploration,combining with merits of jitter sampling and Poisson disk sampling,an advanced Poisson disk sampling method is proposed. The Poisson disk sampling is not restricted to regular grid,while the advanced sampling method is based on this condition combining the jitter sampling method,which avoids the sampling interval too far and the waste of space,meanwhile improves the effectiveness and adjusts the receivers suitably according to physical environment. Up to now,in some areas,like imaging reconstruction,signal processing and so on,Gaussian random matrix is widely used and has a good performance,but in seismic exploration,because of the limitation of modern receivers,the Gaussian random sampling matrix does not comply with the requirements. Here,both simulated and real data experiments prove that advanced Poisson disk sampling has the similar reconstruction result with widely used Gaussian matrix,and replaces Gaussian random matrix when applying into seismic exploration.