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传统的地震勘探数据采样必须遵循奈奎斯特采样定理,而本文基于新发展的压缩感知理论,在突破传统采样定理限制的基础上,利用随机欠采样方法将传统规则欠采样所带来的互相干假频转化成较低幅度的不相干噪声,从而将数据重建问题转为更简单的去噪问题。在数据重建过程中引入凸集投影算法(POCS),采用指数规律衰减的阈值参数,在每次迭代过程中,改变以往从时间到空间都需要进行正反变换的做法,提出只对地震数据空间方向进行正反变换,从而可以减少内存空间,提高运算速度,并且也分析了本文POCS算法的抗噪声与反假频能力,同时我们也对二维和三维地震数据重建进行了比较。理论模型和实际数据表明本文方法效果明显,这对于指导复杂地区数据采集、缺失地震道重建及降低勘探成本方面具有重要的实用价值。
Traditional seismic data sampling must follow the Nyquist sampling theorem. Based on the newly developed compressed sensing theory, based on the breakthrough of traditional sampling theorem limits, this paper uses the random under-sampling method to compare the traditional regular undersampling with each other The interference aliasing translates into a lower amplitude of incoherent noise, which transforms the data reconstruction problem to a simpler one. In the process of data reconstruction, the convex set projection algorithm (POCS) is introduced and the threshold parameter of exponential decay is used. In each iteration, the change of the forward-reverse transform from time to space is required. Only the seismic data space Direction and vice versa, which can reduce the memory space and improve the speed of operation, and also analyzed the anti-noise and anti-aliasing ability of the POCS algorithm in this paper. At the same time, we also compared the two-dimensional and three-dimensional seismic data reconstruction. The theoretical model and practical data show that the proposed method is effective and has important practical value in guiding data acquisition in complex areas, missing seismic trace reconstruction and reducing exploration cost.