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首页> 外文期刊>Bollettino della Unione matematica italiana, B >Bi-dimensional Fourier transform with irregular spatial sampling
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Bi-dimensional Fourier transform with irregular spatial sampling

机译：具有不规则空间采样的二维傅立叶变换

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摘要

Seismic data acquisition is frequently carried out at irregular sampling intervals along spatial coordinates. This causes problems in the subsequent multi-trace data processing which often requires equi-spaced traces and thus the data must be first regularised. To this end, we illustrate a frequency domain method to transform 2D data irregularly sampled in the spatial direction to equivalent equi-spaced data. We follow a probabilistic inversion where the a-posteriori model is the desired (correct and noise free) frequency spectrum, the a-priori model is computed through the Non Uniform Discrete Fourier Transform (also known as Riemann sum) and the noise introduced by the irregular sampling is described empirically, on the basis of the distances between samples. All the variables are assumed to have Gaussian distributions and are described by their means and covariances. Once the optimum frequency spectrum is estimated, a Fourier anti-transform brings the data back into the time-space at constant spatial intervals. The proposed method is applied to synthetic and real seismic data, with various degrees of sampling irregularities and offset gaps, and with different noise contaminations and dips of events. The results are satisfactory and are improved with respect to those obtained by applying a previously developed method.
机译：地震数据采集经常沿着空间坐标以不规则的采样间隔进行。这在随后的多迹线数据处理中引起问题，该处理通常需要等距迹线，因此必须首先对数据进行正则化。为此，我们说明了一种频域方法，可将在空间方向上不规则采样的2D数据转换为等效的等距数据。我们遵循概率倒置的方式，其中a-后验模型是所需（正确且无噪声）的频谱，a-先验模型是通过非均匀离散傅立叶变换（也称为Riemann和）计算的，而噪声是由根据样本之间的距离，凭经验描述不规则采样。假定所有变量均具有高斯分布，并通过其均值和协方差来描述。一旦估计了最佳频谱，傅立叶反变换将以恒定的空间间隔将数据带回到时空。该方法适用于合成和真实地震数据，具有不同程度的采样不规则性和偏移间隙，并且具有不同的噪声污染和事件骤降。结果是令人满意的，并且相对于通过应用先前开发的方法获得的结果而言是改进的。

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