基于样条插值与曲波变换压缩感知的井下微地震监测数据重建

Downhole microseismic monitoring data reconstruction based on spline interpolation and curvelet-based compressive sensing

对于非常规油气开发水力压裂井下微地震监测,由于井中布设的检波器数量有限而导致空间采样不够,致使在进行偏移成像时产生空间假频。为消除假频现象,需要对空间欠采样的数据进行内插。目前基于曲波变换(Curvelet)稀疏约束的地震道插值方法(即压缩感知)已经逐渐被广泛应用,但是对于井下微地震监测数据,由于检波器数量过少,其在时间上的采样点数要远远大于检波器数。在这种情况下,曲波基函数在一定尺度下所能取到的方向信息是有限的,致使其基函数各向异性特征不能很好地发挥,因此插值效果不好。为解决该问题,我们提出了结合样条插值的基于曲波变换稀疏约束地震道插值方法。对于井下微地震监测数据,首先利用样条插值方法对每道数据的特定震相到达时间进行插值,在达到曲波基函数可以取到的方向后(如水平方向),此时曲波基函数可以更稀疏地表示微地震数据体,然后再进行基于曲波变换稀疏约束的道间插值,并进行方向滤波,即可以达到较好的插值效果。我们基于一个井下微地震监测合成数据进行了测试,与数据加密前的地震偏移成像结果对比,内插之后数据偏移成像中的假频得到了压制。

For downhole microseismic monitoring of hydraulic fracturing of unconventional oil/gas reservoirs,the number of borehole receivers is limited and as a result the spatial sampling of seismic wavefield is sparse,which can lead to artifacts in the seismic migration image for downhole microseismic migration.To mitigate this spatial aliasing issue,spatial interpolation is needed.Currently,compressive sensing using the curvelet-based sparsity constraint has been gradually widely used for seismic trace interpolation.However,for the case of downhole microseismic monitoring,because the temporal sampling is much denser than the spatial sampling,the directional information obtained for curvelet bases at certain scales is limited,making it difficult to take full advantage of anisotropic features of curvelet bases.As a result,the result of seismic trace interpolation is poor.To solve this issue,we propose a hybrid method that combines spline interpolation and curvelet-based compressive sensing.First,spline interpolation method is used to calculate the reflection of interpolated traces using those of existing traces.Then the traces are shifted to a certain direction that could well be represented by the curvelet basis,such as the horizontal direction.After shifting the traces,the seismic gather is sparse in the curvelet domain and thus the curvelet-based spartisty constrained interpolation can then be used to more accurately reconstruct more traces in the space domain.We tested the hybrid method on a synthetic downhole microseismic dataset.It shows that the artifacts on seismic migration image using interpolated microseismic data are greatly reduced compare to the migration image from the original sparse data.