Downhole microseismic data reconstruction and imaging based on combination of spline interpolation and curveletsparse constrained interpolation

When using borehole sensors and microseimic events to image,spatial aliasing often occurred because of the lack of sensors underground and the distance between the sensors which were too large. To solve the aliasing problem,data reconstruction is often needed. Curvelet transform sparsity constrained inversion was widely used in the seismic data reconstruction field for its anisotropic,multiscale and local basis. However,for the downhole case,because the number of sampling point is much larger than the number of the sensors,the advantage of the curvelet basis can’t perform very well. To mitigate the problem,the method that joints spline and curvlet-based compressive sensing was proposed. First,we applied the spline interpolation to the first arrivals that to be interpolated. And the events are moved to a certain direction,such as horizontal,which can be represented by the curvelet basis sparsely. Under the spasity condition,curvelet-based compressive sensing was applied for the data,and directional filter was also used to mute the near vertical noises. After that,the events were shifted to the spline line to finish the interpolation workflow. The method was applied to a synthetic model,and better result was presented than using curvelet transform interpolation directly. We applied the method to a real dataset,a microseismic downhole observation field data in Nanyang,using Kirchhoff migration method to image the microseimic event. Compared with the origin data,artifacts were suppressed on a certain degree.