Application Of Sparsity Constrained Inversion To The Interpolation And Imaging Of Microseismic

Any application of prior information can make the final inversion results better. Since the compressive sensing theory was proposed, the prior information that the model was sparse or the model which was in the transform domain was widely used in the seismology. There are mainly two parts in this paper.First, in the perspective of sparse the model, the paper combined the spline interpolation and the curvelet transform. The microseismic data was interpolated and located by migration method. The basis sparse function was also discussed.For downhole microseismic monitoring of hydraulic fracturing of unconventional oil/gas reservoirs. At the same time, we can do not only locating the microseismic events, but also characterized the fracture zone using the microseismic sources. As the budget was limited, just few to ten geophones in the bolehole, The migration aperture and channel spacing are a pair of contradictory variables. Too large channel spacing can lead to the spatial sampling is not enough, resulting in the low velocity zone when the offset imaging to produce spatial false frequency. In order to eliminate the false frequency, the spatial data is needed to be interpolated.In this part, we firstly summarized the seismic interpolation methods, and we analyzed the disadvantages of the others. There are mainly four kinds of methods in seismic interpolation, that is the method based on math transform and signal processing, the method based on predictive filtering, the method based on wave equation and the method based rank reduction. However, if we use these method for the microseismic data interpolation, unsuitable problem would occurred.The method which based on curvelet transform sparsity constrained seismic interpolation was widely used. 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 sparsity constrained interpolation can then 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. At last, the real mircoseismic data was applied the interpolation method. Using the Kirchhoff method to locate the microseismic events, compared with the different data, the location accuracy was improved.In second part, we also sparse the model, using the wavelet transform and Fourier transform to sparse the model. We applied spgl1 method to solve the sparse constrained inversion problem. And we can recognize that compared with second order Tikhonov regularization method, the sparse method can get a better result that to see the sharp boundary. When the geometry of the source and receiver are not good for recognizing the boundary, scattering wave stack which based on timetable was applied to recognize the boundary better.We have to change the observation system when the abnormal target was not suitable to identify by the common observation system which all receivers are on the ground, such as there are obstacles beyond the abnormal target. The velocity model and the observation geometry are both have an effect on the imaging result. Putting the source and the receiver in the bolehole compared with the one on the ground, greatly expand the scope of the observation and got a more reliable imaging result.