The Study And Application Of Wavelet Transform In Potential Data Processing

Wavelet transform is very popular in recent years as a means of mathematical analysis.At present, the application of wavelet transform has been widely used in seismic dataprocessing, but a few papers have discussed about that in potential data processing. As ithas two good characteristics, time-frequency analysis and multi-scale analysis, theapplication of wavelet transform in potential domain is very broad. In this paper, throughmaking vast experiments with the established models and using the MATLAB wavelettools, I try to apply wavelet transform to potential data processing as widely as possible,and therefore improving the accuracy.At the first part of the paper, I want to introduce a very useful image enhancementmethod: Histogram Equalization. It is the default colouring setting in Geosoft and there arespecial tool for it in ModelVision and Voxler, while Surfer, the strongest imaging softwarein geophysics, does not have this function. Hence, I study the algorithm and write aFOTRAN program, through which the colour clr file and the grading lvl file would becreated if the grd file were import. The quick sorting method is applied and the situationthat the grd file would be whitening is also considered. Using the clr file and the lvl file,the imaging effects generated by Surfer software are almost the same as that generated byGeosoft software, and even much better, as the grade is coincide with the colour. Withmore research, I find that Histogram Equalization could not only enhance the local weakanomaly and therefore making the image more clear with strong lays and improving theresolution, especially when imaging the derivation results, but also a very useful way toidentify the boundary. More specifically, the isoline concentration areas could beconsidered as the boundary.Many people have done some research for applying wavelet multi-scale analysis forfield separation. The potential anomaly would be decomposed into approximation, whichcan be considered as the regional field, and different order details, the sum of which can beconsidered as the local field. In this paper, a simple model is established for fieldseparation research, which is the superposition of a simple regional field with two-spheremodel. Large amounts of data shows that: the effect or applying wavelet multi-scaleanalysis for field separation is very good; the level of the decomposition, which is usuallychosen by someone s experience, is the most important factor; in contrast, the wavelet has little effect and you can choose anyone between db4~db9、sym4~sym8、coif3~coif5、bior3.3~bior3.9and dmey wavelet. Then two other field separation methods are compared:upward continuation and trend analysis. The result is that upward continuation is not agood way for field separation unless you just want to analyze the shape of the regionalfield not the amplitude and the effect of trend analysis is as good as that of waveletmulti-scale analysis. So, you have to test to find w hich method is better when processingreal data.In order to meet the requirements of Fast Fourier transform, the number of the datashould be the integral power of2and the ends should be the same, and therefore, thepotential data should be extended before processing. Multiply sphere model is establishedfor the following research and the results are that: if the ends were not the same, seriousGibbs would be created; if the data were extended by the traditional Cosine functionexpansion edge method or pre-extended by the Griding methods provided by Surfersoftware, serious boundary effect would be generated and you need HistogramEqualization to help image. There are9extension methods provided by MATLAB wavelettool. And two of them, the effects of which have no boundary effects at all, are smoothextension of order1and antisymmetric extension-whole point. Moreover, the otherextension methods, which are commonly used in potential data processing, always havesome connection with the9extension methods. For example, zero filling method,extending regional field method and fold expansion method. According to the previousresearch, a new extension method named SPD_Cosine extension method is proposed,which combines the extension method smooth extension of order1and the characteristicof the Cosine function. I rewrite the extension subroutine in the FORTRAN programwritten by someone long before and apply it to the multiply sphere model to calculatehigher derivative, the result of which does not have any boundary effect, and therefore, theaccuracy is highly improved.Then, I discuss the importance of denoising before the potential data been processed.By adding different levels of noise to the gravity anomaly of the multiply sphere modeland using wavelet threshold denoising method, the wavelet and the decomposition levelare discussed, and the advantage is showed by comparing the result of Butterworthfiltering. The wavelet threshold denoising method could not only be applied to thepre-procession in potential data, but also could be used to remove the Gibbs effect orremove the amplified high frequency noise.At the end part of the paper, gravity anomaly in Laos with1:50000scale is processedby all the methods discussed above to test that whether all the methods could be applied to not only the models but also the real data and whether all the conclusions concluded aboveare right. The effects show that: Histogram Equalization could improve the resolution ofthe image and highlight the local weak anomalies, especially when imaging the derivations;the field separation result generated by wavelet multi-scale analysis is quite good andalmost the same as those generated by trend analysis; the derivations calculated by SPD_Cosine extension method do not have any boundary effect; and wavelet thresholddenoising method could eliminate the high-frequency noise, and therefore, the accuracy isimproved.