Probability Density Imaging Of Gravity Tensor Euler Solution Based On Normalized B-spline Function

The traditional Euler deconvolution optimization strategy only uses the construct index of Euler deconvolution,which is difficult to distinguish anomalies and false signs between anomalies.Meanwhile,the absence of the expression of quantity and sequence makes the cluster analysis,which is based on distance and similarity factor,difficult to distinguish adjacent anomalous sources,thus mistakenly identifies the false signs between anomalies as new anomalous clusters.Therefore,the nonparametric probability density estimation based on normalized B-spline is introduced.The similarity and agglomeration degree of each Euler solution are taken as the basis to calculate the value of probability density of Euler solution,so as to achieve the goal of identifying multiple adjacent anomalous sources with Euler solution.As the space of estimation grid increases,B-spline density estimation becomes unfocused.In order to solve this problem,multivariable density estimation is introduced.When the data sample or the estimation grid is too large,traversing each node on the estimation grid means a huge amount of computation and memory consumption.To address the problem,a B-spline density estimation method based on fast Fourier transform(FFT)is constructed.Specifically,by introducing boxed approximation method,the sample data is quickly projected to the estimation grid,so as to realize the discrete convolution of the estimation grid and the density function by means of fast Fourier transform.The thesis mainly carries out the following research:(1)Synthesize one-dimensional and two-dimensional random data by normal function,and verify the algorithm of B-spline density estimation and FFT-based B-spline density estimation.(2)Construct a geophysical model with cubes,horizontal cylinders,and spheres as the research objects,and conduct research on the post-processing and imaging of Euler solution based on B-spline density estimation.(3)Try to apply the theoretical method of this article to actual data in order to provide a certain basis for geological interpretation.One-dimensional and two-dimensional random data verify the correctness and reliability of B-spline density estimation algorithm.The model test shows that: The results of B-spline density estimation are basically consistent with the set values of the model,and only a few deviates from the set values.The probability density isopleth surface diagram based on threedimensional B-spline density estimation more intuitively shows the distribution of abnormal objects.To some extent,the B-spline density estimation method based on FFT is better than the B-spline density estimation method,and the three-dimensional results are more focused.The practical application of B-spline density estimation method shows that the probability density isopleth surface diagram generated by the probability density value of Euler solution can distinguish the clusters composed of Euler solutions,and realize the effective separation and location of adjacent anomalous sources.