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۱Proposing New Methods to Enhance the Low–Resolution Simulated GPR Responses in the Frequency and Wavelet Domains
اطلاعات انتشار: International Journal of Mining & Geo-Engineering، چهل و هشتم،شماره۲، ۲۰۱۴، سال
تعداد صفحات: ۱۴
To date, a number of numerical methods, including the popular Finite–Difference Time Domain (FDTD) technique, have been proposed to simulate Ground–Penetrating Radar (GPR) responses. Despite having a number of advantages, the finite–difference method also has pitfalls such as being very time consuming in simulating the most common case of media with high dielectric permittivity, causing the forward modelling process to be very long lasting, even with modern high–speed computers. In the present study the well–known hyperbolic pattern response of horizontal cylinders, usually found in GPR B–Scan images, is used as a basic model to examine the possibility of reducing the forward modelling execution time. In general, the simulated GPR traces of common reflected objects are time shifted, as with the Normal Moveout (NMO) traces encountered in seismic reflection responses. This suggests the application of Fourier transform to the GPR traces, employing the time–shifting property of the transformation to interpolate the traces between the adjusted traces in the frequency domain (FD). Therefore, in the present study two post–processing algorithms have been adopted to increase the speed of forward modelling while maintaining the required precision. The first approach is based on linear interpolation in the Fourier domain, resulting in increasing lateral trace–to–trace interval of appropriate sampling frequency of the signal, preventing any aliasing. In the second approach, a super–resolution algorithm based on 2D–wavelet transform is developed to increase both vertical and horizontal resolution of the GPR B–Scan images through preserving scale and shape of hidden hyperbola features. Through comparing outputs from both methods with the corresponding actual high–resolution forward response, it is shown that both approaches can perform satisfactorily, although the wavelet–based approach outperforms the frequency–domain approach noticeably, both in amplitude and shape of the outputted hyperbola response.

۲3D Inversion of Magnetic Data through Wavelet based Regularization Method
اطلاعات انتشار: International Journal of Mining & Geo-Engineering، چهل و نهم،شماره۱، ۲۰۱۵، سال
تعداد صفحات: ۱۸
This study deals with the 3D recovering of magnetic susceptibility model by incorporating the sparsity–based constraints in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two sparsity functions were used to recover the smooth parts as well as the sharp boundaries of model parameters. A pre–selected basis namely wavelet can recover the region of smooth behaviour of susceptibility distribution while Haar or finite–difference (FD) domains yield a solution with rough boundaries. Therefore, a regularizer function which can benefit from the advantages of both wavelets and Haar\FD operators in representation of the 3D magnetic susceptibility distributionwas chosen as a candidate for modeling magnetic anomalies. The optimum wavelet and parameter β which controls the weight of the two sparsifying operators were also considered. The algorithm assumed that there was no remanent magnetization and observed that magnetometry data represent only induced magnetization effect. The proposed approach is applied to a noise–corrupted synthetic data in order to demonstrate its suitability for 3D inversion of magnetic data. On obtaining satisfactory results, a case study pertaining to the ground based measurement of magnetic anomaly over a porphyry–Cu deposit located in Kerman providence of Iran. Now Chun deposit was presented to be 3D inverted. The low susceptibility in the constructed model coincides with the known location of copper ore mineralization.
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