Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symm...Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.展开更多
In this paper, a receiver model for ultrasonic ray tracing simulation is described. This is a complementary part of an existing simulation model and is the next step towards a numerical solution to the inverse problem...In this paper, a receiver model for ultrasonic ray tracing simulation is described. This is a complementary part of an existing simulation model and is the next step towards a numerical solution to the inverse problem and thus a NDT methodology for characterization of the dendrite orientation in a weld. The establishment of the receiver model is based on the electromechanical reciprocity principle. A concise retrospect of the weld model and the 2D model is made. The reciprocity principle is applied in an original way to handle the model problem including the back wall. Experimental qualitative validations for both P and SV waves on a specific weld are also made for C-scans included in this paper. Two different cases are studied. The first is a direct incidence of an ultrasonic ray towards the weld, and the second is a reflection from the back surface in the base material followed by an incidence to the weld. Even though mode-converted rays are excluded in the simulations, both the P and SV probe-models show the same behavior as the experimental results. The qualitative validation though reveals that it even if a thorough time-gating of received information would enable exclusion of mode-conversion in the model, inaccuracy of experimental results is affecting the evaluation of the weld model.展开更多
The Principles of coherent interference suppression are presented by a three-sensor array. The formulae of extracting expected signals from strong interference are derived. The selection of sensor space is discussed a...The Principles of coherent interference suppression are presented by a three-sensor array. The formulae of extracting expected signals from strong interference are derived. The selection of sensor space is discussed and then relationships between the space and frequency point, at which the signals can be extracted, are given. When expected signals are band- limit, the conditions of the selected sensor space, which should be satisfied, are given. Lastly, Performance of interference suppression is analyzed when the amplitude of interference power spectra of signals Received by three sensors fluctuates, and the expressions of relative error of the extracted signals and processing gain are derived. The theoretical and simulation results show that signals can be extracted from strong background interference without any information about signals and interference expect for the arriving direction of signals, that the space between sensors should be smaller than half wavelength of upper limit freqency when the expected signals are band-limit, and that performance of extracting signals will decline with the increase of fluctuation of interference spectrum amplitude.展开更多
基金Project(40674071) supported by the National Natural Science Foundation of Chinaproject(KFAS2002-2003) supported by Korea Foundation for Advanced Studies
文摘Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.
基金financed by the Swedish Qualification Center(SQC).Kjell Högberg,Gunnar Werner and Jeanette Gustafsson from SQC provided great help in the experiments.
文摘In this paper, a receiver model for ultrasonic ray tracing simulation is described. This is a complementary part of an existing simulation model and is the next step towards a numerical solution to the inverse problem and thus a NDT methodology for characterization of the dendrite orientation in a weld. The establishment of the receiver model is based on the electromechanical reciprocity principle. A concise retrospect of the weld model and the 2D model is made. The reciprocity principle is applied in an original way to handle the model problem including the back wall. Experimental qualitative validations for both P and SV waves on a specific weld are also made for C-scans included in this paper. Two different cases are studied. The first is a direct incidence of an ultrasonic ray towards the weld, and the second is a reflection from the back surface in the base material followed by an incidence to the weld. Even though mode-converted rays are excluded in the simulations, both the P and SV probe-models show the same behavior as the experimental results. The qualitative validation though reveals that it even if a thorough time-gating of received information would enable exclusion of mode-conversion in the model, inaccuracy of experimental results is affecting the evaluation of the weld model.
文摘The Principles of coherent interference suppression are presented by a three-sensor array. The formulae of extracting expected signals from strong interference are derived. The selection of sensor space is discussed and then relationships between the space and frequency point, at which the signals can be extracted, are given. When expected signals are band- limit, the conditions of the selected sensor space, which should be satisfied, are given. Lastly, Performance of interference suppression is analyzed when the amplitude of interference power spectra of signals Received by three sensors fluctuates, and the expressions of relative error of the extracted signals and processing gain are derived. The theoretical and simulation results show that signals can be extracted from strong background interference without any information about signals and interference expect for the arriving direction of signals, that the space between sensors should be smaller than half wavelength of upper limit freqency when the expected signals are band-limit, and that performance of extracting signals will decline with the increase of fluctuation of interference spectrum amplitude.
