According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the sp...According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of evolution of the universe the catastrophe nature of the Finsler spacetime and its cosmological impli= cations are discussed. It is shown that the nature of the universal evolution could be attributed to the geometric features of the Finsler spacetime. (see Cao, 1993)展开更多
Source location is the core foundation of microseismic monitoring.To date,commonly used location methods have usually been based on the ray-tracing travel-time technique,which generally adopts an L1 or L2 norm to esta...Source location is the core foundation of microseismic monitoring.To date,commonly used location methods have usually been based on the ray-tracing travel-time technique,which generally adopts an L1 or L2 norm to establish the location objective function.However,the L1 norm usually achieves low location accuracy,whereas the L2 norm is easily affected by large P-wave arrival-time picking errors.In addition,traditional location methods may be affected by the initial iteration point used to find a local optimum location.Furthermore,the P-wave arrival-time data that have travelled long distances are usually poor in quality.To address these problems,this paper presents a microseismic source location method using the Log-Cosh function and distant sensor-removed P-wave arrival data.Its basic principles are as follows:First,the source location objective function is established using the Log-Cosh function.This function has the stability of the L1 norm and location accuracy of the L2 norm.Then,multiple initial points are generated randomly in the mining area,and the established Log-Cosh location objective function is used to obtain multiple corresponding location results.The average value of the 50 location points with the largest data field potential values is treated as the initial location result.Next,the P-wave travel times from the initial location result to triggered sensors are calculated,and then the P-wave arrival data with travel times exceeding 0.2 s are removed.Finally,the aforementioned location steps are repeated with the denoised P-wave arrival dataset to obtain a high-precision location result.Two synthetic events and eight blasting events from the Yongshaba mine,China,were used to test the proposed method.Regardless of whether the P-wave arrival data with long travel times were eliminated,the location error of the proposed method was smaller than that of the L1/L2 norm and trigger-time-based location method(TT1/TT2 method).Furthermore,after eliminating the Pwave arrival data with long travel distances,the location accuracy of these three location methods increased,indicating that the proposed location method has good application prospects.展开更多
基金The project was supported by National Natural Science Foundation of China.
文摘According to some local properties of Lorentz transformation, Einstein stated: 'Vetheitiss greater than that of light have no possibility of existence.' He neglected to point out the applicable range of the special theory of relativity. In fact, it could only be applied to the subluminal-speeds. This paper shows that if ones think of the possibility of the existence of the superluminal-speeds and redescribe the special theory of relativity following Einstein's way, it could be supposed that the physical spacetime is a Finsler spacetime, characterized by the metric ds4=gijkldxidxidxkdxl. If so, a new spactime transformation could be found by invariant ds4 and the theory of relativity is discussed on this transformation it is possible that the Finsler spacetime F(x,y) may be endowed with a catastrophic nature. Based on the different properties between the ds2 and ds4, it is discussed that the flat spacetime will also have the catastrophic nature on the Finsler metric ds4. The spacetime transformations and the Physical quantities will suddenly change at the catastrophe set of the spacetime, the light cone. It will be supposed that only the dual velocity of the superluminal-speeds could be observed. If so, a particle with the superluminal-speed v> c could be regarded as its anti-particle with the dual velocity v1=c2/ v< c. On the other hand, it could be assumed that the horizon of the field of the general relativity is also a catastrophic set. If so, a particle with the superluminal-speeds could be projected near the horizon of these fields, and the particle will move on the sauce-like curves. It is very interesting that, in the Schwarzschild fields, the theoretical calculation for the sauce-like curves should be in agreement with tie data of the superluminal expansion of extragalactic radio sources observed year after year. (see Gao, 1992b).The ca- tastrophe of spacetime has some deep cosmological means. According to the some interested subjects in the Process of evolution of the universe the catastrophe nature of the Finsler spacetime and its cosmological impli= cations are discussed. It is shown that the nature of the universal evolution could be attributed to the geometric features of the Finsler spacetime. (see Cao, 1993)
基金Project(cstc2020jcyj-bshX0106)supported by the Chongqing Postdoctoral Science Foundation,ChinaProject(2020M683247)supported by the China Postdoctoral Science Foundation+1 种基金Project(cstc2020jcyj-zdxmX0023)supported by the Key Natural Science Foundation Project of Chongqing,ChinaProject(551974043)supported by the National Natural Science Foundation of China。
文摘Source location is the core foundation of microseismic monitoring.To date,commonly used location methods have usually been based on the ray-tracing travel-time technique,which generally adopts an L1 or L2 norm to establish the location objective function.However,the L1 norm usually achieves low location accuracy,whereas the L2 norm is easily affected by large P-wave arrival-time picking errors.In addition,traditional location methods may be affected by the initial iteration point used to find a local optimum location.Furthermore,the P-wave arrival-time data that have travelled long distances are usually poor in quality.To address these problems,this paper presents a microseismic source location method using the Log-Cosh function and distant sensor-removed P-wave arrival data.Its basic principles are as follows:First,the source location objective function is established using the Log-Cosh function.This function has the stability of the L1 norm and location accuracy of the L2 norm.Then,multiple initial points are generated randomly in the mining area,and the established Log-Cosh location objective function is used to obtain multiple corresponding location results.The average value of the 50 location points with the largest data field potential values is treated as the initial location result.Next,the P-wave travel times from the initial location result to triggered sensors are calculated,and then the P-wave arrival data with travel times exceeding 0.2 s are removed.Finally,the aforementioned location steps are repeated with the denoised P-wave arrival dataset to obtain a high-precision location result.Two synthetic events and eight blasting events from the Yongshaba mine,China,were used to test the proposed method.Regardless of whether the P-wave arrival data with long travel times were eliminated,the location error of the proposed method was smaller than that of the L1/L2 norm and trigger-time-based location method(TT1/TT2 method).Furthermore,after eliminating the Pwave arrival data with long travel distances,the location accuracy of these three location methods increased,indicating that the proposed location method has good application prospects.
