The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have b...The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.展开更多
The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is creat...The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is created here with an analysis of its behavior inside and outside the light cone. The fuzzy causality principle is generalized to field models. Also, this work demonstrates the ability to use fuzzy space to regularize divergences in quantum field theory. The passage to the limit to a system of interacting particles enables the obtaining of the dissipative projection operator, represented earlier. The Liouville equation is solved here by successive approximations in the range of times much larger than the typical scale of fuzziness, by assuming the interaction as a small parameter. As well, here was applied the standard diagram technique.展开更多
文摘The inverse problem of wave equation is the importance of study not only in seismic prospecting but also in applied mathematics. With the development of the research, the inverse methods of 1 - D wave equations have been trending towards the multiple parameters inversion . We have obtained an inverse method with double -parameter, in which medium density and wave velocity can be derived simultaneously. In this paper, to increase the inverse accuracy, the method is improved as follows. Firstly, the formula in which the Green Function is omitted are derived and used. Secondly, the regularizing method is reasonable used by choosing the stable function. With the new method, we may derive elastic parameter and medium density or medium density and wave velocity. Thus, lithology parameters for seismic prospecting may be obtained.After comparing the derived values from the new method with that from previous method, we obtain the new method through which substantially improve the derived accuracy . The new method has been applied to real depths inversion for sedimentary strata and volcanic rock strata in Chaoyanggou Terrace of Songliao Basin in eastern China. According to the inverse results,the gas - bearing beds are determlned.
文摘The proposed work handles the concept of fuzzy space as a set of real numbers with a set finite membership function. Extending standard arithmetic operations through a fuzzy space, the fuzzy Green’s function is created here with an analysis of its behavior inside and outside the light cone. The fuzzy causality principle is generalized to field models. Also, this work demonstrates the ability to use fuzzy space to regularize divergences in quantum field theory. The passage to the limit to a system of interacting particles enables the obtaining of the dissipative projection operator, represented earlier. The Liouville equation is solved here by successive approximations in the range of times much larger than the typical scale of fuzziness, by assuming the interaction as a small parameter. As well, here was applied the standard diagram technique.
