Quantum Genetic Algorithm And Its Application To Inversion Of Geophysics

The earth is the basic space of human's living and development. Human has beenexploring the earth to reveal its secrets, including the origin and evolution. Theessential task of geosciences is to know the earth, and serve the subsistence ofpeople, such as exploring and exploiting the oil and mineral resources,infrastructure construction, environmental protection, prediction and prevention-control of geohazards.Today, conflict between supply and demand of the resources emerges sharply andvitally with time. Energy-saving and enhancing exploration will be the effectivemeasures to keep economic growth sustainably and steadily, to maintain stabilityand unity of society, as well as to improve people's living condition. As thereference of the first magnitude for resources exploration, the geophysicalinversion is one of the most significant means. However, conventional methods canhardly meet the requirement for more complex subsurface conditions andsophisticated processing. So an important route to improve the status is tointroduce newer and more outstanding ideas and algorithms in geophysical domain.Quantum algorithms, developed rapidly in 1990s, are the developing trends ofcomputing science in future, which is based on quantum computer and proved to havepreeminent computing speed, storage capability with exponential level, and morestabile and effective characteristics. Quantum genetic algorithm, based on quantummechanics, can improve computing efficiencies and prevent dropping into a localoptimum. Theoretically, quantum genetic algorithm not only has somecharacteristics of quantum computing, but also has many merits of nonlinear optimalmethods, which do not rely on initial geophysics model, and can synthesize (jointor hybridize) with other optimal algorithms, as well as realize parallel computingto reduce the CPU time-consuming greatly.Based on analysis of prevailing requests of geophysical inversion problems anddrawbacks of inversion methods today in this paper, the author first introducesquantum genetic algorithm in geophysical inversion field which is applied successfully in other optimal fields, considering the global searching and rapidconvergence. Because of encoding with quantum bit and directional updating withquantum rotation gates, this method possesses the great capabilities of parallelcomputing and quantum tunneling effect, to improve the computing accuracy and speedgreatly.Focused on the research of quantum genetic algorithm in finding a solution tothe geophysical inversion problems, this paper consists of five parts as follow.The first part reviews the study status of inversion problems briefly, and showsthe significance, the train of thought, the major content, and the innovation ofthis project's research.The second part gives the review of nonlinear inversion, as well as introducessimulated annealing algorithm, genetic algorithm, artificial neural networkalgorithm and the algorithms recently proposed in geophysical inversion domain byresearchers of China University of Geosciences, such as multi-scale inversion,particle swarm optimization, homotopy method, simulated atomic transitionalgorithm, quantum annealing. Also this part gives discussions of the advantagesan disadvantages of nonlinear inversion methods, as well as the characteristics ofnonlinear, non-unisequeness, and multi-maximum to geophysical inversionproblems. At the end of this part, the paper shows that the study of geophysicalnonlinear inversion is still the main direction of inversion development, and itwill achieve great progress in future.The third part shows the concepts of quantum state, qubit and quantum gate, yetintroduces several quamtum algorithms, such as quantum annealing, quantum geneticalgorithms, quantum neural networks, quantum particle swarm optimization.The fourth part and the fifth part are the main work of this paper. In the fourthpart, the author proposes a realizing scheme for geophysical inversion problemswith nonlinear and multi-minimum properties, based on the fundaments of quantumgenetic algorithm and the key steps of the method, such as the update of quantumgate, step length of search.The fifth part gives many synthetic models in MT and seismic acoustic impedanceinversion and real data of Poyang district in Jiangxi province and Daqing districtin Heilongjiang province to check the feasibility ,the reliability, noise immunityand computing efficiency of quantum genetic algorithm. Results show that quantumgenetic algorithm is a stable and effective nonlinear inversion method with globalconvergence and strong noise immunity.As an innovation in this paper, quantum genetic algorithm is firstly introducedin geophysical inversion domain and achieves success in China. Because of encodingwith quantum bit and directional updating with quantum rotation gates, this methodpossesses the great capabilities of parallel computing and quantum tunneling effect,to improve the computing accuracy and speed greatly. Theoretic analysis and the results of this paper show that quantum geneticalgorithm is a comparatively perfect global searching method, a feasible methodto geophysical inversion problems. Comparing with the traditional nonlinearinversion methods, quantum genetic algorithm does not rely on initial geophysicsmodel, and has better global searching capabilities, faster convergence rates andhigher precision of result, which can meet the requirement of geophysical problemwith nonlinear, multi-minimum, and will prevail in geophysical nonlinear inversionfield greatly.In conclusion, geophysics needs to introduce the advanced ideas and methodsin other fields to solve more complex practical problems effectively in explorationand exploitation of the oil and mineral resources and infrastructure construction,which sustains the heavy task as the pioneer subject of progress in earth sciencesfield, as well as society development in future. During the course of solving theproblems mentioned above, we can only get the exact results with the guidance ofgeological theories and rules. Only combining geology and geophysics tightly, canwe solve practical problems effectively. Nowadays, the research of quantum geneticalgorithm is still under groping stage, and its theory needs to be consummated.So many studies should be done on practical geophysical problems before quantumgenetic algorithm will be widely used in geophysical field.