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Hertz’s contact theory is widely used in elastic solid contact problems. In this paper, the applicability of Hertz’s contact theory in conformal contact problems was examined. Taking deep groove ball bearing and the outer raceway model as an example, both the FEM analyses and the theoretical studies were conducted. It is found that when the radius coefficient of groove curvature is greater than 0.55, Hertz’s theory can be practically applied for conformal contact. Contact problems of rolling bearings are generally solved by Hertz’s contact theory without considering inclusions and inhomogeneities in the material. In this paper, inclusions are presented in the contact analyses, and the corresponding elastic field distribution of the contact-inclusion model is investigated by using the finite element method.

Numerical simulate the sound field of the Ⅱ interface sector cement missing in the vertical well. And study the influencing factors of the characteristic wave amplitude and travel time by the sector missing angle, the fluid ring thickness, and the formation media and so on. It is considered that the sector missing angle has a great influence on the amplitude of the characteristic wave, but has little influence on the first wave travel time. As the sector missing angle increases, the characteristic wave amplitude also increases. When the thickness of the fluid ring is greater than a certain value (5mm), the thickness of the fluid ring increases. The amplitude of the characteristic wave increases gradually when the sector missing angle is the same. From the influencing factors of characteristic wave amplitude change, we can see that the angle change of sector cement missing is equivalent to the fluid ring thickness change.

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Inversion for seismic impedance is an ill-posed and nonlinear problem. Hence inversion results are non-unique and unstable, and low and high frequency components of inversion results are missed. Combining regularization with fast simulated annealing (FSA) can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function including the edge-preserving regularization with absolute and relative constraints. Optimization solution is calculated through a fast simulated annealing method. Moreover, the method uses two kinds of regularization parameters, including "weighting factor" and "scaling parameter" . In the fast simulated annealing procedure, the regularization parameters are adaptively adjusted by the maximum likelihood method in order to improve the inversion result and the convergence speed. We test the method on both synthetic and field data example. Tests on 2-D synthetic data indicate that the inversion results especially the aspects of the discontinuity are significantly sensitive to different regularization functions. The initial values of the regularization parameters are too large or too small to avoid an unstable or over-smoothed result, and affect the convergence speed. The results obtained by constant regularization parameters are smoother than that obtained by adaptively adjusting the regularization parameters, where is reducing and is increasing along with the temperature decreasing. The inversion result of the field data provides more detailed information of both the layers and the faults, and is applicable to field geological cases.