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In the situation of shock wave, the interaction caused by the situation of one shock wave catching up with another is qualitatively analyzed with the result of the wave form: reflection rarefaction and incidence shock wave.

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On the basis of regular wave transformation equation in a reference[1] incorporating comprehensively environmental current,nonlinear dispersion effect,rapidly varying topography effect,energy loss due to bottom friction,refraction and diffraction, the governing equations are derived for irregular multi-directional wave transformation incorporating multi factors according to the principle of superposition of linear wave and the wave directional spectrum theory.

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TEM field is slowly changing in middle to deep depth prospecting, which is characterized by unperceivable wave and dominant dissemination, thus it can be assumed to be quasi-static state approximate and the wave equation of electromagnetic wave radiation is retrogressive and replaced by diffusion equation.

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So, in this paper, a circular cavity witha large radius is used to replace the straight boundary of thehalf space, then the half space problem can be changed tothe scattering problem of two circular cavities to the steadyincident P-wave . Having the aid of the mature cylinderfunction theory, the general solutions of the wave functionscan be given, and an infinite linear algebraic equations ofthe unknown coefficients in the wave functions can be gottenwith the boundary conditions and the Fourier complex seriesexpansion technology, the infinite linear algebraic equationscan be approximately solved by the finite trunction withsatisfying some definite precision, at the basis of thissolution of the equation, the variations and the lay-outs ofthe DSCF at the circular cavity boundary vs. the differentincident angles, the different embedded depths of thecircular cavity as well as the different dimensionless wavenumber of the incident P-wave.

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In the incontinuous cutting, the wave shape of milling can be looked as periodic function. When the milling wave shape with single-tooth was looked as impulse function, by the Fourier Transform, we can find out that it is composed of sine wave with a given frequency and a series of integer multiple frequency. Discussing on the power function is a major tache for studying on the cutting capability of the complex three-dimension groove milling inserts, so to know the facts that affect the single-tooth milling spectral value, and to observe the dynamic milling wave property from the composition of the power spectral, thus we can design and optimize grooves.

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