The Wave Propagation In Inhomogeneous Damaged Media And Inversion

The theory of waves propagation in inhomogeneous damaged zone and inversion of wave motion equations are studied. By the property of media and incident wave to seek of response wave, the problems of wave propagation in inhomogeneous damaged zone media are studied at first. Due to inhomogeneous in physics, the control equation is high-order differential equation with varied coefficient. For wave propagation in a quadratic curve inhomogeneous damaged zone, analytical solutions expressed special functions are gained. But to wave propagation in common inhomogeneous damaged zone, its analytical solutions can not be gained easily and the numerical methods can be applied. Dispersing inhomogeneous zone into layered zones and using boundary and continuous conditions between two layers, wave motion equation is solved. The harmonic wave propagation in inhomogeneous zone is studied, transmissive coefficient and reflective coefficient at the interface between two layers are gained, and transmission array of wave propagation is gained in layered media. Based on transmission array and boundary conditions, the response is obtained. On the base of harmonic solution, the solutions of transitory wave propagation in inhomogeneous zone can be obtained. By using Fourier transform, the transitory wave can be expressed as sum of steady wave. Appling solutions of steady wave propagation in inhomogeneous damaged zone, the response of each corresponding frequency is gained. At last, using of inverse Fourier transform, the result is transmitted to time and the solution of transitory wave propagation is gained. The result of numerical solutions are compared with the result of analytical solutions for wave propagation in inhomogeneous damaged zone. The influence of damaged degree, length of damaged zone and distributing of damage on wave propagation are studied.On the base of forward problem of wave propagation in inhomogeneous damaged zone, using the received and incident wave, the properties of media are inversed. Due to the ill-posed of inversion problems, using Newton iterative method at the course of inversion, the nonlinear equations is transformed into linear equations. Tikhonov's regularization method is applied for solving linear ill-posed problems. The regularization parameters are keys and L-curve method is used to fix on regularization parameter in regularization. The numerical example of inversion shows the effectiveness of this inversed method.