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Recovery of medium properties in three dimensions with three-dimensional parameters variability

Masood K., Zaman F. D.

Journal of Technical Physics

2007

Vol. 48, no 1

29-38

We consider a problem of identification of physical properties of the Earth using the damped wave equation, based on the linearized inversion associated with Horn's inversion theory. We assume that damping and sound speed are well approximated by the background plus the perturbation. Application of the method leads to a linear integral equation involving variations in sound speed and damping. Our aim is to recover these variations in velocity and damping, what in turn yields a map of the interfaces in the interior of the Earth. We consider the three-dimensional inverse problem of determining three-dimensional variations in the propagation speed and damping by considering the damped wave equation. We exploit the high-frequency character of seismic data to simplify the problem.

Direct and inverse acoustic scattering problem over a two-part impedance ground in a moving fluid by using Wiener-Hopf technique

Zaman F. D., Masood K.

Journal of Technical Physics

2005

Vol. 46, no 1

23-35

The aim of this paper is to solve the direct and inverse problem in a moving fluid. We consider the direct and inverse scattering problem of acoustic line source by a two-part boundary of a half-space, having a small variation in propagation speed in the presence of a moving fluid. The problem reduces to the solution of two integral equations by using the Fourier transform and Green's function. One of these equations is solved exactly by the Wiener-Hopf technique while the other is reduced to a Fredholm equation of the first kind whose kernel involves the solution to the first equation. The procedure can be applied to recover the variation in the wave speed over a nonhomogeneous impedance ground.

Shear velocity inversion procedure for love waves

Zaman F. D., Masod K.

Journal of Technical Physics

2003

Vol. 44, no 3

295-301

An inverse solution is presented to the seismic inverse problem for one-dimensional shear velocity variations. The Love waves, travelling in a layer overlying a half-space incident upon delta-function potential, are considered. The equation of motion for Love waves is transformed to the Schrodinger equation and then the potential is recovered by applying Gelfand-Levitan and Marchenko procedure.