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In this thesis research on the scattering from a hydraulic fracture is presented. The solution of a distributed load acting on the surface of an elastic half-space by means of the Cagniard-de Hoop method is presented. In the case of a uniformly distributed normal force (flat compressional transducer) the dominant energy is contained in the beam-shaped region centered along the normal to the transducer surface. In the near field this is seen as the plane P-wave component. The efficient calculation of generalized rays by means of the Cagniard-de Hoop method, provides a tool for the analysis of the Rayleigh wave behavior along the surface as well as in depth. The forward modeling is carried out by means of a finite-difference solution of the first-order velocity-stress elastodynamic system of differential equations. It is shown that all aspects of the problem of simulating observed experimental data can be handled with ease using a finite-difference solution on a staggered grid.