Calculation of zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an elastic half-space

Impulse responses including near-field terms have been obtained in closed form for the zero-offset vertical seismic profiles generated by a horizontal point force acting on the surface of an anelastic half-space. The method is based on the correspondence principle. Through transformation of variables, the Fourier transform of the elastic impulse response is put in a form such that the Fourier transform of the corresponding anelastic impulse response can be expressed as elementary functions and their definite integrals involving distance, angular frequency, phase velocities, and attenuation factors. These results are used for accurate calculation of shear-wave arrival rise times of synthetic seismograms needed for data interpretation of anelastic-attenuation measurements in near-surface sediment.