On the Possibility of Seismic Exploration Using Surface Torque Source and Related Topics*

Abstract

A B S T R A C T KUHN, M. and DRACH, V. 1984, On the Possibility of Seismic "Exploration using Surface Torque Source and Related Topics, Geophysical Prospecting 32, In this study we derive expressions for particle displacement or particle velocity anywhere inside a stratified earth and at its surface due to horizontal torque source located in the top layer. Equivalently, invoking Green's function reciprocity theorem, the solution applies also to the case of a surface or subsurface source when the resulting displacement or velocity is measured within the top layer.In order to evaluate the closed-form analytical solution economically and accurately it is advisable to introduce inelastic attenuation. Causal inelastic attenuation also lends the necessary realism to the computed seismic trace. To provide proof that the analytical solution is indeed correct and applicable to the multilayer case, a thick uniform overburden was assumed to consist of many thin layers. The correctness of the computed particle velocity response can be very simply verified by inspection. The computed response can also serve as a check on other less accurate methods of producing synthetic seismograms, such as the techniques of finite differences, finite elements, and various sophisticated ray-tracing techniques.It is not difficult to construct horizontal surface torque source. It appears that such source is well suited for seismic exploration in areas with a high-velocity surface layer. A realistic source function is analyzed in detail and normalized displacement response evaluated at different incidence angles in the near and the far fields.In an effort to distinguish the features of an SH torque seismogram from a pressure seismogram two models with identical layerings and layer parameters have been set up. As expected the torque seismogram is very different from the compressional seismogram. One desirable feature of a torque seismogram is the fast decay of multiples.Exact synthetic seismograms have many uses; some of them, such as the study of complex interference phenomena, phase change at 'wide angle reflection, channeling effects, dispersion (geometrical and material), absolute gain, and inelastic attenuation, can be carried out accurately and effortlessly. They can also be used to improve basic processing techniques such as deconvolution and velocity analysis.Currently, seismic methods employ source and receiver stations disposed either only horizontally or only vertically. Consequently, the bulk of the collected data consists of either horizontal or vertical profiles.This study concerns the investigation of propagation of horizontally polarized shear waves in field set-ups which are more general than either category. For example, the source may be located anywhere at or near the surface and the sourcegenerated signal recorded at the surface by a string of horizontal geophones oriented perpendicularly to the direction of the profile, or below the surface by a three-component geophone assembly placed at equally spaced intervals against th...

Evanescent Effects in Acoustical Wave Propagation*

“…To improve the economy of the integration algorithm we introduced an insignificant (Q = 3000) amount of inelastic attenuation in the model. This attenuation described also in Kuhn and Drach (1984), is 'isotropic' in the sense that the amplitudes and shapes of the potential or pressure transients are independent of the direction of propagation. This was proven by a series of simple model experiments in an unlimited space using several values of Q, ranging from extremely high to very low.…”

“…In most cases, e.g., Kuhn and Drach (1984), the direct term is implicit in the expression for the total field. The perils of numerically evaluating the expression containing the direct wave will be discussed later.…”

“…The symbols have the same meaning as in Kuhn and Drach (1984), i.e., k = o . s , (6) where w is the circular frequency, s is the horizontal slowness, U, is the body velocity in an acoustical medium of index m, and…”

“…It is often necessary to optimally balance economy and accuracy, and sometimes valuable lessons can be learned from false starts. Other aspects of numerical integration of expressions similar to (1) have been discussed in Kuhn and Drach (1984).…”