Propagation of tube waves generated by an external source in layered permeable rocks

Tube-wave characteristics generated in a fluid-filled borehole may be used to determine enclosing-media parameters and, in particular, to localize petroliferous strata, if any, and estimate their permeabilities. As a rule, tube waves are generated by an external seismic source of explosive type located some distance away from a borehole embedded in a layered medium. The modelling of tube-wave excitation and propagation is a complicated problem, whose solution is necessary for solving the inverse problem.In the present study, an efficient numerical algorithm is presented to compute the tube waves' propagation, caused by external explosive perturbations in a fluid-filled borehole located in a layered enclosing medium. Fluid flow between the borehole interior and the enclosing saturated porous rocks can easily be taken into account within the framework of the algorithm. The solution is obtained by Sommerfeldintegral representation of external field potentials on the borehole axis and subsequent analytical integration of the external field along the borehole intervals of homogeneity; the resultant tridiagonal amplitude matrix is solved numerically.The method was tested in detail. Numerical results for simple medium configurations surrounding a fluid-filled borehole have been obtained. The modelling of tube waves, caused by the incident P, reflected PP, PS and the Rayleigh wave in a fluid-filled borehole of finite length located in an elastic half-space, adequately describes the main features of tube-wave propagation. Tube-wave modelling that includes the presence of a layer with hydraulic conductivity shows a high efficiency of tube-wave generation at the layer boundaries and significant amplitude attenuation inside it. It follows from the results of testing that the algorithm developed can be used for adequate modelling of VSP data.