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The Classic Garvin’s Problem Revisited

¹ Instituto de Ingeniería, UNAM
Cd. Universitaria, Circuito Escolar s/n
Coyoacán 04510; México D.F.
sesma{at}servidor.unam.mx
 (F.J.S.-S.)
² Instituto Mexicano del Petróleo
Eje Central Lázaro Cárdenas No. 152
G. A. Madero 07730, México D.F.
uiturrar{at}imp.mx
 (U.I.-V.)

The exact analytical solution for surface displacements due to a volumetric line source disturbance buried in an elastic homogeneous and isotropic half- space is attributable to W. W. Garvin. These results are in the time domain but the final expressions are only valid for a step-time variation of the load. We give a summary of Garvin’s work and extend it for virtually any given time signal. By analytical and numerical integration of the exact analytical solution we implicitly consider a ramp source function (this simple mathematical trick allows for regular waveforms). This solution can be used as a practical tool to test numerical techniques. Some examples are presented, and synthetic seismograms and polarigrams are displayed.