Elastic Waves Radiating from a Subsurface Reservoir Crack

In order to clarify the radiation pattern of elastic waves from a fluid-filled crack in the earth's crust, dynamic elastic response of a two-dimensional fluid-filled crack is studied, emphasizing the effect of the stiffness due to contact between the asperities on the upper and lower surfaces of the crack. To this end, a singular integral equation is derived for the displacement gap across the crack in the Fourier image space, where the motion of the fluid in the crack is taken into account. The singular integral equation is solved numerically, and the radiation pattern is examined in the intermediate region where the distance from the crack is several ten (10~30) times the representative length of the crack. It is revealed that the radiation pattern and the amplitude of the elastic waves are governed primarily by the stiffness on the crack surface. The aspect ratio, i. e., the ratio of the crack length to the initial aperture of the crack, has only weak effects except in the case of a crack which is completely open initially.