Babinet's principle for elastic waves

Abstract

Babinet's principle for elastic waves gives a relationship between the displacement fields due to complementary diffracting screens. The relationship has been derived using the seismic representation theorem as the starting point. The relationship for rigid complementary screens, for stress-free complementary screens, and for mixed rigid-stress-free complementary screens in each case has the same form. In deriving the relationship it is necessary to assume that the “jumps” across the complementary screens are the same as those that would exist when both complementary screens are present. This assumption has been tested in a seismic modeling experiment that utilized both stress-free and rigid screens. The experiments show that the assumption is valid within the accuracy of the experiment and, consequently, that Babinet's principle for elastic waves is valid to the same degree of accuracy.