Caustics and focusing produced by sedimentary basins: applications of catastrophe theory to earthquake seismology

Abstract

Summary. As high-frequency elastic waves propagate through real media, it is common for caustics and focusing to occur. Typically, rays may envelop a caustic surface in space, or exceptionally they may all coalesce at a focal point. In strong motion seismology, the observed large fluctuations in peak acceleration and intensity of ground shaking may just be a consequence of focusing and caustics created by waves propagating through irregularly shaped sedimentary basins. These basins, acting as deformed optical lenses, are capable of producing a complex network of patches and seemingly isolated pockets of intensified damage or high intensity shaking where the caustic intersects the ground surface. We adapt methods from optics and catastrophe theory to study the properties of caustics induced by typical sedimentary basins. Several hypothetical examples are shown that reflect the fact that these properties are useful to assess quantitatively the degree of wavefield amplification to be expected. A good correlation is found between actual damage patterns and caustic locations computed for the Caracas, Venezuela earthquake of 1967.