Some Integrals Useful in Probabilistic Seismic Hazard Analysis

Closed-form solutions are presented for three simple cases of probabilistic seismic hazard analysis: (1) point source with deterministic median attenuation relation, (2) point source with probabilistic attenuation relation, and (3) a circular source with probabilistic attenuation relation. These solutions are obtained for commonly used models of magnitude exceedance rates and attenuation relations. Although the expressions presented correspond to simple cases, rarely found in real applications, they are believed to be useful as canonical cases against which to calibrate the numerical codes or as the basis to construct quadrature formulas for more complex cases.