A detailed study is made of the Bouchon (1981) trapezoidal integration rule for evaluation of Sommerfeld integrals. A problem with non-propagating arrivals is found with integrands involving the zero order Bessel function. A mid-point rectangular integration rule is offered as a imperfect way to reduce this error. To test numerical evaluation of Hankel transforms, the Haskell (1963) wholespace solution is reformulated, and examples are given of the analytic, Bouchon numerical integration and mid-point numerical integration of the eight dislocation and two explosion Green’s functions.

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