Investigations of tsunamigenesis on a spherically symmetric and elastic Earth using normal mode summations and moment tensor line sources are extended to include general double-couple mechanisms so that computed tsunami waveforms can be compared with specific observations. Amplitudes of 19 tide gauge records of the Kurile Islands sea wave of 13 October 1963 are reproduced within a factor of 2 by either a single line source 250 km in length or by a triplet of parallel line sources separated by 42 km. Both models predict a strong beaming of tsunami strength with wave heights toward the northwest and southeast three to eight times larger than those in the northeast and southwest. For faults over 150 km in length, 2 of the 6 moment tensor components dominate tsunami production. This fact motivated the coining of a new parameter, tsunami moment Mt. By cataloging tsunami fields produced by suites of fault mechanisms, I find that Mt is approximately proportional to the tsunamigenic potential of earthquakes. Despite the critical role of fault mechanism in tsunami generation, many sources have nearly equal tsunami moment and nearly equal ability for sea wave excitation. Estimates of shallow source strength from measurements of elastic surface waves have questionable integrity at both long (>100 sec) and short (>30 sec) periods. Amplitudes of high-frequency waves suffer from saturation due to source size and duration, while low-frequency amplitudes are unstable with respect to small perturbations in fault mechanism because of the influence of the Earth's surface. Many tsunami earthquakes may be artifacts of underestimated source strength resulting from the inefficiency of shallow, nearly vertical dip-slip faults to produce long-period surface waves.