  Coronal shocks are important structures, but there are no direct observations
of them in solar and space physics. The strength of shocks plays a key role in
shock-related phenomena, such as radio bursts and solar energetic particle
(SEP) generation. This paper presents an improved method of calculating Alfven
speed and shock strength near the Sun. This method is based on using as many
observations as possible, rather than one-dimensional global models. Two
events, a relatively slow CME on 2001 September 15 and a very fast CME on 2000
June 15, are selected to illustrate the calculation process. The calculation
results suggest that the slow CME drove a strong shock, with Mach number of
3.43 - 4.18, while the fast CME drove a relatively weak shock, with Mach number
of 1.90 - 3.21. This is consistent with the radio observations, which find a
stronger and longer decameter-hectometric (DH) type II radio burst during the
first event, and a short DH type II radio burst during the second event. In
particular, the alculation results explain the observational fact that the slow
CME produced a major solar energetic particle (SEP) event, while the fast CME
did not. Through a comparison of the two events, the importance of shock
strength in predicting SEP events is addressed.
