Coronal shocks are an important structure but without direct observations in solar and space physics .
The strength of shocks plays a key role in shock-related phenomena , such as radio bursts , SEP generation and so on .
This paper will present an improved method of calculating Alfvén speed and shock strength near the Sun .
In the method , observations as many as possible rather than one-dimensional global models are used .
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 \sim 4.18 while the fast CME drove a relatively weak shock with Mach number of 1.90 \sim 3.21 .
This is consistent with the radio observations that a stronger and longer decameter-hectometric ( DH ) type II radio burst is found during the first event and a short DH type II radio burst during the second event .
Particularly , the calculation results explain the observational fact that the slow CME produced a major solar energetic particle ( SEP ) event while the fast CME did not .
Through the comparison between the two events , the importance of shock strength in predicting SEP events is addressed .