CSIR-NET
96)
The travel time differences between the P and S arrivals at two
stations A and B are 3 sec and 4 sec Respectively, while the
difference in the P- wave arrival time between the same stations is
1sec. What is the ratio of the P-wave velocity to that of S-wave
velocity?
(Thanks
to Chandra sekhar, ANU)
Solution:
Given
that,
Station
A travel time difference given that (t_{s}-t_{p})_{A}= 3 seconds
Station
B travel time difference given that (t_{s}-t_{p})_{B}= 4 seconds
Difference in the P-wave arrival time between the station B to station A is given that,
(t_{p})_{B}-(t_{p})_{A}= 1 seconds
(t_{p})_{B}-(t_{p})_{A}= 1 seconds
\frac{V_{p}}{V_{s}}=?
we
know that,
t_{s}-t_{p}=
D(\frac{1}{V_{s}}-\frac{1}{V_{p}})
(i.e
t_{p}=\frac{D}{V_{p}})
t_{s}-t_{p}=
t_{p}V_{p}(\frac{1}{V_{s}}-\frac{1}{V_{p}})
t_{s}-t_{p}=
t_{p}(\frac{V_{p}}{V_{s}}-1)-----------(1)
From
the above equation,we can derive equations for station B and A
respectively.
(t_{s}-t_{p})_B=
t_{p_B}(\frac{V_{p}}{V_{s}}-1)----------------(2)
(t_{s}-t_{p})_A= t_{p_A}(\frac{V_{p}}{V_{s}}-1)----------------(3)
(t_{s}-t_{p})_A= t_{p_A}(\frac{V_{p}}{V_{s}}-1)----------------(3)
Subtract equation (3) from eq (2),
we
get
(t_{s}-t_{p})_{B}-(t_{s}-t_{p})_{A}={[(t_{p})_{B}(\frac{V_{p}}{V_{s}}-1)]-[(t_{p})_{A}(\frac{V_{p}}{V_{s}}-1)]}
4-3=(\frac{V_{p}}{V_{s}}-1)[(t_{p})_{B}-(t_{p})_{A}]
1=(\frac{V_{p}}{V_{s}}-1)
\frac{V_{p}}{V_{s}}=1+1
\frac{V_{p}}{V_{s}}=2
Very excellent solution Sir.
ReplyDeleteThank you so much sir..
DeleteThis idea given by Chandrasekhar, ANU. Thank you chandu.
Deletegood explanation
ReplyDeleteThank you Satyachari.
DeleteThanks for helping me out!
ReplyDelete