generally P and S wave used for velocity purpose from seismogram but i want to ask about either this step is suitable or not? i think this will give general velocity if it is true?
Only if you want to know a rough velocity average. Vp and Vs velocities gradients are variable as well as you go deep into the crust.
Only for the direct wave This simplified approach works, if you take the hypocentral distance instead of the
As Mr. Avila Jesus and Mr. Rainer Blum said, this is an approximation, and you can use the results for general communication, but it is not precise, and may cause some problems if you want a more accurate result.
First, the epicenter is on the surface of the Earth, while the actual location of the earthquake, the hypocenter, is [in some cases much] located deeper into the crust, so the distance parameter may as well be much larger and the velocity, much greater. The result would be an accurate average velocity.
Second, the crust (in fact, the Earth) is anisotropic, i.e., rock properties (density, shear modulus, mineral structure) vary according to their depth and constitution, and, because Vp and Vs are functions of some of these factors, this causes wave propagation to vary depending on where they are, well, propagating. Even the angle at which the wave incides on the rock may affect its velocity. As a result, the values of Vp and Vs are a composition of factors taking all these variations into account.
Suppose the propagation of waves through granite (~5000m/s) and sedimentary layers (~2000m/s). Before you reach the mentioned values, you would have to determine how much of the path was run on each medium to calculate Vp and Vs in each one of them.
Third, after the direct wave hits (so the general result is good for it), there are several interferences (reflections, arrival of the secondary wave) that make things more complicated for the subsequent waves. By integrating seismic stations, things get easier with more data. And there is also a rule of thumb that Vp = Vs.sqrt(3)
You could look up Rabbel & Mooney (1996), Li (2016) and Singh et al (2018), but for general understanding, you could refer to general Geophysics textbooks.
My answer got somehow mutilated, I simply wanted to stress the fact that you have to consider for the wavepath, e.g. in the case of a Pn- wave. The literature recommended by Henrique Joncew will help.
Regards
Rainer
All above comments are very helpful to your question. I pay my attention to the last parameter T. How can you get the accurate time of seismic wave traveling?
Earthquake takes place in random. We can't get the accurate starting time of a earthquake. If there is just a very small error in the smaller T. As v=s/t the results of v has a large error. So the T is also a important factor to get Vp.
Let tE = time that earthquake occurs (unknown)
tP = time that P wave arrives at station
d = distance between earthquake and station
vP = velocity of P wave
Then, since distance = velocity * time,
d = vP(tP-tE)
Plotted, this looks like:
If we know tP-tE and vP, then we can determine d. The problem is that we don't know tP-tE, since we don't have any way of knowing when the earthquake occurred. All we know is the record of when the earthquake was recorded at a distant station --- we know tP but not tE.In other words, we have one equation but two unknowns.
Luckily, we have another piece of data that is easily read from a seismogram---the arrival time of the S wave, tS. Assuming we also know the velocity of S waves (vS), then we can write a second equation, similar to the first but in terms of S-wave velocity and travel time tS-tE:
d = vS*(tS-tE)
This would also plot as a line, and since vS < vP, would have a steeper slope than the P-wave line plotted above.
Consider these two equations: we now have 2 equations and 2 unknowns (d, tE). So we can solve simultaneously for these two unknowns. Since we're interested mostly in d, not tE, the easiest way to solve is to subtract the first equation from the second, which eliminates tE. The result, after doing this subtraction and solving for d is
d = (tS-tP/(1/vS-1/vP)
On a graph, this looks like:
So we can determine tS - tP from a seismogram, then use it to determine the distance of the station from the earthquake.
OK you can return to refrance
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