From last class:
S R
1
2
3
h
C
1
C
2
(1) Direct wave, simple function of time vs.
distance
(2) Reflected wave, the asymptotic limit
becomes like direct wave
(3) Head wave, straight line with slope 1/C
2
Travel time curve:
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Direct Wave - Seismology - Lecture Notes, Study notes of Geology
These Lecture Notes cover the following aspects of Seismology : Direct Wave, Simple Function, Asymptotic Limit, Direct Wave, Straight Line, Slope, Head Wave, Critical Angles, Evanescenc, Reflected Wave
Typology: Study notes
2012/2013
1 / 7
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From last class:
S 1 R
C (^1) h
C 2
(1) Direct wave, simple function of time vs. distance (2) Reflected wave, the asymptotic limit becomes like direct wave (3) Head wave, straight line with slope 1/C (^2)
Travel time curve:
S R
i
(1) i < ic (2) i = ic (3) i > ic
(1) If i < ic , only have 2 arrivals, the direct wave and the reflected wave. Also, η 2 is a real number. There is no evanescence. For the reflected wave there is no phase shift, ε = 0. (2) If i = ic , begin to create the horizontal head wave as the angle becomes post- critical. The head wave still does not exist at this point or, in other words, at i = ic , the head wave = the reflected wave. (3) There is a critical distance Xc when i = ic, after which you have a head wave and a reflected wave. Distances > Xc are post-critical, and i > ic.
at X=Xc , the phase shift, ε = 0.
Critical angles:
S R
This is similar to parallel layers, but one layer is dipping. In the field, you can get around this by shooting the source twice, once on the right and once on the left, using the same geometry. This will allow you to determine C 1 and C 2 and get the slope of the layer.
S r 1 r 2 r 3 r (^4) r 4 r 3 r 2 r 1 S
(3) Multiple Layers
S R At layer 1, you will see direct, reflected, and head waves.
At layers 2 and 3, you will get reflected and head waves
px 2
2 1/ 2 1 2
px 2
1/C 1
1/C 2
1/C 3
T
= + h η
h η
i i 1
This is related to dix formula. You can use this to get layer thickness, from wave speeds. If the z layers are very thin, it can become a continuum Æ wave speed increasing with depth.
C
C
h C n
1
i
head (^) C
x T 2
T =
(2) Dipping layer
Other problems include:
“Blind layers”. This happens when you have a very thin layer or a low velocity zone (LVZ). Extension to continuous change in wave speed is now easy to solve.
C(z) T Continuum, very thin layers with increasing wave speeds…
z X
X For layered system; Tension Æ 1/c , i.e. related to slowness 1 sin^ i^ sin^ i ( r ) c =^ p^ =^ =^ at distance r c c ( r )
Bottom point, turning depth or bottoming depth
You can get information about where the wave goes horizontal at this point, π 1 i = ⇒ p = c 2 c bottompo int
Can use this to get wave speed at a certain depth…get a c(z) profile by looking at several r’s and bottom points. Forms principle of classical inversion technique to field c(z) from observed travel times.
T(x) = τ +px = τ + dT/dX x
τ p=1/c The intercept relates to^ τ… can be complicated as to whether there is a smooth increase in the wave speed X (^) or a discontinuous increase, or a LVZ.
C(z) Here are two triplications due to discontinuities. It can get really complicated. You cannot invert this data, BUT you can make synthetics and solve the forward problem and calculate what the wave form would look like.
Example: