Download Brian Zurek, seismology-

Lithospheric Layering
Outline
1. Receiver Function Method
2. Mapping time to depth (Basic)
3. Advanced applications
a. Determining Vp/Vs and Moho depth
b. Velocity modeling
c. Determining layers of anisotropy and
dip
Receiver functions
Receiver functions are used to isolate the
response function that describes P-wave to
S-wave conversions at horizontal velocity
interfaces (layers) in the earth below the
receiver (hence the name receiver function)
P-wave to S-wave conversions
Frequency Domain
RF 
hv *
vv *  w
h - horizontal
v - vertical
w - whitening
Forward Model (Convolution)
Generation of recorded signal from Source
and Earth Response
source * response = signal
*
=
Inverse Model (Deconvolution )
Using the signal and source to get the Earth
Response function
signal / source = response
/
=
CASE OF NO NOISE! EVEN SMALL % OF NOISE CAN CREATE
UNSTABLE SOLUTION – INVERSE THEORY and REGULARIZATION
TO SATBALIZE THE SOLUTION
Real Receiver function
3C Seismic Record:
P-wave is the source (vertical)
P-wave + converted S-wave are signal (isotropic-flat layer -> radial)
Outline
1. Receiver Function Method
2. Mapping time to depth (Basic)
3. Advanced applications
a. Determining Vp/Vs and Moho depth
b. Velocity modeling
c. Determining layers of anisotropy and
dip
Move-out correction and Mapping
time to depth
P-wave
x
S-wave
z
tp
Want to know the timing difference
between the direct P arrival (ts) and
the converted S arrival (ts) as a
function of depth.
ts
This can be done if we know the
velocity of the wave-front in the
vertical and horizontal directions
Move-out correction and Mapping
time to depth
P-wave
1/Vpx
1/Vpz
S-wave
Just a geometry problem!
Tpds = ts – tp
TPds p, D  
tp
ts
0
 V z  2  p 2  V z  2  p 2  dz
P
D S

TPpds p, D  
0
 
D
VS z   p 2  VP z   p 2  dz

2
0
2
TPsds p, D   2    VS z   p 2  dz


D
2
Move-out correction and Mapping
time to depth
The horizontal velocity is
known, the rayparmeter - ‘p’
We need to know the Pvelocity as a function of
depth: Vp(z)
Just a geometry problem!
TPds p, D  
0
 V z  2  p 2  V z  2  p 2  dz
P
D S

TPpds p, D  
0
 
D
VS z   p 2  VP z   p 2  dz

2
0
And the ratio between Vp and
Vs (Poisson’s ratio).
2
TPsds p, D   2    VS z   p 2  dz


D
2
Move-out correction and Mapping
time to depth
The horizontal velocity is
known, the rayparmeter - ‘p’
We need to know the Pvelocity as a function of
depth: Vp(z)
And the ratio between Vp and
Vs (Poisson’s ratio).
How much do errors in assumptions
affect the time to depth mapping?
Vp(z) – An avg velocity difference
of 6.2 and 6.5 translates to ~ 3 km at
70 km depth
ie if the Moho is at 70 km and the
crust has an avg velocity of 6.5
km/s, we use 6.2 km/s and compute
a depth of ~ 67 km
Move-out correction and Mapping
time to depth
The horizontal velocity is
known, the rayparmeter - ‘p’
We need to know the Pvelocity as a function of
depth: Vp(z)
And the ratio between Vp and
Vs (Poisson’s ratio).
How much do errors in assumptions
affect the time to depth mapping?
Vp/Vs ratio – An avg difference of
1.72 to 1.79 translates to ~ 7 km at
70 km depth
ie if the Moho is at 70 km and the
crust has an avg Vp/Vs of 1.79, we
use 1.72 to compute a depth of ~ 63
km
Data Coverage
8/03 – 10/04
Teleseismic (blue)
Distance 30-95 Deg
Magnitude >=5.5 mb
N - 179
Teleseismic
Regional (Green)
Distance <30 Deg
Magnitude >=4.5 mb
N - 571
Regional
70 km piercing pts across the array
Cross sections of stacked RF’s
Cross sections of stacked RF’s
Cross sections of stacked RF’s
Cross sections of stacked RF’s
Cross sections of stacked RF’s
Measurement of depth to Moho
assuming Vp of 6.4 and Vp/Vs of
1.75
Outline
1. Receiver Function Method
2. Mapping time to depth (Basic)
3. Advanced applications
a. Determining Vp/Vs and Moho depth
b. Velocity modeling
c. Determining layers of anisotropy and
dip
Moho depth and Vp/Vs ratio
If we assume Vp(z),
we can write a function:
H(Vp/Vs, D) =
Tpms +Tppms + Tpsms
which we can use to
solve
Vp/Vs and D
Figures: Kennett, B
Example from station ES02
Moho depth 71 km
Vp/Vs 1.77
Poisson’s 0.27
Depth below receiver (km)
Pms + Ppms + Psms
Vp/Vs ratio
Pms + Ppms
Non-linear inversion for velocity and
Vp/Vs
Identifying layers of Anisotropy and
Dip
Identifying layers of Anisotropy and
Dip
Identifying layers of Anisotropy and
Dip
Thank You!
The End…
Move-out correction and Mapping
time to depth
P-wave
1/Vpx
1/Vpz
S-wave
Just a geometry problem!
Tppds = (ts – tp) + tp + tp = ts + tp
TPds p, D  
tp
ts
0
 V z  2  p 2  V z  2  p 2  dz
P
D S

TPpds p, D  
0
 
D
VS z   p 2  VP z   p 2  dz

2
0
2
TPsds p, D   2    VS z   p 2  dz


D
2
Move-out correction and Mapping
time to depth
1/Vpz
1/Vpx
P-wave
S-wave
Just a geometry problem!
Tpsds = (ts – tp) + ts + tp = 2*ts
TPds p, D  
0
 V z  2  p 2  V z  2  p 2  dz
P
D S

TPpds p, D  
0
 
D
VS z   p 2  VP z   p 2  dz

2
0
2
TPsds p, D   2    VS z   p 2  dz


D
2
Examples from station ES34
Moho depth 65 km
Vp/Vs 1.76
Poisson’s 0.26
Depth below receiver (km)
Pms + Ppms + Psms
Vp/Vs ratio
Pms + Ppms