IRIS Summer Intern Training Course
Wednesday, May 31, 2006
Anne Sheehan
Lecture 3: Teleseismic Receiver functions
Teleseisms
Earth response, convolution
Receiver functions - basics, deconvolution
Stacking receiver functions
receiver function ‘imaging’
Complicated Earth
Dipping layers
Anisotropic receiver functions
Applications & Examples - Himalaya, Western US
Teleseisms used in Himalayan Receiver Function Study
Want to deconvolve source and
instrument response so we are just left
with the signal from structure
converted pulse:
delay time dt depends on depth
of interface and vp, vs of top
layer
layer 2
vp, vs, density
layer 1
vp, vs,
density
amplitude depends on velocity
contrast (mostly) and density
contrast (weakly) at the interface
converted arrival:
"+" bump = bottom slow, top fast
"-" bump = bottom fast, top slow
dt
amplitude
unfortunately, incident P is not a nice simple bump:
station
source
... to isolate phases
converted near station
need to remove these bits ...
Receiver Function Construction
• Convert seismogram from vertical, NS,
EW components to vertical, radial,
transverse components
Source
Receiver
Surface
SH:
Transverse
z
Wave
propagation
direction
P wave
compression
SV: Radial
y
X
The magic step to isolate near-receiver converted phases via
receiver function analysis:
incident P appears mostly on the vertical component,
converted S appears mostly on horizontal components.
-> call the vertical component the "source" (it's as close as we're
going to get to the true source function) and remove it from the
horizontal components;
what remains is close enough to the converted phases.
how this works:
Linear Systems and Fourier
Analysis
• Recall that for a linear system:
Linear Systems and Fourier
Analysis
• Deconvolution is the inverse of
CONVOLUTION
Linear Systems and Fourier
Analysis
Teton Gravity Research
&
Warren Miller
present:
Craig Jones'
new radical
receiver function movie
amplitude
A single receiver function - hard to interpret
time
one receiver function per earthquake
-function of slowness (incidence angle)
-function of backazimuth (unless flat layered isotropic case)
receiver functions are sensitive to discontinuity structure
"moveout plot":
sort receiver
functions by
incidence angle
(slowness)
radial receiver functions
binned by slowness
station ILAM
(Nepal)
Moho conversion
midcrustal conversion
direct P
Schulte-Pelkum et al., 2005
Tibet station
Moho ~70km
azimuthal variation
arrival time/polarity variation with backazimuth
(corrections for slowness + elevation applied)
transverse components
highly coherent transverse component
receiver functions
attempt at a standard moveout plot for narrow azimuthal range
multiples
depth of
modelled
discontinuity
(km)
common conversion point (CCP) stacking
scale time to
depth along
incoming ray
paths with an
assumed
velocity model
stack all receiver
functions within
common conversion
point bin
stack along profile (red):
Schulte-Pelkum et al., 2005
but where is the decollement?
Linear Systems and Fourier
Analysis
• Using Fourier analysis, deconvolution of linear
system responses becomes a very simple problem
of division in the frequency domain
• Solution in the frequency domain is converted to a
solution in the time domain using the Fourier
transform
f(t) = 1

2
F() =

F()eiwtd
Fourier transform
-


f(t)e-iwtdt
-
inverse Fourier transform
Receiver Function Construction
after Langston, 1979 and Ammon, 1991
• In the earth, the source signal is convolved
with the earth’s response
• We want to extract the information
pertaining to the earth’s response, because it
can tell us about the earth’s structure
• We also have to worry about the instrument
responses from our seismometers
Receiver Function Construction
Theoretical Displacement Response for a P plane wave
Dv(t) = I(t)*S(t)*Ev(t) (vertical)
Dr(t) = I(t)*S(t)*Er(t) (radial)
Dt(t) = I(t)*S(t)*Et(t) (transverse)
Instrument
Displacement
Impulse
Response
Response
Source
Structure
Time
Impulse
Function
Response
(Receiver Function)
•
This is analogous to the form d = Gm
Receiver Function Construction
• Assumption: using nearly vertically incident
events, the vertical component
approximates the source function convolved
with the instrument response
Dv(t) = I(t)*S(t)
Receiver Function Construction
• In the frequency domain, Er and Et can be simply
calculated
Er() = Dr()
I()S()
Et() = Dt()
I()S()
•
this implies that Dv(t)*Er(t) = Dr(t)
= Dr()
Dv()
= Dt()
Dv()
Receiver Function Construction
incident: steep P
converted phase: SV (in plane)
mostly on vertical component
mostly on radial component
SV
P
Out of plane S conversions
(on radial and transverse components)
with dipping interface
with anisotropic layer
synthetic data
Schulte-Pelkum et al., 2005
Azimuthal difference stacking
flip polarity
of all receiver
functions incident
from northerly
backazimuths
before stacking
-> new interface shows up in stack
interface found with azimuthal difference stack has good match with
INDEPTH decollement
found anisotropy suggests ductile shear deformation at depth
Schulte-Pelkum et al., 2005
incident: steep P
mostly on vertical component
out-of-plane S conversions
(on radial and transverse
components):
P
converted phase: SV (in plane)
mostly on radial component
with dipping interface
SV
with anisotropic layer
Receiver function profiles across the Western United States
Western United States crustal thicknesses from receiver functions
Gilbert & Sheehan, 2004
On-line resources:
convolution animation:
http://www-es.fernunihagen.de/JAVA/DisFaltung/convol.html
Chuck Ammon's online receiver function tutorial:
http://eqseis.geosc.psu.edu/~cammon/HTML/RftnD
ocs/rftn01.html