IRIS Summer Intern Training CourseWednesday, May 31, 2006Anne Sheehan
Lecture 3: Teleseismic Receiver functionsTeleseismsEarth response, convolutionReceiver functions - basics, deconvolutionStacking receiver functions
receiver function ‘imaging’Complicated Earth
Dipping layersAnisotropic 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
layer 2 vp, vs, density
layer 1 vp, vs, density
dt
amplitude
converted pulse:
delay time dt depends on depth of interface and vp, vs of top layer
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
unfortunately, incident P is not a nice simple bump:
need to remove these bits ...
... to isolate phases converted near station
source
station
Receiver Function Construction• Convert seismogram from vertical, NS,
EW components to vertical, radial, transverse components
SourceReceiver
Wave propagation direction
SH: Transverse
SV: Radial
P wave compression
Surface
zy
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:
Source Signal: x(t)
Linear System: Response f(t)
Output: y(t) = x(t)*f(t) Y( ) = X( )F( )
Note: * means convolved, not multiplied!
Linear Systems and Fourier Analysis
• Deconvolution is the inverse of CONVOLUTION
Linear Systems and Fourier Analysis
Teton Gravity Research&
Warren Millerpresent:
Craig Jones' new radical
receiver function movie
A single receiver function - hard to interpret
time
ampl
itud
e
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
midcrustal conversion
"moveout plot":sort receiverfunctions byincidence angle(slowness)
station ILAM(Nepal)
radial receiver functionsbinned by slowness
direct P
Moho conversion
Schulte-Pelkum et al., 2005
Moho ~70km
Tibet station
arrival time/polarity variation with backazimuth(corrections for slowness + elevation applied)
azimuthal variation
highly coherent transverse componentreceiver functions
transverse components
attempt at a standard moveout plot for narrow azimuthal range
depth of modelleddiscontinuity(km)
multiples
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 F()eiwtd
2
-
F() = f(t)e-iwtdt-
Fourier transform
inverse Fourier transform
Receiver Function Constructionafter Langston, 1979 and Ammon, 1991
• In the earth, the source signalsource signal is convolved with the earth’s responseearth’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
• This is analogous to the form d = Gm
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)
Displacement
Response
Instrument
Impulse
Response
Source
Time
Function
Structure
Impulse
Response
(Receiver Function)
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
• this implies that Dv(t)*Er(t) = Dr(t)
Er() = Dr() = Dr()
I()S() Dv()
Et() = Dt() = Dt()
I()S() Dv()
Receiver Function Construction
P SV
incident: steep P
mostly on vertical component
converted phase: SV (in plane)
mostly on radial component
with dipping interface with anisotropic layer
Out of plane S conversions
(on radial and transverse components)
synthetic data
Schulte-Pelkum et al., 2005
Azimuthal difference stacking
flip polarityof all receiverfunctions incidentfrom northerlybackazimuthsbefore stacking
-> new interface shows up in stack
Schulte-Pelkum et al., 2005
interface found with azimuthal difference stack has good match with INDEPTH decollementfound anisotropy suggests ductile shear deformation at depth
Schulte-Pelkum et al., 2005
incident: steep Pmostly on vertical component
converted phase: SV (in plane)mostly on radial component
out-of-plane S conversions(on radial and transverse components):
with dipping interface
with anisotropic layer
P
SV
Receiver function profiles across the Western United States
Gilbert & Sheehan, 2004
Western United States crustal thicknesses from receiver functions
Gilbert & Sheehan, 2004
On-line resources:convolution animation:
http://www-es.fernuni-hagen.de/JAVA/DisFaltung/convol.html
Chuck Ammon's online receiver function tutorial:
http://eqseis.geosc.psu.edu/~cammon/HTML/RftnDocs/rftn01.html