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