Evaluation of the Receiver Function in earthquake and exploration seismologyBy Michael Veen

Intro• Aim: Develop high resolution layered Earth model using seismic data.

• Method: Utilize and compare various 3 Multi-component spectral ratio methods to reveal near surface layering

• Multicomponent receivers sense wave components in NS, EW, vertical directions

• Allows isolation of P and S wavefields

• Horizontal component contains S wave data provides info on elastic properties of subsurface

• Joint analysis of P and S data provides info on lithology, porosity, fracturing and anisotropy

Very attractive for oil and gas exploration

Example: 3 component seismic data

Techniques:• 1. Crustal transfer function (Phinney, 1964)

• 2. Periodicity analysis (Gir et al., 1978)

• 3. Receiver function (Langston, 1979)

Spectral ratio• Ratio of frequency components in signal. Eg. Horizontal(w) to vertical(w)

• Important in determining earth structure immediately beneath a recording station

• Requires P wave signal from distant earthquakes

• Fourier analysis to convert signal to frequency domain

Transfer function• Uses spectral ratio of horizontal over vertical components

• Develop theoretical curves expressing this transfer function ratio as a function of angular frequency.

• Vary parameters to obtain a theoretical curve that matches experimental result

• Provides representation of the velocity-density structure beneath the station

• Able to isolate effects of intermediate and deep crustal structure, by observing peaks and troughs in the plots.

Example transfer ratio plot, Phinney 1964

Transfer Function: Flaws• Low frequency bandwidth = poor resolution. Does not reveal details of crust

• Location of peaks and troughs depend on total travel time, not on number of layers

• Matching technique provides little information on layering or the velocity distribution

Periodicity analysis• Requires much shorter data length than the crustal transfer function

9 – 12 seconds compared to 40 seconds

• Uses technique called cepstral analysis on the spectral ratio

• Cepstral anaylsis: Representation of how energy in a waveform is distributed among its frequency components

• Periodic peaks occur in the spectrum

• These peaks are caused by echoes in the signal.

• Periodicity can be thought of as the frequency of these frequency peaks.

• Units: cycles/Hz = seconds

• This method of analysis separates zones of different periodicities within the crust

Cepstrum Example

Periodicity analysis (Gir et al., 1978)

• Provides total thickness of crust and locations of intermediate discontinuities

• Utilizes higher frequency content than CTM = finer detail model

Receiver Function• Best known method for determining earth structure below seismographic

station

• Used over the past 20 years

• Estimate crustal thickness and Vp/Vs ratio beneath station

• Map impedance contrasts in time domain

Earthquake selection• >= magnitude 4 events within mantle

• Located at epicentral distances between 30 to 90 degrees

Receiver function• Some P-wave energy converted to S wave at impedance discontinuities

• Incidence angle at mantle-crust interface typically less than 40 degrees.

P-wave dominant in vertical converted to S dominant in radial (dir source-receiver)

• 3C receiver allows separation into pure P and S wavefields

Assume Uz contains principally P wave arrivals and Ux contains PS arrivals

Receiver function• Theoretical displacement response by a P-wave incident upon a stack of

interfaces written as…

Upp = Src * Path * IRpp

Ups = Src * Path * IRps

* = Convolution operator

U = Displacement

IR = Impulse response

SRC = Earthquake source signature

Path = Earth response from source to deepest conversion point

Receiver function• Result of frequency domain deconvolution:

• Note: this is now independent on nature of source and the path taken to conversion point

• We assume all internal P wave multiples reverberating within the target zone are weak, and so, can be neglected.

IRpp = 1

Receiver function• Requires decomposition from Uz and Ux components to up-going Upp and

Ups wavefields

• Only consider near vertical emergent angles by selecting earthquakes with epicentral distance from 30-90 degrees Incident P-wave angle of 20 +- 10 degrees at Moho and 10 +- 5 degrees at surface

Near enough to vertical

• IR(w) = Ux(w)/Uz(w)

• Inverse FT:

• Note that

Receiver function• Note that RF result is just an impulse/spike at the converted S wave

arrivals.

• Timing and amplitude of arrivals in RF are sensitive to the receiver side earth structure

• RF signals from different earthquakes originating from the same location are stacked to boost S/N, events are migrated to their correct location and inverted to recover elastic (Vp, Vs) properties of the target zone.