Bullard Lab, 1987

Fun with ray theory: 20 years of using the PXINT subroutine

Peter Shearer

IGPP, U.C. San Diego

May 3, 2007 A Chris Fest in Cambridge Schlumberger Cambridge Research

z v 1 v 2

Chris Chapman’s PXINT subroutine

v dx dz

• Part of

WKBJ Seismogram

software package.

• All you need for ray tracing through 1-D seismic velocity models. • Gives analytical solution for horizontal offset

dx

and travel time

dt

for segment of ray path from depth

z

1 to depth

z

2 .

• Three different velocity interpolation options.

The PXINT subroutine!

Why highlight PXINT?

• Chris is probably much prouder of COMPON, THETAC, or CCSQRT.

• But 90% of my research requires only simple ray theory and 1-D models.

• Lots of different topics, but PXINT is the common thread!

dx v 1 dz v 2

~1989 — CD-ROM data distribution • 650 MB capacity • Cheap to produce • Selected events released by NEIC • First reasonably practical access to large global datasets for individual seismologist

Global Stacking using Automatic Gain Control (AGC) • Calculate average absolute value in 5 s bins • Divide each bin by average of previous 24 bins. This normalizes the amplitude of each trace.

• Stack in 0.5˚ distance bins

90 AGC Stack: Long-period vertical 60 30 0 0 90 Distance (degrees) 180 270 360 from

Shearer

(1991)

90 AGC Stack: Long-period transverse 60 30 0 0 90 Distance (degrees) 180 270 360 from

Shearer

(1991)

SH

is faster than

SV SH

(solid) vs.

SV

(dashed) from stacked seismograms

S

(17˚ – 23˚)

SS

(37˚ – 43˚)

SSS

(57˚ – 63˚) from

Shearer

(1991)

AGC Stack: Short-period vertical from

Astiz et al.

(1996)

1988–1994 IRIS “Farm” archive 834 earthquakes 27,000 seismograms Vertical Transverse Radial from

Astiz et al.

(1996)

Stacking using a reference phase Unaligned

SH

waves Aligned

SH

waves 1 minute Stack Reference pulse stacks for 20 different range bins

S

CD-ROM stacks (1991)

P

wave (vertical) Topside reflections QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

PP P

660-km discontinuity

S

wave (transverse)

SS

410-km discontinuity QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

No global 220-km discontinuity

CD-ROM stack:

SS

precursors

SS

-wave stack (transverse) 4 2 es) 0 -2 -4 -6 -8 80 QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

100 120 140 Range (degrees) 160 180

S diff SS SS S660S

410-km discontinuity 520 660 from

Shearer

(1991)

No coherent reflectors above 410 or below 660

Source

SS

precursors are ideal for global mantle discontinuity studies Bounce point Receiver Good global distribution of bounce points from

Flanagan & Shearer

(1998)

Depression in ‘660’ in NW Pacific from

Shearer

(1991)

‘660’ topography from

SS

precursors

Shearer & Masters

(1992)

Flanagan & Shearer

(1998) QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

Gu et al.

(2002) blue = depressed (~10–20 km) red = elevated

CD-ROM stacks (1991)

P

-wave stack (radial)

SV/P

discontinuity conversions (Faber & Muller, 1984)

PcS diff P/SV

discontinuity conversions (

Vinnik

, 1977)

Receiver functions at GSN stations

Shearer

(1991)

Lawrence & Shearer

(2005)

Transition Zone Thickness Models

SS

precursors Receiver functions

Gu et al.

(1998)

Lawrence & Shearer

(2005)

Flanagan & Shearer

(1998)

Slabs in the transition zone

P

-wave tomography

660

topography

Flanagan & Shearer

(1998) from

Karson and van der Hilst

(2000)

Slabs in the transition zone Response of 660-km discontinuity to slab: 50–100 km deflection in vicinity of slab Lesser deflection in large region beneath slab

Relative event location using waveform cross-correlation

Nakamura Poupinet

(1978) (1984)

Ito

(1985)

Fremont & Malone

(1987)

Xie et al.

(1991)

Got et al.

(1994)

Haase et al.

(1995)

Dodge et al.

(1995)

Nadeau et al.

Phillips et al.

(1995) (1997)

Rubin et al.

(1999)

Waldhauser et al.

(1999)

Cross-correlation of pair of similar events P-waves Quake 1 Quake 2 Time (s) Time (s)

Caltech/UCSD Waveform Cross-Correlation Project

• 1984 to 2003 waveforms now online at Caltech • Cross-correlation completed for 17 million event pairs • Two relocated catalogs now available at SCEDC • Hauksson et al. double difference • Shearer et al. cluster analysis (SHLK_1.0) QuickTime™ and a TIFF (Uncompressed) dec ompressor are needed to s ee this pic ture.

QuickTime™ and a TIFF (Unc ompressed) decompres sor are needed to see this picture.

340,000 events in SHLK_1.0. Similar event clusters, shown in black, are relocated using cross-correlation data. Other events are colored by year and are located using phase pick data alone.

Catalog Locations SHLK_1.0 locations

Migration in Reflection Seismology

Assume point scatterers For each pixel in image, sum values from each trace at time of predicted source-to scatterer-to-receiver travel time

* * * * * * ** * *

Complete image is sum of individual point scatterers “Exploding reflector” model

Back-projection to image earthquake rupture QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

Japanese Hi-Net array of 700 stations 2004 Sumatra Andaman earthquake from

Ishii et al.

(2005)

Direct Back-projection

Assume grid of possible source locations Stack along predicted P wave travel time curves

Problem: Incoherent stacking from time shifts from 3-D structure QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

Unmodeled 3-D velocity perturbations cause time shifts in wavefront

Sumatra earthquake

P

-waves Aligned on theoretical (iasp91)

P

-wave travel times

Migration in Reflection Seismology

slow fast slow Problem: Time shifts from 3-D structure can destroy stack coherence Solution: Statics corrections (station terms)

*

Align

P

-waves with cross-correlation

P

onset

Method forces coherent stack at hypocenter QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

Cross-correlation times correct for perturbations along each hypocenter station ray path

But coherence not guaranteed for sources offset from hypocenter Time shifts here not identical to hypocenter shifts QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture.

Calibrated time corrections at hypocenter

Stacks at different source points Time (seconds) from

Ishii et al.

(2005)

Stacks and Time Slice (60 seconds) Time (seconds)

Stacks and Time Slice (300 seconds) Time (seconds)

QuickTime™ and a Video decompressor are needed to see this picture.

Short-period radiation from Hi-net backprojection (

Ishii et al.

, 2005) Harvard multiple CMT solution (

Tsai et al

., 2005)

P

-wave Back-Projection Method

• Suited for a global near-real-time system • Will give rapid information about rupture extent and likely areas of strong ground motion, which go beyond hypocenter and magnitude • We are working with U.S. Geological Survey scientists to implement this method

v 1 v 2 dx dz