Seismic Tomography and Double-Difference Seismic Tomography

Clifford ThurberUniversity of Wisconsin-Madison

Haijiang ZhangUniversity of Science and Technology of China

Acknowledgements

• Felix Waldhauser, for hypoDD, sharing data, and providing many constructive comments

• Bill Ellsworth, for suggesting the name "tomoDD"

• Charlotte Rowe for assistance• Defense Threat Reduction Agency, NSF, and

USGS for financial support

Outline

• Seismic tomography basics – conventional and double-difference

• Synthetic tests and example applications• Usage of tomoDD

Consider residuals from one earthquake

*

*

*

* *

0 90 180 270STATION AZIMUTH

LATE

EARLY

Arrival Time Misfit

Trial Location

MapView

Interpretation #1 - earthquake is farther north

*

*

*

* *

0 90 180 270STATION AZIMUTH

LATE

EARLY

*

* * * *

Arrival Time Misfit

MapView

True Location

Is mislocation the only explanation?

*

*

*

* *

0 90 180 270STATION AZIMUTH

LATE

EARLY

Arrival Time Misfit

Trial Location

MapView

Alternative interpretation - velocity structure is slower near event and to the south and

faster near the northern station!

*

*

* *

0 90 180 270STATION AZIMUTH

LATE

EARLY

*

FASTER

SLOWER

MapView

True Location

Alternative interpretation - velocity structure is slower near event and to the south and

faster near the northern station!

*

*

* *

0 90 180 270STATION AZIMUTH

LATE

EARLY

** * * *

FASTER

SLOWER

Compensate for Structure

MapView

True Location

Alternative interpretation - velocity structure is slower near event and to the south and

faster near the northern station!

*

*

* *

0 90 180 270STATION AZIMUTH

LATE

EARLY

** * * *

FASTER

SLOWER

Compensate for Structure

MapView

True Location

How can we determine the heterogeneity?

How does seismic tomography work?"Illuminate" fast velocity anomaly

with waves from earthquake to array

Localizes anomaly to a "cone"

How does seismic tomography work?"Illuminate" fast velocity anomaly

with waves from earthquake to array

Localizes anomaly to a "cone"

"Illuminate" fast anomaly with waves from another earthquake

Localizes anomaly to another "cone"

Combine observations from multiple earthquakes to image anomaly

h

hslowness si = 1/velocity

s1 s2

s3 s4

Simple Seismic Tomography Problem

h

hslowness si = 1/velocity

s1 s2

s3 s4

Simple Seismic Tomography Problem

h

h

d = G m

slowness si = 1/velocity

data model

s1 s2

s3 s4

Simple Seismic Tomography Problem

h

h

d = G m

slowness si = 1/velocity

data model

s1 s2

s3 s4

Simple Seismic Tomography Problem

QUESTIONS SO FAR?

Consider pairs of closely-spaced earthquakes

01

1

1

1 1

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

0 2

2

2

2 2

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

03

3

3

3 3

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

04

4

4

4 4

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

04

4

4

4 4

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

So relative arrival times tell you relative locations

Consider effect of heterogeneity - linear horizontal velocity gradient

01

0 90 180 270AZIMUTH

LATE

EARLY

SLOWER ====> FASTER

Relative Arrival Time

1

1

1 1

gray = homogeneous case

Consider effect of heterogeneity – linear horizontal velocity gradient

01

1

1

1 1

0 90 180 270AZIMUTH

LATE

EARLY

SLOWER ====> FASTER

Relative Arrival Time

1

1

1 1

gray = homogeneous case

0 2

0 90 180 270AZIMUTH

LATE

EARLY

SLOWER ====> FASTER

Relative Arrival Time

2

2

2 2

gray = homogeneous case

0 2

2

2

2 2

0 90 180 270AZIMUTH

LATE

EARLY

SLOWER ====> FASTER

Relative Arrival Time

2

2

2 2

gray = homogeneous case

03

3

3

3 3

0 90 180 270AZIMUTH

LATE

EARLY

SLOWER ====> FASTER

Relative Arrival Time

3

3

3 3

gray = homogeneous case

04

4

4

4 4

0 90 180 270AZIMUTH

LATE

EARLY

SLOWER ====> FASTER

Relative Arrival Time

4

4

4 4

gray = homogeneous case

Ignore heterogeneity – some locations will be distorted, some residuals will be larger!

04 2

1

3

4 21

3

gray = true white = relocated

Consider effect of different heterogeneity - low velocity fault zone

01

1

1

1 1

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

FAST SLOW FAST1

1

1 1

gray = homogeneous case

0 2

2

2

2 2

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

FAST SLOW FAST2

2

2 2

gray = homogeneous case

03

3

3

3 3

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

FAST SLOW FAST

3

3

3 3

gray = homogeneous case

04

4

4

4 4

0 90 180 270AZIMUTH

LATE

EARLY

Relative Arrival Time

FAST SLOW FAST

gray = homogeneous case

4

4

4 4

Result - locations are very distorted!

04 2

1

3

4 2

1

3

gray = true white = relocated

Implications

• Ignoring heterogeneous earth structure will bias estimated locations from true locations

• Different heterogeneities have different "signatures" in arrival time difference patterns - so there should be a "signal" in the data that can be modeled

Implications

• Ignoring heterogeneous earth structure will bias estimated locations from true locations

• Different heterogeneities have different "signatures" in arrival time difference patterns - so there should be a "signal" in the data that can be modeled

QUESTIONS?

Our DD tomography approach• Determine event locations and the velocity

structure simultaneously to account for the coupling effect between them.

• Use absolute and high-precision relative arrival times to determine both velocity structure and event locations.

• Goal: determine both relative and absolute locations accurately, and characterize the velocity structure "sharply."

Seismic tomography

Arrival-time residuals can be linearly related to perturbations to the hypocenter and the velocity structure:

Nonlinear problem, so solve with iterative algorithm.

Double-difference seismic tomography

For two events i and j observed at the same station k

Subtract one from the other

Note:

Combine conventional and double-difference tomography into one system of equations

involving both absolute and double-difference residuals

absolute

doubledifference

Test on "vertical sandwich" model• Constant velocity (6 km/s) west of "fault"• Sharp lateral gradient to 4 km/s• Few km wide low-velocity "fault zone"• Sharp lateral gradient up to 5 km/s• Gentle lateral gradient up to 6 km/s• Random error added to arrival times but not

differential times (so latter more accurate)• Start inversions with 1D model

Conventional tomography solution

True model, all depths

Double-difference tomography solution

True model, all depths

Difference between solutions and true modelDouble difference Conventional

Marginal resultsnear surface

Poor resultsat model base

DD resultssuperior

throughoutwell resolved

areas

Peacock, 2001

Application to northern Honshu, Japan

Examples of previous results for N. HonshuNakajima et al., 2001

Zhao et al., 1992

Note relative absence of structural variations within the slab

Events, stations, and inversion grid

Y=40 km

Y=-10 km

Y=-60 km

Zhang et al., 2004

Cross section at Y=-60 kmVp

Vp/Vs

Vs

Test 1: with mid-slab anomaly

Vp Vs

Inputmodel

Recoveredmodel

Test 2: without mid-slab anomaly

Vp Vs

Inputmodel

Recoveredmodel

Preliminary study of the southern part of New Zealand subduction zone

Preliminary study of the New Zealand subduction zone - Vp

Preliminary study of the New Zealand subduction zone - Vs

Preliminary study of the New Zealand subduction zone - Vp/Vs

Comparing Northern Honshu (top) to New Zealand (bottom)

Application to ParkfieldFollowing 4 workshops in 2003-2004, a site just north of the rupture zone for the M6

Parkfield earthquake was chosen for SAFOD because:

Surface creep and abundant shallow seismicity allow us to accurately target the subsurface position

of the fault.

Clear geologic contrast across the fault - granites on SW side and Franciscan melange on NE -

should facilitate fault's identification (or so we thought!).

Good drilling conditions on SW side of fault (granites).

Fault segment has been the subject of extensive geological and geophysical studies and is within the most intensively instrumented part of a major plate-

bounding fault anywhere in the world (USGS Parkfield Earthquake Experiment).

San

And

reas

Fau

lt Zo

ne

Phase 1: Rotary Drilling to 2.5 km (summer 2004)

Phase 2: Drilling Through the Fault Zone (summer 2005)

Phase 3: Coring the Multi-Laterals (summer 2007)

Resistivities: Unsworth & Bedrosian, 2004

Earthquake locations: Steve Roecker, Cliff Thurber, and Haijiang Zhang, 2004

SAFOD Drilling Phases

Pilot Hole (summer 2002)

Target Earthquake

1

2 3

PASO-DOS, SUMMER 2001 – FALL 2002

Relationship of Seismicity to 3D Structure – Fault-Normal View

NE SW

Z=7.0 km

Z=-0.5 km

Viewed from the northwest

Relationship of Seismicity to 3D Structure – Fault-Parallel View

SE NW

Z=7.0 km

Z=-0.5 km

Viewed from the northeast

Zoback et al. (2011)

Revised Locations of Target Events and Borehole Features

SUMMARY

• DD tomography provides improved relative event locations and a sharper image of the velocity structure compared to conventional tomography.

• In both Japan and New Zealand, we find evidence for substantial velocity variations within the down-going slab, especially low Vp/Vs zones around the lower plane of seismicity.

• In Parkfield, earthquakes "hug" the edge of the high-velocity zone and repeating earthquakes correlate with structures seen in borehole.

Extensions of tomoDD

• Regional scale tomoDD

• Adaptive tomoDD

• Global scale tomoDD

Regional scale version tomoFDD

• Considers sphericity of the earth.• Finite-difference ray tracing method

[Podvin and Lecomte, 1991; Hole and Zelt, 1995] is used to deal with major velocity discontinuities such as Moho and subducting slab boundary.

• Discontinuities are not explicitly specified.

Insert the Earth into a cubic box.

Use the rectangular box

to cover the region of interest

2D slice

Treating sphericity of the Earth

Flanagan et al., 2000

Adaptive-mesh version tomoADD

• Uneven ray distribution requires irregular inversion mesh.

• Linear and natural-neighbor interpolation based on tetrahedral and Voronoi diagrams.

Zhang and Thurber, 2005, JGR

Uneven ray distribution• Nonuniform station geometry• Noneven distribution of sources• Ray bending• Missing data

Mismatch between ray distribution and cells/or grids causes instability of seismic tomography

Using damping and smoothing → possible artifacts

The advantage of adaptive grid/cells (or why do we bother to use?)

• The distribution of the inversion grid/cells should match with the resolving power of the data.– The inverse problem is better conditioned.– Weaker or no smoothing constraints can be

applied.– Less memory space (less computation time?)

Construct tetrahedral and Voronoi diagrams around irregular mesh

• Represent the model with different scales• Represent interfaces• Place nodes flexibly

Linear interpolation

• Based on tetrahedra in 3D

kk

k f) (φ)v(

4

1

rr

)r(r)r(r)r(r

)r(r)r(r)r(rr13121k

13121

)(φk

Natural neighbor (NN) interpolation

)(f)(φ)v( k

n

kk rrr

1

where is the natural-neighbor “coordinate”

)(φk r

linear interpolation vs. natural neighbor interpolation

• Linear interpolation– Using 4 nodes– Continuity in first derivatives– Easier to calculate

• Natural neighbor interpolation– Using n nodes– Continuity in both first and 2nd derivatives– More difficult to calculate

Automatic construction of the irregular mesh

Application to SAFOD project

~800 earthquakes, ~100 shots, subset of high-resolution

refraction data (Catchings et al.,

2002); 32 "virtual

earthquakes" (receiver gathers from Pilot Hole)

The inversion grids for (a) P and (b) S waves at the final iteration using only the absolute data.

The DWS value distribution (ray sampling density) for P waves

Regular grid Irregular grid

The across-strike cross-section of P-wave velocity structure through Pilot Hole

(absolute and differential data)

Natural neighbor interpolationLinear interpolation

Global scale DD tomography