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 anomalywith waves from earthquake to array
Localizes anomaly to a "cone"
How does seismic tomography work?
"Illuminate" fast velocity anomalywith 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
s1s2
s3 s4
Simple Seismic Tomography Problem
h
hslowness si = 1/velocity
s1s2
s3 s4
Simple Seismic Tomography Problem
h
h
d = G m
slowness si = 1/velocity
data model
s1s2
s3 s4
Simple Seismic Tomography Problem
h
h
d = G m
slowness si = 1/velocity
data model
s1s2
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 2
1
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 FAST
1
1
1 1
gray = homogeneous case
0 2
2
2
2 2
0 90 180 270AZIMUTH
LATE
EARLY
Relative Arrival Time
FAST SLOW FAST
2
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. Honshu
Nakajima et al., 2001Zhao 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 km
Vp
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
An
dre
as F
ault
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(rr
13121k
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