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**Seismic Tomography and Double-Difference Seismic Tomography**

Haijiang Zhang University of Science and Technology of China Clifford Thurber University of Wisconsin-Madison

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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

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**Outline Seismic tomography basics – conventional and double-difference**

Synthetic tests and example applications Usage of tomoDD

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**Consider residuals from one earthquake**

Arrival Time Misfit * LATE * * * Trial Location EARLY * Map View STATION AZIMUTH

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**Interpretation #1 - earthquake is farther north**

Arrival Time Misfit True Location * * LATE * * * * * * * EARLY * Map View STATION AZIMUTH

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**Is mislocation the only explanation?**

Arrival Time Misfit * LATE * * * Trial Location EARLY * Map View STATION AZIMUTH

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Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! FASTER * LATE * True Location * * SLOWER EARLY Map View * STATION AZIMUTH

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Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! Compensate for Structure FASTER * LATE * True Location * * * * * * SLOWER EARLY Map View * STATION AZIMUTH

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**How can we determine the heterogeneity?**

Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! Compensate for Structure FASTER * LATE * True Location * * * * * * SLOWER EARLY Map View * STATION AZIMUTH How can we determine the heterogeneity?

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**How does seismic tomography work?**

"Illuminate" fast velocity anomaly with waves from earthquake to array Localizes anomaly to a "cone"

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**How does seismic tomography work?**

"Illuminate" fast velocity anomaly with waves from earthquake to array "Illuminate" fast anomaly with waves from another earthquake Localizes anomaly to a "cone" Localizes anomaly to another "cone"

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**Combine observations from multiple earthquakes to image anomaly**

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**Simple Seismic Tomography Problem**

slowness si = 1/velocity h s3 s4

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**Simple Seismic Tomography Problem**

slowness si = 1/velocity h s3 s4

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**Simple Seismic Tomography Problem**

slowness si = 1/velocity h s3 s4 d = G m data model

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**Simple Seismic Tomography Problem**

slowness si = 1/velocity h s3 s4 d = G m QUESTIONS SO FAR? data model

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**Consider pairs of closely-spaced earthquakes**

Relative Arrival Time 1 1 LATE 1 1 EARLY 1 AZIMUTH

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Relative Arrival Time 2 LATE 2 2 2 EARLY 2 AZIMUTH

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Relative Arrival Time 3 LATE 3 3 3 EARLY 3 AZIMUTH

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Relative Arrival Time 4 LATE 4 4 4 EARLY 4 AZIMUTH

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**So relative arrival times tell you relative locations**

4 LATE 4 4 4 EARLY 4 AZIMUTH So relative arrival times tell you relative locations

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**Consider effect of heterogeneity - linear horizontal velocity gradient**

Relative Arrival Time 1 1 LATE 1 1 EARLY 1 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

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**Consider effect of heterogeneity – linear horizontal velocity gradient**

Relative Arrival Time 1 1 1 LATE 1 1 1 1 EARLY 1 1 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

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**SLOWER ====> FASTER**

Relative Arrival Time 2 LATE 2 2 2 EARLY 2 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

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**SLOWER ====> FASTER**

Relative Arrival Time 2 2 LATE 2 2 2 2 2 EARLY 2 2 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

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**SLOWER ====> FASTER**

Relative Arrival Time 3 LATE 3 3 3 3 3 3 EARLY 3 3 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

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**SLOWER ====> FASTER**

Relative Arrival Time 4 4 LATE 4 4 4 4 4 EARLY 4 4 AZIMUTH SLOWER ====> FASTER gray = homogeneous case

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**gray = true white = relocated**

Ignore heterogeneity – some locations will be distorted, some residuals will be larger! 1 1 4 4 2 2 3 3 gray = true white = relocated

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**Consider effect of different heterogeneity - low velocity fault zone**

Relative Arrival Time 1 1 1 LATE 1 1 1 1 EARLY 1 1 FAST SLOW FAST AZIMUTH gray = homogeneous case

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**gray = homogeneous case**

Relative Arrival Time 2 2 LATE 2 2 2 2 2 EARLY 2 2 FAST SLOW FAST AZIMUTH gray = homogeneous case

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**gray = homogeneous case**

Relative Arrival Time 3 3 LATE 3 3 3 3 3 EARLY 3 3 FAST SLOW FAST AZIMUTH gray = homogeneous case

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**gray = homogeneous case**

Relative Arrival Time 4 4 LATE 4 4 4 4 4 EARLY 4 4 FAST SLOW FAST AZIMUTH gray = homogeneous case

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**Result - locations are very distorted!**

1 1 4 4 2 2 3 3 gray = true white = relocated

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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

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**Implications QUESTIONS?**

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?

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**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."

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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.

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**Double-difference seismic tomography**

For two events i and j observed at the same station k Subtract one from the other Note:

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Combine conventional and double-difference tomography into one system of equations involving both absolute and double-difference residuals double difference absolute

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**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

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**Conventional tomography solution**

True model, all depths

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**Double-difference tomography solution**

True model, all depths

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**superior throughout well resolved areas**

Difference between solutions and true model Double difference Conventional Marginal results near surface DD results superior throughout well resolved areas Poor results at model base

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**Application to northern Honshu, Japan**

Peacock, 2001

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**Examples of previous results for N. Honshu**

Nakajima et al., 2001 Zhao et al., 1992 Note relative absence of structural variations within the slab

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**Events, stations, and inversion grid**

Y=40 km Y=-10 km Y=-60 km Zhang et al., 2004

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Cross section at Y=-60 km Vp Vs Vp/Vs

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**Test 1: with mid-slab anomaly**

Input model Vp Vs Recovered model

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**Test 2: without mid-slab anomaly**

Input model Vp Vs Recovered model

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**Preliminary study of the southern part of New Zealand subduction zone**

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**Preliminary study of the New Zealand subduction zone - Vp**

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**Preliminary study of the New Zealand subduction zone - Vs**

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

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

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**Application to Parkfield**

Following 4 workshops in , 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).

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**SAFOD Drilling Phases 1 2 3 Pilot Hole (summer 2002)**

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) San Andreas Fault Zone 1 2 3 Target Earthquake Resistivities: Unsworth & Bedrosian, 2004 Earthquake locations: Steve Roecker, Cliff Thurber, and Haijiang Zhang, 2004

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PASO-DOS, SUMMER 2001 – FALL 2002

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

Z=-0.5 km NE SW Z=7.0 km Viewed from the northwest

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

NW Z=-0.5 km Z=7.0 km Viewed from the northeast

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**Revised Locations of Target Events and Borehole Features**

Zoback et al. (2011)

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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.

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**Extensions of tomoDD Regional scale tomoDD Adaptive tomoDD**

Global scale tomoDD

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**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.

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**Treating sphericity of the Earth**

Insert the Earth into a cubic box. 2D slice Use the rectangular box to cover the region of interest Flanagan et al., 2000

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**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

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**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

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**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?)

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**Construct tetrahedral and Voronoi diagrams around irregular mesh**

Represent the model with different scales Represent interfaces Place nodes flexibly

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Linear interpolation Based on tetrahedra in 3D

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**Natural neighbor (NN) interpolation**

where is the natural-neighbor “coordinate”

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**linear interpolation vs. natural neighbor 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

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**Automatic construction of the irregular mesh**

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**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)

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

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

Regular grid Irregular grid

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**Natural neighbor interpolation**

The across-strike cross-section of P-wave velocity structure through Pilot Hole (absolute and differential data) Linear interpolation Natural neighbor interpolation

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**Global scale DD tomography**

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