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Seismic Tomography and Double-Difference Seismic Tomography Clifford Thurber University of Wisconsin-Madison Haijiang Zhang University of Science and Technology of China

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

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Interpretation #1 - earthquake is farther north * * * ** STATION AZIMUTH LATE EARLY * **** Arrival Time Misfit Map View True Location

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Is mislocation the only explanation? * * * ** STATION AZIMUTH LATE EARLY Arrival Time Misfit Trial Location Map View

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

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

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Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station! * * ** STATION AZIMUTH LATE EARLY * **** FASTER SLOWER Compensate for Structure Map View True Location 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 Localizes anomaly to a "cone" "Illuminate" fast anomaly with waves from another earthquake Localizes anomaly to another "cone"

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Combine observations from multiple earthquakes to image anomaly

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h h slowness s i = 1/velocity s1s1 s2s2 s3s3 s4s4 Simple Seismic Tomography Problem

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h h slowness s i = 1/velocity s1s1 s2s2 s3s3 s4s4 Simple Seismic Tomography Problem

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h h d = G m slowness s i = 1/velocity data model s1s1 s2s2 s3s3 s4s4 Simple Seismic Tomography Problem

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h h d = G m slowness s i = 1/velocity data model s1s1 s2s2 s3s3 s4s4 Simple Seismic Tomography Problem QUESTIONS SO FAR?

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Consider pairs of closely-spaced earthquakes AZIMUTH LATE EARLY Relative Arrival Time

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AZIMUTH LATE EARLY Relative Arrival Time

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AZIMUTH LATE EARLY Relative Arrival Time

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AZIMUTH LATE EARLY Relative Arrival Time

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AZIMUTH LATE EARLY Relative Arrival Time So relative arrival times tell you relative locations

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Consider effect of heterogeneity - linear horizontal velocity gradient AZIMUTH LATE EARLY SLOWER ====> FASTER Relative Arrival Time gray = homogeneous case

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Consider effect of heterogeneity – linear horizontal velocity gradient AZIMUTH LATE EARLY SLOWER ====> FASTER Relative Arrival Time gray = homogeneous case

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

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

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

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

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

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Consider effect of different heterogeneity - low velocity fault zone AZIMUTH LATE EARLY Relative Arrival Time FAST SLOW FAST gray = homogeneous case

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

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

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

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Result - locations are very distorted! 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 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 absolute double difference

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

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Peacock, 2001 Application to northern Honshu, Japan

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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 Vp/Vs Vs

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Test 1: with mid-slab anomaly VpVs Input model Recovered model

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Test 2: without mid-slab anomaly VpVs Input model 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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San Andreas Fault Zone 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

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PASO-DOS, SUMMER 2001 – FALL 2002

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Relationship of Seismicity to 3D Structure – Fault-Normal View NESW Z=7.0 km Z=-0.5 km Viewed from the northwest

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Relationship of Seismicity to 3D Structure – Fault-Parallel View SENW Z=7.0 km Z=-0.5 km Viewed from the northeast

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Zoback et al. (2011) Revised Locations of Target Events and Borehole Features

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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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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

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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 Linear interpolation –Using 4 nodes –Continuity in first derivatives –Easier to calculate Natural neighbor interpolation –Using n nodes –Continuity in both first and 2 nd 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 gridIrregular grid

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

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Global scale DD tomography

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