Presentation on theme: "Seismic Tomography and Double-Difference Seismic Tomography"— Presentation transcript:
1 Seismic Tomography and Double-Difference Seismic Tomography Haijiang ZhangUniversity of Science and Technology of ChinaClifford ThurberUniversity of Wisconsin-Madison
2 AcknowledgementsFelix Waldhauser, for hypoDD, sharing data, and providing many constructive commentsBill Ellsworth, for suggesting the name "tomoDD"Charlotte Rowe for assistanceDefense Threat Reduction Agency, NSF, and USGS for financial support
3 Outline Seismic tomography basics – conventional and double-difference Synthetic tests and example applicationsUsage of tomoDD
4 Consider residuals from one earthquake Arrival Time Misfit*LATE***Trial LocationEARLY*MapViewSTATION AZIMUTH
5 Interpretation #1 - earthquake is farther north Arrival Time MisfitTrue Location**LATE*******EARLY*MapViewSTATION AZIMUTH
6 Is mislocation the only explanation? Arrival Time Misfit*LATE***Trial LocationEARLY*MapViewSTATION AZIMUTH
7 Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station!FASTER*LATE*True Location**SLOWEREARLYMapView*STATION AZIMUTH
8 Alternative interpretation - velocity structure is slower near event and to the south and faster near the northern station!Compensate for StructureFASTER*LATE*True Location******SLOWEREARLYMapView*STATION AZIMUTH
9 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 StructureFASTER*LATE*True Location******SLOWEREARLYMapView*STATION AZIMUTHHow can we determine the heterogeneity?
10 How does seismic tomography work? "Illuminate" fast velocity anomaly with waves from earthquake to arrayLocalizes anomaly to a "cone"
11 How does seismic tomography work? "Illuminate" fast velocity anomaly with waves from earthquake to array"Illuminate" fast anomaly with waves from another earthquakeLocalizes anomaly to a "cone"Localizes anomaly to another "cone"
12 Combine observations from multiple earthquakes to image anomaly
13 Simple Seismic Tomography Problem slowness si = 1/velocityhs3s4
14 Simple Seismic Tomography Problem slowness si = 1/velocityhs3s4
15 Simple Seismic Tomography Problem slowness si = 1/velocityhs3s4d = G mdatamodel
16 Simple Seismic Tomography Problem slowness si = 1/velocityhs3s4d = G mQUESTIONS SO FAR?datamodel
17 Consider pairs of closely-spaced earthquakes Relative Arrival Time11LATE11EARLY1AZIMUTH
28 gray = true white = relocated Ignore heterogeneity – some locations will be distorted, some residuals will be larger!11442233gray = true white = relocated
29 Consider effect of different heterogeneity - low velocity fault zone Relative Arrival Time111LATE1111EARLY11FAST SLOW FASTAZIMUTHgray = homogeneous case
30 gray = homogeneous case Relative Arrival Time22LATE22222EARLY22FAST SLOW FASTAZIMUTHgray = homogeneous case
31 gray = homogeneous case Relative Arrival Time33LATE33333EARLY33FAST SLOW FASTAZIMUTHgray = homogeneous case
32 gray = homogeneous case Relative Arrival Time44LATE44444EARLY44FAST SLOW FASTAZIMUTHgray = homogeneous case
33 Result - locations are very distorted! 11442233gray = true white = relocated
34 ImplicationsIgnoring heterogeneous earth structure will bias estimated locations from true locationsDifferent heterogeneities have different "signatures" in arrival time difference patterns - so there should be a "signal" in the data that can be modeled
35 Implications QUESTIONS? Ignoring heterogeneous earth structure will bias estimated locations from true locationsDifferent heterogeneities have different "signatures" in arrival time difference patterns - so there should be a "signal" in the data that can be modeledQUESTIONS?
36 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."
37 Seismic tomographyArrival-time residuals can be linearly related to perturbations to the hypocenter and the velocity structure:Nonlinear problem, so solve with iterative algorithm.
38 Double-difference seismic tomography For two events i and j observed at the same station kSubtract one from the otherNote:
39 Combine conventional and double-difference tomography into one system of equations involving both absolute and double-difference residualsdouble differenceabsolute
40 Test on "vertical sandwich" model Constant velocity (6 km/s) west of "fault"Sharp lateral gradient to 4 km/sFew km wide low-velocity "fault zone"Sharp lateral gradient up to 5 km/sGentle lateral gradient up to 6 km/sRandom error added to arrival times but not differential times (so latter more accurate)Start inversions with 1D model
41 Conventional tomography solution True model, all depths
42 Double-difference tomography solution True model, all depths
43 superior throughout well resolved areas Difference between solutions and true modelDouble difference ConventionalMarginal resultsnear surfaceDD resultssuperior throughout well resolved areasPoor resultsat model base
44 Application to northern Honshu, Japan Peacock, 2001
45 Examples of previous results for N. Honshu Nakajima et al., 2001Zhao et al., 1992Note relative absence of structural variations within the slab
46 Events, stations, and inversion grid Y=40 kmY=-10 kmY=-60 kmZhang et al., 2004
48 Test 1: with mid-slab anomaly Input modelVpVsRecovered model
49 Test 2: without mid-slab anomaly Input modelVpVsRecovered model
50 Preliminary study of the southern part of New Zealand subduction zone
51 Preliminary study of the New Zealand subduction zone - Vp
52 Preliminary study of the New Zealand subduction zone - Vs
53 Preliminary study of the New Zealand subduction zone - Vp/Vs
54 Comparing Northern Honshu (top) to New Zealand (bottom)
55 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).
56 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 Zone123Target EarthquakeResistivities: Unsworth & Bedrosian, 2004Earthquake locations: Steve Roecker, Cliff Thurber, and Haijiang Zhang, 2004
59 Relationship of Seismicity to 3D Structure – Fault-Normal View Z=-0.5 kmNESWZ=7.0 kmViewed from the northwest
60 Relationship of Seismicity to 3D Structure – Fault-Parallel View NWZ=-0.5 kmZ=7.0 kmViewed from the northeast
61 Revised Locations of Target Events and Borehole Features Zoback et al. (2011)
62 SUMMARYDD 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.
63 Extensions of tomoDD Regional scale tomoDD Adaptive tomoDD Global scale tomoDD
64 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.
65 Treating sphericity of the Earth Insert the Earth into a cubic box.2D sliceUse the rectangular box to cover the region of interestFlanagan et al., 2000
66 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
67 Uneven ray distribution Nonuniform station geometryNoneven distribution of sourcesRay bendingMissing dataMismatch between ray distribution and cells/or grids causes instability of seismic tomographyUsing damping and smoothing → possible artifacts
68 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?)
69 Construct tetrahedral and Voronoi diagrams around irregular mesh Represent the model with different scalesRepresent interfacesPlace nodes flexibly
71 Natural neighbor (NN) interpolation where is the natural-neighbor “coordinate”
72 linear interpolation vs. natural neighbor interpolation Using 4 nodesContinuity in first derivativesEasier to calculateNatural neighbor interpolationUsing n nodesContinuity in both first and 2nd derivativesMore difficult to calculate
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