EFFICIENT AND ACCURATE CALCULATON OF RAY THEORY SEISMIC ... · Introduction EFFICIENT AND ACCURATE...
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Introduction EFFICIENT AND ACCURATE CALCULATON OF RAY THEORY SEISMIC TRAVEL TIME THROUGH VARIABLE RESOLUTION 3D EARTH MODELS Sanford Ballard, James R. Hipp and Christopher J. Young,, Sandia National Laboratories Ray Tracing After considering Eikonal solvers, ray shooters and finite difference ray Distributed Computing The ray bender requires on Several studies have suggested that using 3D Earth models to locate seismic events can improve the accuracy and reduce the uncertainty of the computed locations. We describe a fully 3D global Earth model representation and a compatible travel time calculator based on the ray pseudo-bending algorithm of Um and Thurber (1987). Together, these codes provide a practical means to efficiently and accurately calculate travel times for infinite frequency rays through global, variable resolution 3D Earth models. Ray tracing in 3D Distributed Network JPPF Driver Java Parallel Processing Framework www.jppf.org Large Problem Split into tasks Pseudo-Bending Snell’s Law benders, we chose to implement the ray pseudo-bending algorithm described by Um and Thurber (1987) enhanced by Zhao et al. (1992) and Zhao and Lei (2004). The ray bender requires on average approxim-ately 0.125 seconds to compute one source-receiver travel time on a single computer processor. To mitigate these negative performance impacts, we have multi-threaded the algorithm so it can be run in concurrent mode using is computationally expensive but we compensate by implementing our codes in a heterogeneous distributed computing environment. We are using these codes to evaluate published 3D models and to generate new models using tomographic inversion. We are currently modifying our seismic event location code and will soon be able to assess improvements in location capability that result from using 3D models. Windows Laptop Windows Desktop Solaris Workstations Rack-mounted Servers (Windows, Solaris, Linux) Our implementation reduces the likelihood that the pseudo-bending algorithm will return a local minimum by starting the ray calculation from several different starting rays. Specifically, interfaces are defined that include first order discontinuities plus additional interfaces at levels of the model where local minima are anticipated. Rays are computed that are constrained to bottom in each layer between these interfaces. The computed rays might be reflected off the top of the layer, turn within the layer, or diffract along the interfaces at the top and/or bottom of the layer. computer. We have also implemented our algorithm in a distributed computing environment using the Java Parallel Processing Framework (JPPF; www.jppf.org) allowing us to run many travel time calculations simultaneously on a heterogeneous cluster of multiprocessor PC, Mac, Unix and Linux computers. In our current configuration we use up to 200 processors to trace rays in parallel. all available processors on a single multiprocessor Travel Time Tomography O lti t li t d 3D Earth Model Representation Regular latitude-longitude grids are not suitable for global models due to convergence of meridians at the poles. We construct a global tessellation of triangles by starting with a regular polyhedron (tetrahedron, octahedron, icosahedron or tetra-hexahedron) and recursively subdividing the triangles until the desired resolution is achieved. Variable resolution in the geographic dimension is achieved by only subdividing triangles where additional resolution is desired. Finding the triangle in which a given geographic position is located is efficiently implemented using a multi-level triangle walking algorithm. At each node of the tessellation, a radial profile of Earth properties is defined. The radial positions of nodes are defined relative to the actual topography of the Earth referenced to the GRS80 ellipsoid, thereby removing the necessity to implement ellipticity and elevation The computed ray that is seismologically valid and that has the shortest travel time is retained. Our ultimate goal is to produce a global, seamless, 3D velocity model from the core-mantle boundary to the Earth’s topographic / bathymetric surface. In pursuit of that goal, we have developed a tomographic inversion system based on the standard LSQR algorithm (Page and Saunders, 1982) and applied it to a regional 200 180 160 140 120 100 80 60 40 20 0 Cell Area 1000 km 2 actual topography of the Earth referenced to the GRS80 ellipsoid, thereby removing the necessity to implement ellipticity and elevation corrections. Variable resolution in the radial direction is achieved by defining profiles from one of the major discontinuities in the model out to the topographic/bathymetric surface of the Earth. To verify the validity of the Bender we constructed a 3D version of the radially symmetric AK135 model (Kennett et al., 1995), using the successive tessellation subdivision method described above. The difference in travel time computed with the Bender and calculated using the 1D TauP travel time calculation algorithm (Buland and Chapman, 1983) as implemented in the TaupToolkit software (Crotwell et al., 1999) are compared below. The differences at all local, regional and teleseismic distances are at most a few hundredths of a second, indicating that the Best Fit Dynamic Model Fixed Ray Model 1982) and applied it to a regional tomography problem centered on the crust and upper mantle of the Indian Subcontinent and the Tibetan Plateau. Tomography is highly non- unique. Our goal is to produce a model that achieves lower residuals in order to improve event location and reduce uncertainty not to accurately nds) 0.04 0.05 0 o 80 o 70 o 60 o 50 o 40 o 30 o 20 o 120 o 110 o 100 o 90 o 10 o Bender is very accurate, even for long path lengths. Different Starting Model uncertainty, not to accurately image the Earth for the purpose understanding Earth dynamics. Important issues include: use of fixed vs. dynamic rays, inclusion of event and/or site terms in the inversion, selection of optimal damping and regularization parameters, and the selection of an appropriate starting model. Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. The views expressed here do not necessarily reflect the opinion of the United States Government, the United States Department of Energy, or Sandia National Laboratories. Distance (degrees) Bender - TauP Toolkit (secon 0 15 30 45 60 75 90 105 120 0 0.01 0.02 0.03 Summary We are developing the capability to compute seismic event locations using global, seamless, variable resolution 3D Earth models. A key goal of this work is to implement a system with computational performance that meets operational monitoring requirements.
Transcript of EFFICIENT AND ACCURATE CALCULATON OF RAY THEORY SEISMIC ... · Introduction EFFICIENT AND ACCURATE...
Introduction
EFFICIENT AND ACCURATE CALCULATON OF RAY THEORY SEISMIC TRAVEL TIME THROUGH VARIABLE RESOLUTION 3D EARTH MODELS
Sanford Ballard, James R. Hipp and Christopher J. Young,, Sandia National Laboratories
Ray TracingAfter considering Eikonal solvers, ray shooters and finite difference ray
Distributed ComputingThe ray bender requires on
Several studies have suggested that using 3D Earthmodels to locate seismic events can improve theaccuracy and reduce the uncertainty of the computedlocations. We describe a fully 3D global Earth modelrepresentation and a compatible travel time calculatorbased on the ray pseudo-bending algorithm of Um andThurber (1987). Together, these codes provide apractical means to efficiently and accurately calculatetravel times for infinite frequency rays through global,variable resolution 3D Earth models. Ray tracing in 3D
Distributed Network
JPPF DriverJava Parallel Processing Frameworkwww.jppf.org
Large ProblemSplit into tasks
Pseudo-Bending Snell’s Law
benders, we chose to implement the ray pseudo-bending algorithm described by Um and Thurber (1987) enhanced by Zhao et al. (1992) and Zhao and Lei (2004).
The ray bender requires on average approxim-ately 0.125 seconds to compute one source-receiver travel time on a single computer processor. To mitigate these negative performance impacts, we have multi-threaded the algorithm so it can be run in concurrent mode using y g
is computationally expensive but we compensate byimplementing our codes in a heterogeneous distributedcomputing environment.
We are using these codes to evaluate published 3Dmodels and to generate new models using tomographicinversion. We are currently modifying our seismicevent location code and will soon be able to assessimprovements in location capability that result fromusing 3D models.
Windows Laptop
Windows Desktop
Solaris Workstations
Rack-mounted Servers(Windows, Solaris, Linux)
Our implementation reduces the likelihood that the pseudo-bending algorithm will return a local minimum by starting the ray calculation from several different starting rays. Specifically, interfaces are defined that include first order discontinuities plus additional interfaces at levels of the model where local minima are anticipated. Rays are computed that are constrained to bottom in each layer between these interfaces. The computed rays might be reflected off the top of the layer, turn within the layer, or diffract along the interfaces at the top and/or bottom of the layer.
computer. We have also implemented our algorithm in a distributed computing environment using the Java Parallel Processing Framework (JPPF; www.jppf.org) allowing us to run many travel time calculations simultaneously on a heterogeneous cluster of multiprocessor PC, Mac, Unix and Linux computers. In our current configuration we use up to 200 processors to trace rays in parallel.
gall available processors on a single multiprocessor
Travel Time TomographyO lti t l i t d
3D Earth Model RepresentationRegular latitude-longitude grids are not suitable for global models due to convergence of meridians at the poles. We construct a global tessellation of triangles by starting with a regular polyhedron (tetrahedron, octahedron, icosahedron or tetra-hexahedron) and recursively subdividing the triangles until the desired resolution is achieved. Variable resolution in the geographic dimension is achieved by only subdividing triangles where additional resolution is desired. Finding the triangle in which a given geographic position is located is efficiently implemented using a multi-level triangle walking algorithm.
At each node of the tessellation, a radial profile of Earth properties is defined. The radial positions of nodes are defined relative to the actual topography of the Earth referenced to the GRS80 ellipsoid, thereby removing the necessity to implement ellipticity and elevation
The computed ray that is seismologically valid and that has the shortest travel time is retained.
Our ultimate goal is to produce a global, seamless, 3D velocity model from the core-mantle boundary to the Earth’s topographic / bathymetric surface. In pursuit of that goal, we have developed a tomographic inversion system based on the standard LSQR algorithm (Page and Saunders, 1982) and applied it to a regional
200180160140120100806040200
Cell Area1000 km2
actual topography of the Earth referenced to the GRS80 ellipsoid, thereby removing the necessity to implement ellipticity and elevation corrections. Variable resolution in the radial direction is achieved by defining profiles from one of the major discontinuities in the model out to the topographic/bathymetric surface of the Earth.
To verify the validity of the Bender we constructed a 3D version of the radially symmetric AK135 model (Kennett et al., 1995), using the successive tessellation subdivision method described above. The difference in travel time computed with the Bender and calculated using the 1D TauP travel time calculation algorithm (Buland and Chapman, 1983) as implemented in the TaupToolkit software (Crotwell et al., 1999) are compared below. The differences at all local, regional and teleseismic distances are at most a few hundredths of a second, indicating that the
Best Fit Dynamic Model
Fixed Ray Model
1982) and applied it to a regional tomography problem centered on the crust and upper mantle of the Indian Subcontinent and the Tibetan Plateau.
Tomography is highly non-unique. Our goal is to produce a model that achieves lower residuals in order to improve event location and reduce uncertainty not to accurately
nds) 0.04
0.05
0o
80o70o60o
50o
40o
30o
20o
120o
110o
100o
90o
10o
Bender is very accurate, even for long path lengths.
Different Starting Model
uncertainty, not to accurately image the Earth for the purpose understanding Earth dynamics.
Important issues include: use of fixed vs. dynamic rays, inclusion of event and/or site terms in the inversion, selection of optimal damping and regularization parameters, and the selection of an appropriate starting model.
Sandia is a multi-program laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000. The views expressed here do not necessarily reflect the opinion of the United States Government, the United States Department of Energy, or Sandia National Laboratories.
Distance (degrees)
Ben
der-
TauP
Tool
kit(
seco
n
0 15 30 45 60 75 90 105 1200
0.01
0.02
0.03
SummaryWe are developing the capability to compute seismic event locations using global, seamless, variable resolution 3D Earth models. A key goal of this work is to implement a system with computational performance that meets operational monitoring requirements.
