Modeling the Combined Effects of Deterministic and Statistical Structure for Optimization of Regional Monitoring
Christopher J. Sanborn, Michele Fitzpatrick, Steven Walsh, and Vernon F. Cormier Physics Department, University of Connecticut, Storrs
REFERENCES
o Sanborn, et al, Radiative3D: http://rainbow.phys.uconn.edu/geophysics/wiki/
o Menke, W., Raytrace3d, www.iris.edu/software/downloads/plotting/
o Shearer, P.M., and P.S. Earle, in Advances in Geophysics, Volume 50: Earth Heterogeneity and Scattering Effects on Seismic Waves, H. Sato and M.C. Fehler (ed.), 2008.
o N. D. Selby, D. Bowers, A. Douglas, R. Heyburn, and D. Porter, 2005: Seismic Discrimination in Southern Xinjiang: The 13 March 2003 Lop Nor Earthquake, BSSA.
o Sato, H., Fehler, M. C., and Maeda, T., 2012: Seismic wave propagation and scattering in the heterogeneous earth (2nd Ed.), Springer.
o Fisk, M.D., 2002: Accurate Locations of Nuclear Explosions at the Lop Nor Test Site Using Alignment of Seismograms and IKONOS Satellite Imagery, BSSA.
o Kim, Won-‐Young, Paul G. Richards, Diane Baker, Howard Patton, and George Randall, Improvements to a Major Digital Archive of Seismic Waveforms from Nuclear Explosions, AFRL-‐RV-‐HA-‐TR-‐2010-‐1024, Final Report, 23 March 2010.
ABSTRACT RADIATIVE TRANSPORTThe differences between earthquakes and explosions are largest in the highest recordable frequency band. In this band, scattering of elastic energy by small-‐scale heterogeneity (less than a wavelength) can equilibrate energy on components of motion and stabilize the behavior of the Lg wave trapped in the Earth's crust. Larger-‐scale deterministic structure (greater than a wavelength) can still assume major control over the efficiency or blockage of the Lg and other regional/local seismic waves. This project proposes to model the combined effects of the large-‐scale (deterministic) and the small scale (statistical) structure to invert for improved structural models and to evaluate the performance of yield estimators and discriminants at selected IMS monitoring stations in Eurasia. This will be accomplished by synthesizing seismograms using a radiative transport technique to predict the high frequency coda (>5 Hz) of regional seismic phases at stations having known large-‐scale three-‐dimensional structure, combined with experiments to estimate the effects of multiple-‐scattering from unknown small-‐scale structure. EARTH STRUCTURE
DETERMINISTIC STRUCTURE Examples: • Changes in Moho depth • Lateral variation in seismic velocity
STATISTICAL STRUCTURE Example: • fine-‐scale deviations of seismic
velocity, due to material inhomogeneity, small cracks and fissures, etc. Random heterogeneity can be parameterized by scale-‐length and strength parameters.
From a modeling standpoint, we divide Earth structure into two categories, based on the approach used in simulation:SOFTWARE TOOL: RADIATIVE3D
FUNDED BY: AFRL/DOE Contract No. FA9453-‐12-‐C-‐0207, May 30, 2012 through May 29, 2015Address correspondence to: [email protected] or [email protected]
We are developing Radiative3D to be a next-‐generation tool for synthetics generation in models with complex deterministic and statistical structure. Features include:
✦ Simulates realistic earthquake and explosion radiation patterns, parameterized via moment-‐tensor elements
✦ Propagates rays in full 3D ✦ Radiative transport well-‐suited to high-‐frequency synthetics ✦ Complex 3D model structure via tetrahedral grid ✦ Produce synthetic envelopes, travel time curves, or
videos of energy propagation through 3D models ✦ Realistic scattering patterns in full 3D ✦ Realistic reflection/transmission handled at discontinuous
interfaces, including P-‐wave / S-‐wave conversion ✦ Modeling of intrinsic attenuation; separately model
intrinsic vs. scattering “Q”. Homepage: http://rainbow.phys.uconn.edu/geophysics/wiki/
CONCLUSIONS
✦ Radiative transport is a computationally efficient method of synthesizing the very high frequency (>2.0 Hz) seismic wave field where differences between explosion and earthquake sources are largest.
✦ By incorporating both known large-‐scale and unknown small-‐scale 3-‐D structure, radiative transport can be used to predict the behavior of ratios of regional phases along specific paths, the homogenization of source radiation patterns with range, and uncertainties in travel-‐time picks.
Future Work: ✦ Completion of planned Radiative3D features, including
incorporation of intrinsic attenuation, spatial gradients in velocity, and anisotropy of heterogeneity scale lengths.
✦ Use of Radiative3D to model chosen paths for refinement of attenuation and scattering models in regions of interest.
Radiative transport is a physical modeling technique that tracks energy transport as a particle flux, using ray tracing to solve for the trajectories of millions of particles representing small quanta of elastic energy. RT is a suitable alternative to solving the full wave equation when ray theory criteria are met, and is particularly advantageous for high frequency modeling. Another advantage of radiative transport is that scattering from small-‐scale heterogeneity can be handled statistically, rather than requiring ultra-‐fine model meshes which would otherwise be needed to simulate the heterogeneity deterministically.
SOUTHERN XINJIANG: MARCH 13, 2003
DEPTH STUDY MATCH QUALITY
SCATTERING MODEL
Scattering Amplitudes:
• Scattering is treated as a stochastic process occurring on a mean-free path basis, with deflection angle and conversions determined by probability distributions:
gPP (⌅, ⇥) =l4
4⇤
��XPPr (⌅, ⇥)
��2 P✓2l
�0sin
⌅
2
◆
gPS(⌅, ⇥) =
1
�0
l4
4⇤
��XPS� (⌅, ⇥)
��2 P✓
l
�0
q1 + �2
0 � 2�0 cos⌅
◆
gSP(⌅, ⇥) = �0
l4
4⇤
��XSPr (⌅, ⇥)
��2 P✓
l
�0
q1 + �2
0 � 2�0 cos⌅
◆
gSS(⇤, �) =l4
4⇥
⇣��XSS⇥ (⇤, �)
��2 +��XSS
� (⇤, �)��2⌘P
✓2l sin
⇤
2
◆
von Kármán Spectrum:
• Inhomogeneities exist at a range of scale lengths.
• Corner frequency determined by a.
• Rapid fall-off after 1/a, determined by kappa.
• Power spectrum affects scattering deflection angle and P/S conversion.
κ = 1.0 0.5 0.3
Dependence on Parameters:
Above: affect of scattering parameters on two scattering characteristics: mean free path, or average distance between scattering events, and dipole projection, which is a measure of scattering directionality (positive values indicate dominant forward scattering, negative indicates dominant back-‐scattering.) Below left: von Kármán spectrum for various kappa values on a log-‐log scale. Below right: illustration of a random walk, with scattering events deflecting phonon paths from origination at source to collection at receiver. Bottom: simulated perturbation fields for various kappa values (scale-‐length a held fixed). Characterizing Media:
• Material heterogeneity treated as perturbation against locally-uniform velocity and density background
• Four parameters describing Scattering Media:
• eps: average fractional velocity perturbation size (dV/V0)
• nu: ratio of density-perturbation to velocity-perturbation
• a: scale length, or auto-correlation “corner”
• kappa: von Kármán parameter
WAVEFRONT EVOLUTION
We focused our attention on the March 13, 2003, mb 4.8 Southern Xinjiang earthquake that occurred near Chinese nuclear test site Lop Nor. This earthquake is an interesting test case for source discrimination efforts. Selby, et al, 2005 published a strike, dip, and rake solution for this event which we used for source modeling in our study.
Strike: 125° ± 10° Dip: 40° ± 10° Rake: 90° ± 10° Depth: 33 km
We sought to model this event using Radiative3D, and conducted simulation runs at 2.0 Hz and 3.0 Hz (presented panels right). For comparison, shown below are band-‐passed recordings of this event from station MAK (below left), and also (below right) are recordings in the same frequency bands from an explosion signal recorded at MAK from the July 29, 1996 nuclear test at Lop Nor (mb 4.9):
Seismic envelope synthetics were produced using Radiative3D with a hypothesized Earth model serving as a simplified representation of the Lop Nor region. The model was constructed of layers of uniform velocity, with interface planes separating the layers. Current functionality in Radiative3D allows these interface planes to take on arbitrary orientation. Depth profiles from CRUST2.0 and elevations and Moho depths from ETOPO and Cornell Moho at three locations (Lop Nor, MAK, and WUS) were used to locate and orient the planes. Model cross-‐sections with depth profiles between LOP and MAK and LOP and WUS, along with a table of scattering parameters and quality factors (“Q”) used, are shown below.
nu eps a (km) kappa QSediment Layer: 0.8 0.01 0.25 0.2 50
Crust Layers: 0.8 0.04 0.20 0.3 1000
Mantle Layers: 0.8 0.008 0.20 0.5 150
2.0 Hz
3.0 Hz
4.0 Hz
Earthquake
2.0 Hz
3.0 Hz
4.0 Hz
Explosion
Scattering parameters by depth region:
FREQUENCY AND STATION COMPARISONThe travel-‐time curves each combine output from 160 virtual seismometers positioned in a linear array from source location to seismic stations MAK and WUS. Below are envelope traces from the last in each array, the one at the station location. These can be compared with real data collected from those stations (comparisons shown panel below).
The envelopes (above) and travel-‐time curves (left) were produced from synthetic data computed in parallel on mixed hardware non-‐dedicated workstations, and comprise trajectory computations for 4.8 billion phonons (2.4B each for 2Hz, 3Hz runs). The synthetic runs utilized in total 138 cpu-‐hours (2Hz run) and 217 cpu-‐hours (3Hz run).
2.0 Hz
3.0 Hz
MAK WUS
MAK WUS
2.0 Hz
3.0 Hz
Synthetics were generated in our Lop Nor model for a source event patterned after the 2003-‐03-‐13 earthquake. Source depth was set to 32 km, as reported by the NEIC. Shown here are travel-‐time curves (left) and envelopes (right) for stations MAK and WUS at frequencies of 2.0 Hz and 3.0 Hz. Crustal body wave phases Pg and Lg are visible in the travel-‐time plots. Scalloping is most likely due to path multiples from surface and Moho reflections. Differences between MAK and WUS are primarily due to source orientation.
MAK WUS
2.0 Hz
3.0 Hz
3.0 Hz
WUS
2.0 Hz
MAK
Pg
Lg
Selby, et al, 2005 note that regional surface wave analysis suggests a source depth of 6±1 km, in contrast to the 33 km depth published by the USGS’s National Earthquake Information Center (NEIC). This motivated us to investigate the effects of source depth on our synthetics. Below are travel-‐time curves at 2.0 Hz produced using Radiative3D along the azimuth to station MAK for earthquake and explosion sources at a variety of depths. In particular, we modeled the 2003-‐03-‐13 earthquake at depths of 6 km and 32 km, and we modeled a pure isotropic explosion source at 2 km and 6 km depth. Comparisons to real data appear in the panel at right.
Earthquake
Explosion
dept
h = 2.0 km
dept
h = 32
.0 km
dept
h = 6.0 km
Explosion
dept
h = 6.0 km
Earthquake
Explosion, 2.0 km
Explosion, 6.0 km
2.0 Hz
Depth: 6 km
3.0 Hz
Depth: 6 km
2.0 Hz
Depth: 32 km
3.0 Hz
Depth: 32 km
Above: 2.0 Hz and 3.0 Hz comparisons modeling earthquake source depth at 6.0 km. Below: source depth modeled at 32.0 km. The 2.0 Hz synthetics compare much more favorably than the 3.0 Hz. At 2.0 Hz, numerous qualitative features are well matched at both depths. The 6.0 km comparison matches particularly well, exclusive of a time shift. Note that certain phases, including Pn and Sn, would not appear in our synthetics due to Moho/upper-‐mantle velocity gradients not represented in our current Lop Nor model, but are expected to appear with future model refinements.
Shown below are comparisons between our synthetic envelopes (blue) and data recorded at station MAK (tan). The MAK data was band-‐pass filtered and enveloped to facilitate comparison to our single-‐frequency synthetics. Note that each plot is mirrored across the x-‐axis, but that the z-‐order of the plots are reversed, to facilitate visual comparison between the synthetic and the recorded data series.
Synthetic envelope and travel-‐time curves are computationally intensive due to the large number of phonons that must be cast in order to catch a sufficient number at the virtual seismometer locations. Wavefront plots, however, such as those shown below, can be produced in substantially less time, since every phonon is useable. The plots below show phonon propagation through Earth models and show how the wave fronts evolve with time. Left: elevation view of earthquake and explosion sources in a simplified prototype model. Right: plan view of earthquake source in Lop Nor model. Red markers represent P phonons and blue markers represent S phonons. Interface reflections, ray-‐bending, and coda development through scattering are all visible. Transitions between P and S polarization can happen via scattering or reflection/transmission. Movies of energy propagation can be produced in about 20 minutes of computation time.Earthquake Time-Series:
Explosion Time-Series:
T=10.8
T=15.1T=7.0T=3.7T=0.8
T=10.8
T=15.1T=7.0T=3.7T=0.8
Earthquake Time-Series:
Explosion Time-Series:
T=10.8
T=15.1T=7.0T=3.7T=0.8
T=10.8
T=15.1T=7.0T=3.7T=0.8
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