Radiative Transport Modeling of High Frequency Regional Seismograms for Event Discrimination
Christopher J. Sanborn, Steven Walsh, Michele Fitzpatrick, and Vernon F. Cormier Physics Department, University of Connecticut, Storrs
REFERENCES
(1) C. J. Sanborn, et al., Radiative3Dhttp://rainbow.phys.uconn.edu/geowiki/Radiative3D
(2) Cao, S., and K. J. Muirhead (1993). Finite difference modelling of Lg blockage, Geophys. J. Int.
(3) Zhang, T. R., and T. Lay (1995). Why the Lg phase does not traverse oceanic crust, B.S.S.A.
(4) Mendi, C. D., B. O. Ruud, and E. S. Husebye (1997). The North Sea Lg-‐blockage puzzle, Geophys. J. Int.
(5) Sato, H., M. C. Fehler, and T. Maeda (2012). Seismic wave propagation and scattering in the heterogeneous earth (2nd Ed.), Springer.
(6) Ballard, S., J. Hipp, A. Encarnacao, C. Young, and B. Kraus (2012). A Generalized Earth Model Software Utility (GeoTess).
ABSTRACT RADIATIVE TRANSPORT
The 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 Earth's crust. Larger-‐scale deterministic structure (greater than a wavelength) still assumes major control over the efficiency or blockage of the Lg and the efficiency of other regional phases. We model high frequency regional seismic wave codas (2-‐4 Hz) for the combined effects of the large-‐scale 3-‐D (deterministic) and the small scale (statistical) structure with a radiative transport algorithm. The algorithm propagates packets of body wave energy with ray theory through a large-‐scale deterministic 3-‐D structure, and includes the effects of multiple scattering by small-‐scale statistical structure. Coda envelopes are synthesized to illustrate sensitivities to variations in the parameters describing small-‐scale statistical heterogeneity, intrinsic attenuation, Lg blockage due to large-‐scale variations in crustal thickness, and the effects of tectonic release estimated from the seismograms of nuclear tests. We predict that event discriminants based on P/Lg amplitude ratios will best separate earthquake and explosion populations at frequencies 2 Hz and higher. 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 [1]
FUNDED BY: AFRL Contract No. FA9453-‐15-‐C-‐0069, July 1, 2015 through June 30, 2018Address correspondence to: [email protected] or [email protected]
Radiative3D is a free and open source radiative transport code for synthetics generation in 3D Earth models with complex deterministic and statistical structure. Features include:
Simulates earthquake and explosion radiation patterns, parameterized via moment-‐tensor elements Radiative transport well-‐suited to high-‐frequency synthetics Complex 3D model structure via tetrahedral grid; planned support for GeoTess model format.[6] Produces 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/geowiki/Radiative3D
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: Code validation: test predictions of Radiative3D against those from numerical syntheses in 3D structure. 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.
SIMULATIONS IN CRUSTAL PINCH/BULGE MODELS [2],[3],[4]
HETEROGENEITY AND SCATTERING MODEL [5]
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
PINCH AND BULGE STRUCTURES
HETEROGENEITY SPECTRUM AND CODA PRODUCTION
Pinch with Basin Pinch without Basin Crust BulgeFlat Crust
Four test cases: (a) Flat crust, (b) crust pinch with sedimentary overlay and mantle upwelling, (c) crust pinch without sedimentary overlay, and (d) crust bulge protruding into mantle.
Travel time curves (above) illustrate disruption of Lg and Pg energy in each pinch/bulge scenario.
Energy curves (right) give insight into effects of structure. These show time-‐integrated energy as a function of distance for each test case.
Pinch with sedimentary basin (case b) was associated with the greatest energy reduction at long range (950 km).
Bulge structure was associated with negligible energy reduction at 950 km range.
Pinch structures were associated with local amplification of energy signal in the pinched region. Bulge structure was associated with local attenuation.
PINCH VS. SCATTERING EFFECTS ON LG
Four test cases: (a) Flat crust, (b) crust pinch with sedimentary overlay and mantel upwelling, (c) flat crust with anomalous high scattering in localized region (d) crust pinch and high-‐scattering in pinch region.
Lg effects were isolated through use of strike-‐slip focal mechanism and choice of Lg-‐favoring azimuth for seismometer array.
Travel time curves illustrate disruption of Lg energy in each scenario:
Each test case (b, c, and d) was associated with a reduction of energy at long range compared to baseline test case (a).
Scattering structure (case c) results in substantial attenuation but does not visibly disrupt the envelope shape beyond the scattering region.
Pinch structure (case b) attenuates and disrupts the envelope shape beyond the pinch region.
Scattering structure (case c) results in visible back-‐scatter in travel time curve (c).
Both pinch and scatter structures were associated with local amplification of energy signal in the variation region, followed (in cases b and d) by a correction at the end of the region.
Travel time curves: Color density indicates energy amplitude (square-‐root of energy) as a fraction of a distance-‐dependent reference curve determined by a power-‐law fit to the baseline (non-‐pinched, non-‐scattering) test case. Reference curve (dashed line) and time-‐integrated energy (solid line) are shown as overlay plots, along with related statistics, on a 4th-‐root scale to accommodate compressed vertical space. (Energy curves are shown in greater detail on a logarithmic scale in the Energy Comparison figure at right.) Crust variation region is outlined by dashed vertical demarcation lines. Major regional phase velocities are indicated via velocity slope lines.
Energy curves: Each series represents time-‐integrated energy collected at a surface seismometer as a function of distance from source event for a given test condition. The series identified as “baseline” is the flat-‐crust, non-‐scattering condition (case a). The dashed line series is a power-‐law fit to the baseline condition that serves as a color-‐density reference for the travel time curves. The distance range encompassing the crust variation region is demarcated by vertical dashed lines.
Non-‐Pinched + Scattering Pinched + Scattering
PinchedNon-‐Pinched
Non
-‐Sca
ttering
High Sc
atter Z
one
(a) (b)
(d)(c)
Varying heterogeneity parameters in simple layered Earth models illustrates competing effects of mean free path and dipole projection measures on coda production from multiple scattering.
E.g. corner scale a: (figure panel right) – Increasing a decreases mean free path, thereby increasing rate of scatter events.
Increasing rate of scatter events generally increases coda production. However, increasing a also increases scattering amplitude in the forward-‐scattering direction, as indicated by increased dipole projection measure. (See “Dependence on Parameters,” panel above.)
This means each individual scatter event is less deflectionary, reducing the cumulative effect of multiple scattering on phonon trajectory, and reducing coda production.
This results in a “sweet spot” at which coda production is maximized. Sweet spot will occur in the neighborhood of a ≈ λ, where λ is the wavelength.
“Short”(a = 0.1 km)
“Long”(a = 12 km)
“Just Right”(a = 1.0 km)
Long
er Co
rner S
cale a Sh
orter
t = 27 sec. t = 56 sec. t = 83 sec. t = 114 sec. t = 129 sec. t = 195 sec.
Using Radiative3D, we simulated crust pinch, crust bulge, and enhanced heterogeneity structures in a 3D simplified crust and upper mantle model consisting of a low-‐velocity sediments layer, a crust layer, a high-‐gradient Moho transition layer, and upper mantle structure based on AK-‐135.
Crust variation zone, 100 km wide, defined between distance ranges 370 km to 470 km from source event. (Tapering for pinch/bulge structures begins at 310 km and normal thickness resumes at 530 km.)
Variation zone is either: a pinch or bulge in the crust layer, a zone of anomalously high heterogeneity (scattering region), or both.
Model layers follow Earth-‐like curvature, and include intrinsic attenuation and mild background heterogeneity.
Source event is chosen as a vertical strike-‐slip focal mechanism in order to isolate Lg and Pg effects through azimuth selection of seismometer array.
Simulations for a given model setup, source type, and frequency produce three-‐component envelopes at each seismometer location, and travel time curves for each array.
50-‐Million phonons per run. Approx. 2–4 hours execution time, single-‐threaded, on Intel Core i7 desktop workstation per run.
Crust Pinch Model: (Profile View)
Earthquake Time-‐Series:
Pg
Lg
Pg
Lg
Map View and Source Mechanism:
Pinch/Bulge Model: The test model is fan-‐shaped, azimuthally symmetric, and follows Earth curvature. The pinch, bulge, or high-‐scattering region is shown as a shaded, arc-‐shaped band. Source location is indicated by the red dot. Seismometer placement, gather area, and orientation (RTZ) is indicated by the green disc arrays.
The time series below shows phonon propagation through a crust pinch Earth model and illustrates how wave fronts evolve with time. Red markers represent P-‐phonons and blue markers represent S-‐phonons.
Modeling Approach:
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