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Journal Club17/03/2015
Uncertainty loops in travel-time tomography from nonlinear wave
physics.Erica Galetti et al.
Phys. Rev. Lett., 114, 145801 (2015) Published April 10th.
Abstract
Relevant topics:• Seismic waves;• Seismic interferometry;• Data fit and tomographic models.
Seismic Waves
• Body Waves:– Travels inside Earth;– Two types:
• Primary or P- waves: Longitudinal, the fastest, go through all kind of material;
• Secondary or S- waves: Transversal, 60% P-waves speed, can´t go through fluids;
• Surface Waves:– Travels on surface; slower than body waves;– Three main types:
• Rayleigh waves: ripples, 90% of S-waves speed;• Love waves;• Stoneley waves;
Love Waves
Augustus Edward Love (1863-1940)
• Sedleian professor – Queen´s college, Oxford.• Theory of Elasticity;• Prediction: 1911
• Polarized surface waves: interference of S-waves, confined;
• Horizontal shifting;– Decay as .– Travel around earth several times before dissipating after
the event.– The most destructive waves around earthquake epicenter.
Seismic interferometry• Reconstruction of subsurface reflection response;
– Green´s function.
• Crosscorrelation/convolution/deconvolution of two seismic traces;– Natural traces: earthquake data, seismic noise;– Artificial traces: dynamite;– Procedures: Inter-receiver, inter-source, source-receiver;
Procedure• Crosscorrelation of horizontal components of all pairs of
seismometers across UK– 2001-2003, 2006-2007, and 2010
• Estimation of Love-wave components of Green´s function: inter-source interferometry.
• Seismometer• Ray paths • Frequency-time analysis to
measure time-travel between seismometers.
• Nonlinear stochastic tomographic method (RJMCMC) to obtain group velocity and standard deviation.
RJMCMC• Reversible-Jump Markov chain Monte Carlo algorithm.• Generate a series of velocity models: ensemble.• Estimate data uncertainties if unavailable.
m=m’m=m
Main result
Standard deviation map using linearized tomography
Standard deviation map using author´s approach
Loops!
Mean velocity of Love waves (T=10 s)
160 000 velocity model samples
Origin of loops(a) Fixed shape and size, increasing velocity.
(b) Changing both, size and velocity.
(c) Changing shape
Uncertainty map: standard deviation across all models in green box
Inverse problem (tomography)• For any measured travel time, a similar set of plots exist.• Any travel time
– only constrains the maximum velocity of a circumnavigable low velocity anomaly
– Only constrains the anomaly´s boundary (geometrical).
• Around low velocity anomalies...
Upperbounded Velocity Inside High velocity uncertainty at the borders
Summary
• Uncertainty Loops – Appear to exhibit finer spatial detail;– Thickness depends on the geometry of available
seismometer arrays.
• First “observation”– Only dominate when both model parameterization and ray
paths are allowed to vary freely avoiding linearization.– New vision about using ray paths for tomography.