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.