Journal Club 17/03/2015 Uncertainty loops in travel-time tomography from nonlinear wave physics. Erica Galetti et al. Phys. Rev. Lett., 114, (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 ( ) Sedleian professor – Queen´s college, Oxford. Theory of Elasticity; Prediction: 1911

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 – , , 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) 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.