Three earthquakes mark the dip of a subducting slab beneath a volcanic arc; all three…
PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · Seismology, tectonics and geodynamics · Seismology, tectonics and geodynamics
The Solid Earth, Ch Surface waves, free oscillations and seismic tomography
Problem
Three earthquakes mark the dip of a subducting slab beneath a volcanic arc; all three are recorded on the same coastal station. Ray tracing through the reference model of chapter 5 gives, for each earthquake, the path length of the ray inside the slab (cell S) and inside the surrounding mantle wedge (cell W), and the travel-time residual actually measured relative to that reference model. Data: earthquake 1 (deep) has LS=250km, LW=50km and δt=−2.78s; earthquake 2 (mid-depth) has LS=120km, LW=180km and δt=−1.33s; earthquake 3 (shallow) has LS=30km, LW=270km and δt=−0.33s. The reference shear speed at these depths is v=4.5kms−1.
((a)) Explain, in terms of Fermat's principle, why the path lengths LS and LW used to build G may be taken from rays traced through the reference model, even though the true slab is not part of that model.
((b)) Assemble the 3×2 matrix G (columns: cell S, cell W; entries in km) and write the linear system d=Gm for the three residuals.
((c)) Solve the damped normal equations with ϵ2=1000km2 for m^=(m^S,m^W), and hence find the fractional shear-speed anomaly δvS/vS in the slab cell.
((d)) Using the quoted sensitivity ∂lnvS/∂T≈−10−4K−1, convert this anomaly into a temperature contrast δT for the slab relative to the reference mantle, and say whether the sign is physically reasonable for a subducting slab.
((e)) A second station records three more earthquakes whose rays all pass through the wedge cell only, never through the slab. Would adding these rays to the inversion improve how well the slab cell S is resolved? Give a reason.