Two published tomographic images report the same shear-speed anomaly, (slow)
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
Two published tomographic images report the same shear-speed anomaly, δvS/vS=−2% (slow), at the same depth beneath a subduction zone: region A, directly beneath the volcanic arc where many rays cross, and region B, in a gap between stations where few rays cross. A checkerboard resolution test, run alongside each image using the same rays and damping as the real inversion, recovers 90% of an input anomaly's amplitude at region A (RAA=0.90) but only 15% of it at region B (RBB=0.15). A geologist argues: "Both regions show the same −2% anomaly, so both are about 200K hotter than the reference mantle, and we should trust both features equally."
((a)) Check the arithmetic behind the 200K figure, using ∂lnvS/∂T≈−10−4K−1.
((b)) The resolution matrix relates the recovered image to the true model by m^≈Rmtrue (ignoring leakage from neighbouring cells). Using this, estimate the true anomaly, and the temperature contrast it would imply, that would have to be present at each of A and B to produce the observed −2% image.
((c)) Say which of the two features is safe to interpret at face value and which is not, and why.