FROM ONE BOUNDARY TO A WHOLE IMAGE
Seismic waves and imaging, from rock boundaries to tomography
A P wave that reaches a rock boundary at 40 degrees can send more than half of its energy onward as S waves. Seismologists use such conversions, arrival times and whole waveforms to locate earthquakes and map rock they cannot see. Learn the rules that set the angles and amplitudes, locate a quake and test its error ellipse, invert ray delays into a map and read what is resolved, then fit waveforms with the adjoint method and see why they need low frequencies first.
Waves and sources · Chapters 1–5
What a boundary does to a wave, and where a quake began
Derive the P and S speeds, bend rays with Snell’s law, split a P wave into four at a boundary, then locate an earthquake from arrival times and test how far its error ellipse can be trusted.
Start with the two wave speeds →Imaging the rock · Chapters 6–8
Tomography, waveform inversion and their limits
Turn ray delays into a map and read its resolution matrix, fit whole waveforms with an adjoint gradient and see cycle skipping, then read a published study of resolution tests yourself.
Start with tomography →Eight chapters, with examples and experiments
01 L1
Why a solid rock carries two kinds of seismic wave
Why does an earthquake send out two body waves at two different speeds, and what sets each speed?
Read and try →02 L1
Snell’s law and the critical angle for seismic waves
Which way does a seismic ray bend at a rock boundary, and when does a transmitted wave stop going through?
Read and try →03 L2
How a P wave shares its energy at a rock boundary
When a P wave hits a boundary between two rocks, how much of its energy goes into each outgoing wave?
Read and try →04 L2
Locating an earthquake from P and S arrival times
How do a few stations that only record arrival times find where and when an earthquake started?
Read and try →05 L2
Error ellipses for earthquake locations, and what they leave out
How big is the uncertainty of an earthquake location, and when can the error ellipse be trusted?
Read and try →06 L2
Travel-time tomography and what the resolution matrix shows
How do many ray travel times become a map of fast and slow rock, and which parts of that map can be believed?
Read and try →07 L3
Adjoint gradients and cycle skipping in waveform inversion
How can thousands of rock speeds be fitted to recorded waveforms, and why does the fit sometimes converge to a wrong model?
Read and try →08 L4
Reading Rawlinson and Spakman (2016) on resolution tests in seismic tomography
How should I read a checkerboard or spike test in a tomography paper, and what does Rawlinson and Spakman’s analysis say it can and cannot show?
Read and try →