A moment tensor solution for a seismic event shows that all three diagonal components are large and equal, with near-zero off-diagonal elements. What does this indicate about the source?
AA pure strike-slip fault, because all principal stresses are equal
BA pure thrust fault, because the equal diagonal components indicate horizontal compression
CA volumetric (isotropic) source such as a volcanic explosion or implosion, not a fault slip
DA double-couple source with M₀ = the diagonal value
A pure double-couple (fault slip) produces eigenvalues of +M₀, 0, −M₀ — not equal values. Equal and same-sign diagonal components of the moment tensor represent isotropic expansion (or contraction) — volume change in all directions. This is the signature of a volcanic explosion, a collapsing magma chamber, or an underground explosion. The moment tensor framework is valuable precisely because it can detect these non-fault sources that the traditional focal mechanism (which assumes double-couple) cannot represent.
Question 2 Multiple Choice
Why must moment tensor inversion use recordings from seismic stations distributed at many different azimuths around the earthquake, rather than a cluster of stations all in one direction?
ADistant stations record fewer noise artifacts and produce cleaner waveforms
BThe moment tensor has six independent components, and each station constrains a different linear combination of them — poor azimuthal coverage leaves some components underdetermined
CSeismic waves travel faster in certain directions and need multiple stations to average out the velocity variation
DRegulations require station coverage for legal attribution of fault responsibility
Each observed seismogram at a given station is a linear combination of the six moment tensor components, weighted by the Green's functions for that particular source-station geometry. Different azimuths sample different combinations of these components. If all stations are in the same direction, many combinations are not independently sampled, and several components remain poorly constrained — the inversion is underdetermined. Good azimuthal coverage is essential for resolving all six components simultaneously.
Question 3 True / False
For a pure double-couple earthquake source, the three eigenvalues of the seismic moment tensor are +M₀, 0, and −M₀, where M₀ is the scalar seismic moment.
TTrue
FFalse
Answer: True
This eigenvalue structure is the mathematical signature of a double-couple: two equal and opposite principal moments with a null axis. It reflects the force-couple geometry of shear faulting — equal amounts of compression and tension at 45° to the fault, with a null axis perpendicular to the fault plane. When a moment tensor is decomposed and the null eigenvalue is exactly zero, the source is consistent with pure fault slip. Non-zero null eigenvalues indicate CLVD or isotropic components, signaling a more complex source.
Question 4 True / False
Moment tensor inversion determines which of the two nodal planes is the actual fault plane, because the seismic radiation pattern differs between the fault plane and the auxiliary plane.
TTrue
FFalse
Answer: False
This is a fundamental limitation of the moment tensor: the seismic radiation pattern from a pure double-couple is identical whether you treat either nodal plane as the fault. The moment tensor cannot distinguish the true fault plane from the auxiliary plane on the basis of far-field seismic data alone. Resolving this ambiguity requires additional information: surface rupture observations, aftershock distribution along one of the planes, geological context, or local geodetic data (GPS, InSAR). This is one reason why moment tensor solutions always report two possible nodal planes.
Question 5 Short Answer
What are Green's functions in the context of moment tensor inversion, and why does the accuracy of the Earth velocity model affect the quality of the moment tensor solution?
Think about your answer, then reveal below.
Model answer: Green's functions are the theoretical seismograms that would be recorded at each station if a single elementary force couple (one of the six basis force systems) acted at the source location. They encode how seismic waves travel through the Earth's crust from that source to each recording station. In moment tensor inversion, the observed waveforms are modeled as weighted sums of these Green's functions, and the weights — the six moment tensor components — are solved by least-squares. If the velocity model used to compute the Green's functions is inaccurate, the predicted wave arrival times and amplitudes will not match the observed waveforms well, and the inversion will distribute the mismatch into incorrect moment tensor components. Better velocity models produce more accurate Green's functions and therefore more reliable moment tensor solutions.
This is why moment tensor inversions for small earthquakes (where local velocity structure matters most) are harder than for large events (where long-period waves average over larger volumes and are less sensitive to local heterogeneity). Global agencies use long-period waveforms partly to reduce sensitivity to imperfect velocity models.