A focal mechanism beach ball diagram has two nodal planes. What do these two planes represent?
AThe fault plane and the Earth's surface
BThe fault plane and the mathematically equivalent auxiliary plane — seismic data alone cannot distinguish which is which
CThe two conjugate fault planes that both ruptured during the earthquake
DThe horizontal and vertical projections of the fault
The P-wave radiation pattern from a double-couple source is symmetric: two orthogonal nodal planes produce identical first-motion patterns. One is the actual fault plane; the other is the auxiliary (conjugate) plane that is a mathematical artifact of the double-couple model. Seismic waveforms alone cannot distinguish between them — additional geological or geodetic information (e.g., the orientation of a known fault, surface rupture, or aftershock distribution) is needed to identify the true fault plane.
Question 2 True / False
On a beach ball diagram, the black (compressional) quadrants directly indicate the regions of Earth's surface where the fault ruptured.
TTrue
FFalse
Answer: False
The black and white quadrants indicate the P-wave first-motion pattern at seismometers around the globe, not the geographic location of fault rupture. Black (compressional) quadrants show the directions from which seismometers recorded an initial upward ground motion (compression); white (dilatational) quadrants show initial downward motion. The pattern encodes the geometry of faulting (strike, dip, rake), not fault location.
Question 3 Short Answer
The stress tensor at a point in the crust has three principal stress axes (σ₁ ≥ σ₂ ≥ σ₃). In a normal faulting regime, how are these axes typically oriented, and which one drives the fault slip?
Think about your answer, then reveal below.
Model answer: In a normal faulting regime, σ₁ (maximum compressive stress) is vertical, σ₂ is horizontal intermediate, and σ₃ (minimum, or least compressive) is horizontal. Gravity drives the overburden down, making the vertical stress maximum. The crust extends horizontally, and faults dip steeply, allowing the hanging wall to slide down under gravity. σ₁ being vertical is the defining characteristic of an extensional (normal faulting) stress regime.
Anderson's theory of faulting relates the three fault types to the orientation of principal stresses relative to Earth's surface. Normal faulting: σ₁ vertical. Reverse/thrust faulting: σ₃ vertical (horizontal compression dominates). Strike-slip faulting: σ₂ vertical. Eigenvalues of the stress tensor give the magnitudes of the three principal stresses; eigenvectors give their orientations — which is why eigenvalue decomposition is the core mathematical tool.