Questions: Seismic Velocity-Density-Composition Relationships

Question 1

A seismic tomography model reveals a region of anomalously low P-wave velocity in the upper mantle. What geological interpretation is most consistent with this observation?

• A. The region contains unusually dense, cold material — consistent with a subducting oceanic slab
• B. The region likely contains elevated temperature, partial melt, or less dense material — consistent with a mantle plume or asthenospheric upwelling
• C. Low velocity must indicate a compositional boundary where granitic crust extends unusually deep into the mantle
• D. Velocity anomalies in the mantle cannot be interpreted geologically without direct sampling

Answer: (B)

Seismic velocity decreases when elastic moduli decrease or density decreases relative to the surrounding material. Elevated temperature reduces elastic moduli, and partial melt reduces both moduli and effective density — both lower velocity. Mantle plumes and asthenospheric upwellings are warmer and may contain small fractions of melt, producing the observed low-velocity anomaly. Conversely, cold, dense subducting slabs produce high-velocity anomalies. This velocity-temperature-composition relationship is what makes seismic tomography a tool for imaging mantle dynamics.

Question 2

Birch's law predicts that P-wave velocity increases linearly with density for rocks of similar mean atomic weight. What is the practical implication when a seismic model shows Vp = 7.0 km/s in the lower crust?

• A. The rock type is uniquely determined as mafic granulite — no other crustal rock has exactly this velocity
• B. Without additional density information (e.g., from gravity data), multiple rock types are consistent with this velocity, and composition cannot be uniquely determined
• C. The velocity exceeds typical crustal values, indicating the model must contain errors
• D. Birch's law applies only to mantle rocks, so this velocity cannot be interpreted for crustal material

Answer: (B)

Birch's law shows that rocks of different mean atomic weight (iron content, for instance) fall on different Vp-density lines. A measured Vp = 7.0 km/s could correspond to gabbro, mafic granulite, or eclogite — these have similar velocities but different densities and compositions. Adding an independent density estimate from gravity data, and plotting the (Vp, ρ) pair on a Birch's law diagram, significantly narrows the possibilities. Velocity alone is ambiguous; velocity plus density is much more diagnostic. This is why gravity-seismic joint interpretation is standard practice.

Question 3

According to Birch's law, measuring P-wave velocity alone is sufficient to uniquely identify the rock type and composition at depth.

• T. True
• F. False

Answer: False

Birch's law plots Vp against density for different rock types, showing that rocks of similar mean atomic weight fall along the same line but rocks of different compositions occupy different lines. This means the same velocity can correspond to different rock types if they have different densities. For example, Vp = 7.0 km/s is consistent with gabbro, granulite, or eclogite depending on the density. Velocity alone is therefore ambiguous for compositional interpretation. Combining velocity with an independent density estimate (from gravity data or mineral physics) dramatically reduces this ambiguity, which is why Birch's law is used in joint seismic-gravity interpretation rather than seismic interpretation alone.

Question 4

Abrupt seismic velocity jumps like the Mohorovičić discontinuity are interpreted as compositional boundaries rather than simple effects of increasing pressure.

• T. True
• F. False

Answer: True

Pressure and temperature both affect seismic velocity, but their effects are gradual with depth. If the Moho were purely a pressure effect, velocity would increase smoothly. Instead, the Moho shows a sharp jump from ~7 km/s to ~8 km/s over a narrow depth range — far too rapid to be a pressure-induced gradual change. This abrupt change is consistent with a compositional transition from felsic/mafic crustal rocks to olivine-dominated peridotite mantle. Other sharp discontinuities at 410 km and 660 km depth are interpreted as phase transitions (minerals changing crystal structure under pressure), also distinguishable from gradual pressure effects by their abruptness.

Question 5

Explain why seismic tomography images would be geologically meaningless without empirical velocity-density-composition relationships like Birch's law. What information do these relationships add?

Model answer: Seismic tomography produces images of where P- or S-wave velocities are relatively fast or slow compared to a reference model. Without empirical relationships connecting velocity to rock type, temperature, and density, these images show only patterns of wave speed — they are physically real but geologically uninterpretable. Birch's law and laboratory measurements at controlled pressure and temperature provide the translation key: a low-velocity anomaly becomes 'warm mantle or partial melt,' a high-velocity anomaly becomes 'cold, dense subducting slab.' Adding gravity data constrains density independently, and combining the two with Birch's law allows joint inversion that further constrains composition. Without these relationships, tomography would be like seeing different shades of gray in an X-ray with no knowledge of which shades correspond to bone, tissue, or air. The empirical relationships convert abstract wave-speed patterns into actual geology.

This connects to a broader principle in geophysics: observations are always indirect, and interpretation requires a physical model linking the observation to the quantity of interest. Seismology measures travel times; mineral physics provides the velocity-composition link; the combination produces geological insight. Birch's law is one of the most important of these linking relationships, and its empirical robustness across decades of laboratory measurements is what makes quantitative interpretation of Earth's interior possible.