Question 1 of 10: Density — Values, Gravity Contrast, and Seismic Velocity/Reflectivity

Question 1: Density — Values, Gravity Contrast, and Seismic Velocity/Reflectivity (16.66% of paper)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Density (ρ) is one of the few physical properties in geophysics that a geophysicist can rarely measure directly at depth — it must almost always be inferred indirectly, through gravity or through seismic velocity, which is exactly why understanding both connections matters.

Typical values. Loose, unconsolidated sediments (sand, gravel, till) run roughly 1.6–2.0 g/cm³; sedimentary rocks span about 2.0–2.7 g/cm³ (shale ≈ 2.2–2.6, sandstone ≈ 2.0–2.6, limestone ≈ 2.3–2.7); crystalline igneous/metamorphic rocks run higher, granite ≈ 2.6–2.7, gabbro/basalt ≈ 2.7–3.1, gneiss ≈ 2.6–2.9; ore minerals are often much denser — galena ≈ 7.5, pyrite ≈ 5.0, magnetite ≈ 5.2 g/cm³ — while engineering fill, peat and organic soils can sit below 1.5 g/cm³. Water is 1.0 g/cm³ and air effectively 0, so porosity and saturation state (an unfilled void, water-filled void, or air-filled void space) are often the single largest control on a rock's bulk density in near-surface engineering settings.

Gravity and density contrast. The gravity method measures small perturbations in the Earth's gravitational field caused by lateral variations in subsurface density; a body produces an anomaly only in proportion to Δρ (its density contrast with the surrounding host), not its absolute density. A positive density contrast (target denser than host) produces a positive gravity anomaly — e.g. a massive sulphide ore body (ρ≈4.5) in granitic host rock (ρ≈2.65), or a buried basalt flow in sediments. A negative contrast produces a gravity low — e.g. a karst cavity or abandoned mine void (air- or water-filled, ρ≈0–1.0) in limestone (ρ≈2.6), a salt dome (ρ≈2.2) rising through denser clastic sediments (ρ≈2.5–2.6), or a buried waste trench (loosely backfilled soil) in undisturbed till. Locating a tunnel void or a salt structure is therefore a direct gravity-low target, while locating massive sulphides is a gravity-high target.

Seismic velocity. P- and S-wave velocities depend on both the elastic moduli and the density of the medium through the standard elastic-wave relations:

$$V_P=\sqrt{\dfrac{K+\tfrac{4}{3}\mu}{\rho}},\qquad V_S=\sqrt{\dfrac{\mu}{\rho}}$$

where $K$ is the bulk modulus, $\mu$ the shear modulus and $\rho$ the bulk density. Density appears in the denominator of both, so for a fixed set of elastic moduli, higher density lowers velocity — but in real rocks density and the moduli both increase together with consolidation, cementation and confining pressure, so $V_P$ and $V_S$ usually still increase with depth/compaction even though the density term alone would push the other way; the moduli effect dominates. This is why fluid-saturated, unconsolidated, high-porosity material (low moduli, only moderately low density) has markedly lower velocity than dense, well-cemented rock. Because $V_S$ has no bulk-modulus term, it is insensitive to pore-fluid compressibility, which is the basis of fluid/lithology discrimination from $V_P/V_S$ ratios.

Reflectivity. A seismic reflection is generated at any interface where acoustic impedance $Z=\rho V$ changes. The normal-incidence reflection coefficient is

$$R=\dfrac{Z_2-Z_1}{Z_2+Z_1}=\dfrac{\rho_2 V_2-\rho_1 V_1}{\rho_2 V_2+\rho_1 V_1}$$

so both density and velocity contrasts contribute to $R$, and either alone can produce a reflection even if the other property is unchanged — a common source of misinterpretation when reflectivity is attributed to velocity contrast alone. A hard, dense limestone over soft, low-density shale gives a strong positive $R$ (bright reflector); the reverse ordering gives a polarity-reversed reflection of the same magnitude. Where $Z_2\approx Z_1$ (e.g. two lithologically similar units), $R\to0$ and the interface is seismically "transparent" even though it may be a sharp geological boundary.