The Role of Physics in Geophysics

Don L. Anderson

Subrahmanyan Chandrasekhar famously declared “When you really understand physics, there are no paradoxes.” [quoted in Physics Today, March 2007]. But there are still paradoxes, “results not up to expectations”, conundrums, surprises and mysteries in seismology, viz. “…mysteries remain.” [Humphreys & Schmandt, Physics Today, August. 2011]. Corollaries of Chandrasekhar’s dictum include “paradoxes etc. are the result of unphysical or hidden assumptions and false paradigms”. Physics includes ray theory, wave propagation, anisotropy, elasticity, thermodynamics and, therefore, seismology.

Some of the effects of 19th century physics (Birch, 1952) on the geotherm and mantle dynamics include:

• Temperature dependence of thermal conductivity gives concave-up & hot conductive geotherms.
• Radioactivity yields subadiabaticity in the ‘convecting mantle’.
• Secular cooling results in a thermal bump (overshoot) in the geotherm.
• Temperature dependent viscosity yields a thick long-lived surface boundary layer.
• High potential temperatures (Tp) in the boundary layer “sub-solidus melting”.
• No horizontal isotherms or constant T interfaces.
• Decreasing potential temperature with depth in sub-boundary regions.
• Decreasing, with time,  core-mantle boundary temperature.
• The mantle is cooling and convection organizes itself.

Chandrasekhar would not consider these to be counter-intuitive or paradoxes. When this physics (plus broadband seismology) is applied to the mantle the results are quite different from prevailing models and this applies to petrology and geochemistry as well as to seismology and geophysics.

Some of the hidden and apparently innocuous assumptions routinely made in modeling include;

• Constant properties
• Adiabaticity (e.g. below a thin plate)
• Homogeneity (vigorous convection)
• Unphysical and isotropic scaling relations (Vp, Vs, T)
• Non-cooling interfaces (LAB, CMB)
• Isotropy or unrealizable forms of anisotropy (2 or 3 parameters)
• Maxwell demons & violations of the 2nd Law (definition of “impossible” in physics)
• Horizontal isotherms; 1D & 2D “approximations”
         

The bottom line is that cooling from the top and subduction control mantle dynamics. The locations of passive upwellings–tomographic “upwellings”–are too broad and slow to be active (buoyancy driven). Anisotropy suggests that some ridge segments extend into the transition region. Intraplate magmatism is due to mostly passive upwellings interacting with the heterogeneous and surface hot boundary layer (the thermal bump). The depths of the 410- and 650-km discontinuities should correlate.

Slabs at 650 km provide a fixed reference system–not “hot spots”.

Reference

Birch, F. (1952), Elasticity and constitution of the Earth's interior, J. Geophys. Res., 57, 227-286.