EARTH 350-0 Physics of the Earth (ISP)

Course Objectives

After listening to a geological research talk, a former ISP director once told me: "I've learned two important things today: there really is an integrated science, and it's called geology." It is my hope that you may develop a similar impression in this course.

EARTH 350 aims to present a glimpse of the Earth and Planetary Sciences as a real integrated science, combining aspects of mathematics, physics, astronomy, chemistry, biology, computer science, etc. Due to time limitations, we will dwell mostly on linkages to mathematics and physics, but you should see glimpses of most of these other fields from time to time, too. Furthermore, the syllabus of EARTH 350 aims to be coordinated with that of MATH 381 (formerly 391-1), which most of you will be taking contemporaneously. (Occasionally I've been able to walk in to class and use some of that day's mathematics notes remaining on the blackboard, but sadly that does not happen often.)

Among the many things into which I hope you will gain insight and understanding in this course are the following questions.

• How does the planet on which we live really work?
  • You should be able to explain the basic structure of Earth's interior.
  • You should be able to explain plate tectonics in terms of such concepts as plate-boundary processes and triple-junction stability.
  • You should be able to interpret paleomagnetic data in terms of relative plate motions.
  • You should be able to assess the respective roles of conductive and convective heat transport within the planet.
• How do partial differential equations relate to real-world phenomena?
  • You should be able to use the heat equation to model planetary heat flow.
  • You should be able to use the wave equation to model seismic wave propagation.
  • You should be able to use Laplace's equation to model planetary gravity fields.
  • You should be able to solve the above equations subject to various physical boundary conditions.
  • You should be able to describe the physical meaning of solutions to these equations.
  • You should be able to use dimensional analysis to anticipate the form of some solutions.
• What can we learn from remote sensing, and what are its limitations?
  • You should be able to explain some similarities and differences between geophysical remote sensing (e.g., magnetic, thermal, acoustic, gravitational, electrical) and medical remote sensing (e.g., x-ray, ultrasonic, CAT, PET, MRI).
  • You should be able to interpret gravity anomalies in terms of internal planetary structure.
  • You should be able to interpret basic seismological data in terms of internal Earth structure and plate-boundary processes.
  • You should be able to explain modes of information loss during remote sensing (e.g., orientation of magnetized seafloor, downward continuation of gravity fields).
• How do various mathematical representations of physical entities work?
  • You should be able to explain how the Helmholtz representation theorem allows separation of physically distinct seismic waves into scalar and vector potentials.
  • You should be able to explain how Fourier-type expansions in harmonic functions (e.g., spherical harmonics based on Legendre polynomials) can be used to represent physical entities ranging from seismological Earth structure and planetary gravity fields to electronic orbitals and antibody docking sites.

Importantly, this class is not about memorizing formulas. It is about understanding fundamental concepts and methods and about applying ideas to new situations and problems.