What causes tsunamis and controls their propagation? How does magma rise through Earth's crust and erupt from volcanoes? What controls the formation and evolution of Earth's ice sheets? What processes determine the large-scale structure and motion of Earth? How do fluids flow through the subsurface? Drawing from fundamental principles of continuum mechanics and thermodynamics, we develop mathematical theories for flow and deformation of fluids and solids, heat conduction, mantle flow, plate flexure, and porous flow. Complementing a topical focus on water waves, volcanoes, mantle flow and lithospheric flexure, ice sheets, and groundwater, this course also introduces process-based modeling in geophysics. This course will give you the skills to examine a complex natural system, identify the underlying physical processes responsible for system behavior, and write equations that mathematically describe these processes. Scaling arguments and dimensional analysis provide intuition that is refined through analytical and numerical solution of the governing equations and validated through comparison with observations.Enrollment Options: There are two "versions" of this course, which differ only in the level of difficulty of problem sets. To take the "standard" version, both undergraduates and graduates should enroll in GEOPHYS GEOPHYS 120 for 3 units. To take the "advanced" version, undergraduates should enroll in GEOPHYS GEOPHYS 120 for 5 units and graduates should enroll in GEOPHYS GEOPHYS 220 for 3 units. No prior background in geoscience or continuum mechanics is required. Mathematically, we will be working with partial differential equations, so familiarity with partial derivatives is necessary (CME 100 or MATH 51). Experience solving differential equations (CME 102 or MATH 53) is recommended but not required - the focus of the class is less on solving equations and more on setting up problems (using physics and math) and conceptually relating terms in the equations to processes. Calculus-based mechanics (PHYSICS GEOPHYS 41) is essential, as we will use principles from mechanics to write mass and momentum balance equations. We will utilize some thermodynamics (for heat transport), so PHYSICS GEOPHYS 45 is recommended but not required. The "standard" version of the course will mainly consider problems in one spatial dimension, so vector calculus like gradient, divergence, curl, and various theorems will be used only occasionally in class and not in problem sets. Similarly, we will largely avoid treating stress and strain as tensors, and problem sets for the "standard" version of the class will not require working with tensors. Vector calculus and some tensors will be required for problem sets for the "advanced" version. Undergraduate students have also found it useful, but not essential, to take partial differential equations (e.g., MATH 131P) before or during the course; this is not required.
3-5 units · Letter or Credit/No Credit · GER: WAY-FR, WAY-SMA
What causes tsunamis and controls their propagation? How does magma rise through Earth's crust and erupt from volcanoes? What controls the formation and evolution of Earth's ice sheets? What processes determine the large-scale structure and motion of Earth? How do fluids flow through the subsurface? Drawing from fundamental principles of continuum mechanics and thermodynamics, we develop mathematical theories for flow and deformation of fluids and solids, heat conduction, mantle flow, plate flexure, and porous flow. Complementing a topical focus on water waves, volcanoes, mantle flow and lithospheric flexure, ice sheets, and groundwater, this course also introduces process-based modeling in geophysics. This course will give you the skills to examine a complex natural system, identify the underlying physical processes responsible for system behavior, and write equations that mathematically describe these processes. Scaling arguments and dimensional analysis provide intuition that is refined through analytical and numerical solution of the governing equations and validated through comparison with observations.Enrollment Options: There are two "versions" of this course, which differ only in the level of difficulty of problem sets. To take the "standard" version, both undergraduates and graduates should enroll in GEOPHYS 120 for 3 units. To take the "advanced" version, undergraduates should enroll in GEOPHYS 120 for 5 units and graduates should enroll in GEOPHYS 220 for 3 units. No prior background in geoscience or continuum mechanics is required. Mathematically, we will be working with partial differential equations, so familiarity with partial derivatives is necessary (CME 100 or MATH 51). Experience solving differential equations (CME 102 or MATH 53) is recommended but not required - the focus of the class is less on solving equations and more on setting up problems (using physics and math) and conceptually relating terms in the equations to processes. Calculus-based mechanics (PHYSICS 41) is essential, as we will use principles from mechanics to write mass and momentum balance equations. We will utilize some thermodynamics (for heat transport), so PHYSICS 45 is recommended but not required. The "standard" version of the course will mainly consider problems in one spatial dimension, so vector calculus like gradient, divergence, curl, and various theorems will be used only occasionally in class and not in problem sets. Similarly, we will largely avoid treating stress and strain as tensors, and problem sets for the "standard" version of the class will not require working with tensors. Vector calculus and some tensors will be required for problem sets for the "advanced" version. Undergraduate students have also found it useful, but not essential, to take partial differential equations (e.g., MATH 131P) before or during the course; this is not required.
Offered in Autumn 2026 at Stanford University.