SOES6002: Modelling in Environmental and Earth System Science Geophysical modelling Tim Henstock School of Ocean & Earth Science University of Southampton

Geophysics Modelling l Data analysis => structure and physical properties l Effective medium modelling l Geodynamic modelling l Most powerful when all three are recursively combined with experimental observations

Mid-ocean ridges l Ocean crust/lithosphere formed here within past ~200Ma l Important for heat budget of Earth l Important for chemical balance of oceans l Many types of process operate, probably strong time-dependence l Most important for shallow features mediated by magma-hydrothermal interaction l Use as example of geodynamic modelling

Large scale: l Model lithosphere formation and long-term heat flow by advection-diffusion equation: l Isostatic balance and heatflow over ~150Ma determines required parameters l Initial conditions on scale ~10km irrelevant beyond ~1Ma

Large scale: l Successes: »Match observed depth-age relationship »Match observed heat flow decay l Failures: »Measured conductive heat flow near axis much lower than prediction »Does not let us constrain any details at axis

Detailed scale: l Try to use observations to constrain model setup: Seabed Melt sill

Detailed scale: Upper crust Lower crust Mantle Sill +- axial intrusion zone

Problems: l Fundamental physics, advection- diffusion eqn (even steady state) actually: »We can no longer make many of the normal approximations »Several important factors are difficult to model “properly”

Latent heat: l Energy is released as melt solidifies l Latent heat »Heat budget and temperatures OK, instantaneous release of energy at point l Excess temperature »Heat budget OK, temperatures invalid (possible effects on conduction) l Increase heat capacity during solidification »Ideal, but extra terms in adv-diff equation

Hydrothermal: l Hydrothermal circulation enhances heat transport l Nusselt number/enhanced conductivity »Heat fluxes OK, temperatures wrong (isothermal convective system with 2 boundary layers?) l Explicit model of fluid flow »May be correct, but strong dependence on permeability structure and water properties

Hydrothermal: l Disagreements over depth variation!

Time dependence: l All processes likely to vary in time l Melt transport/emplacement »Dyking events ~hours/days repeat at interval ?years »EPR ?steady state, MAR melt present at <10% of locations studied (probably) l Hydrothermal systems unstable »At MAR large hydrothermal systems only present few% of time »Pattern of convection time dependent, driven by melt emplacement…..

Mechanics: l Decide on approximations, then fix correct equation, eg (time-averaged) l Next sort out boundary conditions »Fix T, dT/dz, d 2 T/dz 2 l Finally solve (probably numerically)

Testing: l Must get model predictions into testable form, ie compare with experiments »Seismic velocity »Temperature structure/history »Heat flow l But…… »Usually only work at top of system »Must worry about quality of observations as well as the physics of the model

Testing: l Eg seismic velocity »Lab expts convert T to dv

Testing: l Consider what we are trying to achieve: »“Most realistic” – complicated model, matches or not »“Hypothesis testing” – is a particular factor significant/required »Alternative explanations

Hypothesis testing:

But beware: l Just because a particular class of model predicts a particular feature of the observations this does not mean »The model is correct »The class of model is the only one which will predict that feature!

Example:

Geophysics Modelling l Data analysis => structure and physical properties l Effective medium modelling l Geodynamic modelling l Most powerful when all three are recursively combined with experimental observations

Electromagnetic fields in the Earth

Beware ….. l Garbage in, garbage out…. l Use of an appropriate model algorithm l Parameterization l Careful checking

Data analysis l Forward modelling l Hypothesis testing – classes of models l Inverse modelling

Successive iterations

Inversion l Seek minimum misfit ….. l Or seek minimum structure l Combine both in Occam and similar methods l ‘Objective Function’ l Requires robust estimates of errors (random and systematic) in your data

Conclusions l Modelling is an indispensable and extremely powerful tool l But must be applied with care and using a self-critical approach l A priori data from other sources is always valuable l Having a physically and mathematically sound modelling algorithm is necessary but not sufficient……..