SOES6002: Modelling in Environmental and Earth System Science Geophysical modelling Tim Henstock School of Ocean & Earth Science University of Southampton
Dec 31, 2015
SOES6002: Modelling in Environmental and Earth
System Science
Geophysical modellingTim Henstock
School of Ocean & Earth Science
University of Southampton
Geophysics Modelling
Data analysis => structure and physical properties
Effective medium modelling Geodynamic modelling Most powerful when all three are
recursively combined with experimental observations
Mid-ocean ridges
Ocean crust/lithosphere formed here within past ~200Ma
Important for heat budget of Earth Important for chemical balance of oceans Many types of process operate, probably
strong time-dependence Most important for shallow features
mediated by magma-hydrothermal interaction
Use as example of geodynamic modelling
Large scale:
Model lithosphere formation and long-term heat flow by advection-diffusion equation:
Isostatic balance and heatflow over ~150Ma determines required parameters
Initial conditions on scale ~10km irrelevant beyond ~1Ma
TTvt
T 2.
Large scale:
Successes:» Match observed depth-age relationship» Match observed heat flow decay
Failures:» Measured conductive heat flow near
axis much lower than prediction» Does not let us constrain any details at
axis
Problems:
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”
0).().( TkTvC p
Latent heat:
Energy is released as melt solidifies Latent heat
» Heat budget and temperatures OK, instantaneous release of energy at point
Excess temperature» Heat budget OK, temperatures invalid
(possible effects on conduction)
Increase heat capacity during solidification» Ideal, but extra terms in adv-diff equation
Hydrothermal:
Hydrothermal circulation enhances heat transport
Nusselt number/enhanced conductivity» Heat fluxes OK, temperatures wrong
(isothermal convective system with 2 boundary layers?)
Explicit model of fluid flow» May be correct, but strong dependence on
permeability structure and water properties
Time dependence:
All processes likely to vary in time Melt transport/emplacement
» Dyking events ~hours/days repeat at interval ?years
» EPR ?steady state, MAR melt present at <10% of locations studied (probably)
Hydrothermal systems unstable» At MAR large hydrothermal systems only
present few% of time» Pattern of convection time dependent, driven
by melt emplacement…..
Mechanics:
Decide on approximations, then fix correct equation, eg (time-averaged)
Next sort out boundary conditions» Fix T, dT/dz, d2T/dz2
Finally solve (probably numerically)
0... 2TkTkvdTCTvC
dT
dCT pp
p
Testing:
Must get model predictions into testable form, ie compare with experiments» Seismic velocity» Temperature structure/history» Heat flow
But……» Usually only work at top of system» Must worry about quality of observations as
well as the physics of the model
Testing:
Consider what we are trying to achieve:» “Most realistic” – complicated model,
matches or not» “Hypothesis testing” – is a particular
factor significant/required» Alternative explanations
But beware:
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!
Geophysics Modelling
Data analysis => structure and physical properties
Effective medium modelling Geodynamic modelling Most powerful when all three are
recursively combined with experimental observations
Beware …..
Garbage in, garbage out…. Use of an appropriate model
algorithm Parameterization Careful checking
Inversion
Seek minimum misfit ….. Or seek minimum structure Combine both in Occam and similar
methods ‘Objective Function’ Requires robust estimates of errors
(random and systematic) in your data