Transcript PPT - School of Ocean and Earth Science

SOES6002: Modelling in
Environmental and Earth System
Science
Geophysical modelling
Tim 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
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Mid-ocean ridges
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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:
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Model lithosphere formation and long-term
heat flow by advection-diffusion equation:
T
 v.T   2T
t
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Isostatic balance and heatflow over
~150Ma determines required parameters
Initial conditions on scale ~10km irrelevant
beyond ~1Ma
Large scale:
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Successes:
» Match observed depth-age relationship
» Match observed heat flow decay
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Failures:
» Measured conductive heat flow near
axis much lower than prediction
» Does not let us constrain any details at
axis
Detailed scale:
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Try to use observations to constrain
model setup:
Seabed
Melt sill
Detailed scale:
Sill +- axial
intrusion
zone
Upper crust
Lower crust
Mantle
Problems:

Fundamental physics, advectiondiffusion eqn (even steady state)
actually:
.( C p vT )  .(kT )  0
» We can no longer make many of the
normal approximations
» Several important factors are difficult to
model “properly”
Latent heat:
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Energy is released as melt solidifies
Latent heat
» Heat budget and temperatures OK,
instantaneous release of energy at point
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Excess temperature
» Heat budget OK, temperatures invalid
(possible effects on conduction)
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Increase heat capacity during solidification
» Ideal, but extra terms in adv-diff equation
Hydrothermal:
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Hydrothermal circulation enhances heat
transport
Nusselt number/enhanced conductivity
» Heat fluxes OK, temperatures wrong
(isothermal convective system with 2
boundary layers?)
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Explicit model of fluid flow
» May be correct, but strong dependence on
permeability structure and water properties
Hydrothermal:
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Disagreements over depth variation!
Time dependence:
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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)
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Hydrothermal systems unstable
» At MAR large hydrothermal systems only
present few% of time
» Pattern of convection time dependent, driven
by melt emplacement…..
Mechanics:
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Decide on approximations, then fix
correct equation, eg (time-averaged)
 dC p

  T
 C p v.T    C p dT.v  k.T  k 2T  0
 dT

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Next sort out boundary conditions
» Fix T, dT/dz, d2T/dz2
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Finally solve (probably numerically)
Testing:
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Must get model predictions into testable
form, ie compare with experiments
» Seismic velocity
» Temperature structure/history
» Heat flow
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But……
» Usually only work at top of system
» Must worry about quality of observations as
well as the physics of the model
Testing:
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Eg seismic velocity
» Lab expts convert
T to dv
Testing:
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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:
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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
Data analysis => structure and
physical properties
 Effective medium modelling
 Geodynamic modelling
 Most powerful when all three are
recursively combined with
experimental observations
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Electromagnetic fields in the Earth
Beware …..
Garbage in, garbage out….
 Use of an appropriate model
algorithm
 Parameterization
 Careful checking
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Data analysis
Forward modelling
 Hypothesis testing – classes of
models
 Inverse modelling
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Successive iterations
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
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Conclusions
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Modelling is an indispensable and extremely
powerful tool
But must be applied with care and using a
self-critical approach
A priori data from other sources is always
valuable
Having a physically and mathematically sound
modelling algorithm is necessary but not
sufficient……..