Transcript SOC Interview 1999 Talk - University of Southampton

SOES6002: Modelling in
Environmental and Earth System
Science
CSEM Lecture 1
Martin Sinha
School of Ocean & Earth Science
University of Southampton
Geophysics:
Applying physics to study the earth
 Use physically-based methods to
investigate structure

» Seismology, gravity, magnetics, EM

Use physical principles to
understand processes
» Deformation, melting, magnetic field
generation, mid-ocean ridges
Geophysical methods:
Aim: to derive structural images of
the interior of the solid earth
 To determine the physical properties
of specific regions of the interior
 Examples:

Earthquake seismology

Reflection seismology

Electromagnetic sounding

Geophysical properties
Can for example determine:
 P wave seismic velocity
 S wave seismic velocity
 Electrical resistivity
 Density
 magnetization

Structural features





Sharp boundaries:
Changes in acoustic impedance
Regions of steep gradients in a physical
property
Vs regions that are largely homogeneous
In many cases, understanding processes
is dependent on understanding structures
Where models come in



Typically, we make a set of observations
at the solid earth surface (land surface,
sea surface, sea floor)
These may be passive measurements
(eg. Gravity or magnetic field, earthquake
seismograms)
Or may be active surveys – seismic shots,
electromagnetic transmitters
Role of models
In geophysics, modelling comes in
several flavours:
 To allow us to analyse geophysical
measurements made at the surface
and interpret them in terms of
structures and physical properties
within some region of the earth’s
interior

Role of models 2
To compare surface measurements
and structures and physical
properties in the sub-surface with the
predictions of geodynamic models
 Effective medium modelling, for
mapping between ‘geophysical’
parameters and ‘lithological’
parameters

Electromagnetic Sounding



Propagation of fields depends primarily on
electrical resistivity
Electrical conduction dominated by fluid
phases – seawater, hydrothermal fluids,
and magma
EM methods ideally suited to studies of
fluid-dominated geological systems
Effective Medium Modelling



Both seismic P-wave velocity and
electrical resistivity depend on water-filled
porosity in the upper oceanic crust
Trade-off between porosity and degree of
interconnection – represented as aspect
ratio of void spaces
Effective medium modelling of both data
types allows a resolution of this trade-off
Solid Matrix – No porosity
Pores with aspect ratio 1
Aspect ratio about 0.2
This week:




Use active source EM sounding as an
example, for learning about modelling of
geophysical responses
Forward modelling – predicting the
response of a given structure
Hypothesis testing – are observed results
consistent with given classes of models?
Inverse modelling – given the data, what
is the underlying structure?
SOES6002: Modelling in
Environmental and Earth System
Science
CSEM Lecture 2
Martin Sinha
School of Ocean & Earth Science
University of Southampton
Lecture 2
The governing equations
 Diffusion equation and skin depth
 Propagation of fields away from a
point dipole
 What we measure and units
 Example – homogeneous sea floor
(‘half-space’) of varying resistivity

Governing Equations
Ohm's Law:
J 
E

Maxwell’s Equations

. E 
0
. B  0
B
 E  
t
E
    J s  0
t
0 
B
E
Re-arranging …..
Rearranging these, and assuming that all components have a
harmonic time variation proportional to exp(-it), gives:

1
  E  i  0  i  0   E   i 0 J
s



2

1
  B  i  0  i  0   B   0   J
s



2
Solutions:
Solutions of these equations take the form:
1
(i) for

1
(ii) for

  0
   0
Wave Equation
Diffusion Equation
Diffusion of a plane wave
Taking the case of a monochromatic plane wave
propagating in the positive x direction, and ignoring the
radiative contribution, yields solutions of the form : -

E x   E e
0

B x   B e
0
x

x

s
s
i
e
i
e










x

x

s
t

s
t











The skin depth
Where s is the electromagnetic skin depth, and is equal
to the distance over which the amplitude is attenuated by
a factor 1/e; and the phase is altered by a delay of
radian :
s 
2
0 
Exponential decay
Field of a dipole
The ‘skin depth attenuation’ equation
applies to a plane wave
 In our case, the transmitter
approximates to a point dipole
 In the absence of any attenuation,
the amplitude of the field from a point
dipole is proportional to 1/r3 where r
is distance from the dipole.

So for a dipole field:
So for a point dipole source,
 The field amplitude decreases
proportionally to distance cubed (the
‘geometric spreading’ component
 And IN ADDITION the amplitude
decreases some more due to the
skin-depth attenuation process (the
‘inductive component’

Resistivity determination
In principle, then, if we make a
measurement of amplitude
 If we know the source amplitude
 If we know the geometry
 We can determine the amount of
inductive loss
 Hence the length of a skin depth
 Hence the resistivity of the sea floor

What we measure
Source strength: defined by product of
current amplitude and dipole length
 Expressed as Ampere metres (Am)
 Typical system eg DASI = 104 Am
 Electric field E at receiver is a potential
gradient
 Expressed in Volts per metre (Vm-1)
 Typical signals in range 10-6 to 10-11 Vm-1

Normalized field
It is usual to ‘normalize’ the value of
the electric field amplitude at the
receiver by dividing it by the source
dipole moment
 Hence normalised field is expressed
in V m-1 / Am = V A-1 m-2

Current Density
It is also useful to express amplitude
at the receiver in terms of current –
since that’s how we specify the
transmitter amplitude
 We can use Ohm’s law (see earlier)
together with sea water resistivity to
convert E into J, current density expressed in Amperes per metre2
(Am-2)

Dimensionless amplitude



This has the advantage that our amplitude
measurement is now in effect a ratio
between current density at the receiver
and current at the transmitter
We can go one step further by normalizing
for the ‘geometric spreading’
We do this by multiplying the normalized
current density by distance cubed
Units/dimensions
Current density
Am-2
 Normalize by source dipole moment

Am-2 /Am = m-3
 Normalize again by (range cubed)
 Units now m-3 x m3 = dimensionless
 i.e. a simple ratio

Dimensionless Amplitude
J
E
 sw
and
3
Jr
S
M

Where S is dimensionless amplitude; J is current
density; sw is seawater resistivity; E is electric
field; r is source-receiver range; and M is source
dipole moment
What S looks like ….
Dimensionless Amplitudes
0.4
0.35
0.3
0.25
10 ohm-m
50 ohm-m
0.2
200 ohm-m
0.15
0.1
0.05
0
0
2
4
6
Range (km)
8
10
12