SOES6002: Modelling in Environmental and Earth System Science CSEM Lecture 1 Martin Sinha School of Ocean & Earth Science University of Southampton

Geophysics: l Applying physics to study the earth l Use physically-based methods to investigate structure »Seismology, gravity, magnetics, EM l Use physical principles to understand processes »Deformation, melting, magnetic field generation, mid-ocean ridges

Geophysical methods: l Aim: to derive structural images of the interior of the solid earth l To determine the physical properties of specific regions of the interior l Examples: l Earthquake seismology l Reflection seismology l Electromagnetic sounding

Geophysical properties l Can for example determine: l P wave seismic velocity l S wave seismic velocity l Electrical resistivity l Density l magnetization

Structural features l Sharp boundaries: l Changes in acoustic impedance l Regions of steep gradients in a physical property l Vs regions that are largely homogeneous l In many cases, understanding processes is dependent on understanding structures

Where models come in l Typically, we make a set of observations at the solid earth surface (land surface, sea surface, sea floor) l These may be passive measurements (eg. Gravity or magnetic field, earthquake seismograms) l Or may be active surveys – seismic shots, electromagnetic transmitters

Role of models l In geophysics, modelling comes in several flavours: l 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 l To compare surface measurements and structures and physical properties in the sub-surface with the predictions of geodynamic models l Effective medium modelling, for mapping between ‘geophysical’ parameters and ‘lithological’ parameters

Electromagnetic Sounding l Propagation of fields depends primarily on electrical resistivity l Electrical conduction dominated by fluid phases – seawater, hydrothermal fluids, and magma l EM methods ideally suited to studies of fluid-dominated geological systems

Effective Medium Modelling l Both seismic P-wave velocity and electrical resistivity depend on water-filled porosity in the upper oceanic crust l Trade-off between porosity and degree of interconnection – represented as aspect ratio of void spaces l 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: l Use active source EM sounding as an example, for learning about modelling of geophysical responses l Forward modelling – predicting the response of a given structure l Hypothesis testing – are observed results consistent with given classes of models? l 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 l The governing equations l Diffusion equation and skin depth l Propagation of fields away from a point dipole l What we measure and units l Example – homogeneous sea floor (‘half-space’) of varying resistivity

Governing Equations Ohm's Law:

Maxwell’s Equations

Re-arranging ….. Rearranging these, and assuming that all components have a harmonic time variation proportional to exp(-i  t), gives:

Solutions:

Diffusion of a plane wave

The skin depth

Exponential decay

Field of a dipole l The ‘skin depth attenuation’ equation applies to a plane wave l In our case, the transmitter approximates to a point dipole l In the absence of any attenuation, the amplitude of the field from a point dipole is proportional to 1/r 3 where r is distance from the dipole.

So for a dipole field: l So for a point dipole source, l The field amplitude decreases proportionally to distance cubed (the ‘geometric spreading’ component l And IN ADDITION the amplitude decreases some more due to the skin-depth attenuation process (the ‘inductive component’

Resistivity determination l In principle, then, if we make a measurement of amplitude l If we know the source amplitude l If we know the geometry l We can determine the amount of inductive loss l Hence the length of a skin depth l Hence the resistivity of the sea floor

What we measure l Source strength: defined by product of current amplitude and dipole length l Expressed as Ampere metres (Am) l Typical system eg DASI = 10 4 Am l Electric field E at receiver is a potential gradient l Expressed in Volts per metre (Vm -1 ) l Typical signals in range to Vm -1

Normalized field l It is usual to ‘normalize’ the value of the electric field amplitude at the receiver by dividing it by the source dipole moment l Hence normalised field is expressed in V m -1 / Am = V A -1 m -2

Current Density l It is also useful to express amplitude at the receiver in terms of current – since that’s how we specify the transmitter amplitude l We can use Ohm’s law (see earlier) together with sea water resistivity to convert E into J, current density - expressed in Amperes per metre 2 (Am -2 )

Dimensionless amplitude l 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 l We can go one step further by normalizing for the ‘geometric spreading’ l We do this by multiplying the normalized current density by distance cubed

Units/dimensions l Current density Am -2 l Normalize by source dipole moment l Am -2 /Am = m -3 l Normalize again by (range cubed) l Units now m -3 x m 3 = dimensionless l i.e. a simple ratio

Dimensionless Amplitude 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 ….