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

2. 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

3. 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

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

5. 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

6. 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

7. 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

8. 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

9. 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

27. 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

29. Solid Matrix – No porosity

30. Pores with aspect ratio 1

31. Aspect ratio about 0.2

38. 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?

39. SOES6002: Modelling in Environmental and Earth System Science CSEM Lecture 2 Martin Sinha School of Ocean & Earth Science University of Southampton

40. 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

41. Governing Equations Ohm's Law:

42. Maxwell’s Equations

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

44. Solutions:

45. Diffusion of a plane wave

46. The skin depth

47. Exponential decay

48. 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.

49. 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’

50. 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

51. 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 10 -6 to 10 -11 Vm -1

52. 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

53. 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 )

54. 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

55. 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

56. 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

57. What S looks like ….