Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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(-it), 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 Bx 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