SOES6002: Modelling in Environmental and Earth

System ScienceCSEM Lecture 3

Martin SinhaSchool of Ocean & Earth Science

University of Southampton

Recap and plan:

Yesterday: basic principles of CSEM sounding. Modelling for uniform seafloor resistivity

Today: sensitivity patterns, boundary conditions vertical variations in resistivity, CSEM sounding

Recap from yesterday

Dimensionless Amplitudes

0.001

0.01

0.1

10 2 4 6 8 10 12

Range (km)

10 ohm-m50 ohm-m200 ohm-m

Boundary conditions

Apart from the general form of the governing equations, we haven’t gone deeply into the mathematics

But two useful boundary conditions are useful:

Eparallel is continuous Jnormal is continuous

Transport of energy

As we see, different resistivities for a uniform seafloor lead to different patterns of amplitude vs range

What happens if seafloor resistivity varies?

First step – what is the path taken by the flow of energy?

Poynting Vectors

0.75 Hz, 100 ohm-m, azimuthal

Sensitivity

Poynting vectors show local direction of transport of energy

Another way of investigating this is to look at sensitivity

For a given transmitter position and receiver position, if we make a small change to the resistivity of a small element of the sea floor, how much does this affect the measured amplitude?

Sensitivity pattern

Sensitivity pattern

Sensitivity follows a broadly U-shaped region between source and receiver

At longer source receiver offsets, sensitivity extends deeper beneath the seafloor – so ‘averages’ over a greater depth range

Hence we can perform a ‘sounding’ study by increasing the offset

4 models

50 ohm-m half space 200 ohm-m half space 1 km thick layer, 50 ohm-m overlying

200 ohm-m half space 1 km thick layer, 200 ohm-m

overlying 50 ohm-m half space

1 layer and 2 layer models

Layered sructures

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 2 4 6 8 10 12

range (km)

Sazi

m

50 half space200 half space200-50 layered50-200 layered

Behaviour:

At long offsets, the slope of the curve corresponds to the effect of the deeper layer

Amplitudes are shifted up and down by the effect of the shallower layer

At short offsets, would see only the shallow layer effect

SOES6002: Modelling in Environmental and Earth

System ScienceCSEM Lecture 4

Martin SinhaSchool of Ocean & Earth Science

University of Southampton

Lecture 4

The importance of frequency Can we detect isolated, thin,

conductive layers? The air wave problem

What about frequency?

Our choice of frequency depends on skin depth

We need to choose f so that skin depth is comparable to our scale of investigation

But higher f means shorter skin depths, so high frequencies intrinsically see less deep than low frequencies

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

Skin depth (m) in various materials

3 models at 8 Hzresponses at 8 Hz

0.001

0.01

0.1

10 2 4 6 8 10 12

range (km)

S az

im 50 half space200 half space50 over 200

Frequency issues

Higher frequencies have better resolution

But they also have poorer penetration depth

So we always face a trade-off between these two

In real surveys, it’s often useful to collect data at multiple frequencies

Thin layers

Can we detect, e.g., the presence of a thin conductive layer (for example a melt lens) within the sea bed?

There’s clearly going to be a resolution problem – diffusive signal propagation is not necessarily a good way of finding thin layers

2 models, 2 frequencies

Thin Layers

0.0001

0.001

0.01

0.1

10 2 4 6 8 10 12

Half-space 1 Hz

Half-space 8 Hz

Thin layer 1 Hz

Thin layer 8 Hz

Thin layer model

Model consists of a 50 ohm m half-space, with a 100 m thick conductive layer (2 ohm-m) embedded in it at a depth of 1 km

It does have an evident effect on the data, but the effect depends on frequency

Effect of shallow water

Varying water depth

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0 2 4 6 8 10 12

range (km)

S az

im

5km

3km

1km

0.5km

0.35km

The ‘Air wave’ interaction

In deep water, very little of the signal reaches the sea surface – so the surface has little effect on signal propagation

In shallow water, the surface does have an effect

The ‘Air Wave’ – propagation up, along and down again – can be a problem