Problem 10. Reduction to pole This is where the magnetic anomaly is transformed to be that of the anomaly at the north pole (as if the same body is placed.

Problem 10

Reduction to pole

This is where the magnetic anomaly is transformed to be that of the anomaly at the north pole (as if the same body is placed at the pole)

The result is that the anomaly becomes more symmetric and is more centred above the causative body.

By comparison with the theoretical curves, the width of the anomaly suggest a Z of between 3.6 and 3.8 m., and a horizontal location of ~ 23 m (Just to the right of the positive peak).

With 2m/z2 = 1, and z = 3.7m, the max height of the anomaly is ~ 0.9 nT. In the observed data, the max height of the anomaly is ~190 nT. Thus we need to make 2m/z2 = 190/0.9 ~210 (to match the observed data)m = 210 x 3.72/2 ~ 1440 Wbm

Lecture 7

• GPR• The Exam• Set exercise

Electromagnetic (EM) waves (also referred to as radio waves).

All electromagnetic radiation consists of oscillating electric and magnetic fields

Heat and light from the sun

Frequencies between 30 kHz and 300 GHz are widely used for telecommunication.AM radio: 180 kHz -1.6 MHzTV: 470 to 854 MHz.

Cellular mobiles operate within ranges 872-960 MHz, 1710-1875 MHz and 1920 - 2170 MHz.

An electomagnetic (EM) wave is generated at surface.

This wave travels down through the subsurface.

The generated wave has a “conical” footprint.

The source is a short pulse of EM energy with a frequency of 10-1000 MHz

c

V

The velocity of the wave is most dependent on the permittivity of the rocks, with wet conductive porous rocks having a permittivitythat is up to 10-20 times larger than dry rocks.

The velocity of the EM wave in dry rocks is ~0.2 m/nsThe velocity of the EM wave in wet rocks is ~0.05 m/ns[Note that 0.05m/ns = 5 x 107 m/s]

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12

12

VV

VVk

The EM wave is reflected back to surface when there is a change in velocity (electrical properties of the rocks) and the amplitude of this reflected energy is increased when the velocity contrast is increased.

The reflection coefficient (k) is:

The arriving EM wave is detected by theantenna and plotted as a function of travel-time.

Plot as a radargram (most common) or velocity tomogram or as reflection amplitudes

Depth slices

radargram

Depth penetration in metres for different materials

Depth of penetration is poor in conductive layers, good indry rocks (insulators) and excellent in ice.

Hand-held

Variety instrument designs

Some allow you to produce images in the field

Applications

Relatively new technique

Applications increased in recent years

Penetration in ice is excellent

Is now being used to determine ice thickness inthe Arctic, Antarctic, lakes, glaciers and Mars

0 m

300 m

Locating man-made objects beneath the ground

Underground storage tanks are centred at top of hyperbolae

Forensic applications

Locating graves, buried bodies

Locating buried geological features

Karsts in limestone

Locating top of bedrock

Over time, bridges and road surfaces deteriorate. Re-paving hides the effects of deterioration, but inside the road surface, damage still exists.

Ground Penetrating Radar surveys, can be used to identifying areas of damage.

Used to look at asphalt thickness onairplane runways

GPRHigh resolution imagingWide range applicationsUninvasiveRelatively cheap and fast

Limited penetrationAffected by rainDifficult to survey in vegetated terrains

Examination

Answer any 2 of 4 questions

Exam format is as per my example on the ESE website

Formulae will be supplied – but you need to know how to use them

Question 1: Write short notes using illustrations where appropriate on four of the following five topics: (50 marks)i. Corrections to gravity data;ii. Geometrical spreading and attenuation in seismology;iii. Magnetic properties of rocks;iv. Constant spacing traverse (CST) resistivity surveys ; v. The term “Induced polarization”.

Answers – all straight from notes and problem sheetsi) Drift, latitude, Free air, Bouguer, Eotvos, Terrain(explain what they are, what is their purpose) 12.5 marks each and 11.25 minutes each

Question 1:

i. Corrections to gravity data;

Do not tell me about gravimeters, regional versus residual gravity anomalies, isostatic anomalies

You will only get marks for answering the question

Question 3:i) Describe the acquisition and plotting of seismic refraction data (25 marks).ii) A numerical calculation – for example determine the seismic velocity and dip of a sub-surface layer (equations would be given).

First half – descriptive, straight from notes

Second half will be a “close” to something that youhave done in the problems

Question 2:i) A company wishes to identify the location of a faulted contact between a basalt and a porous water-filled sandstone. The contact is sub-vertical and buried beneath unconsolidated soils and sands. They conduct gravity, magnetic, refraction and resistivity surveys across the area. Outline how these geophysical data might change across the contact, and use annotated sketches to illustrate how these surveys might be used to identify the contact. (40 marks)

ii) Identify some reasons why these surveys may fail to locate the contact. (10 marks)

NOT Straight from notes

You would need to guess what the velocity, gravity, resistivity and magnetic signature of these two rock types was.

Question 4:Write an essay entitled “Forward and inverse modelling of geophysical data”.

This year, this question will be about “non-uniqueness”

Exercise for next week is to read about non-uniquenessin modelling and interpretation of geophysical data

Question 4

Use any sources you can

Lecture notesExtracts from Dobrin’s text book are on the ESE sitePaper by Colin Zelt (Geophysical Journal Int., 1999, v. 139, p. 183-204). Also on ESE site.

Paper by Colin Zelt

Describes modellingstrategies and model assessment

Modelling seismic data Determine crustal velocity model that fits travel-time data

Paper by Colin Zelt (Geophysical Journal Int., 1999, v. 139, p. 183-204)

Introduction

Travel-time data – insensitive to velocity gradient versus a velocity discontinuity

Problem - Non-uniquenessA range of models may fit the data equally as well

Solution - Need model assessmentIn final model, need to distinguish between structure that is required by data and structure that is consistent with the data

Introduction

Section 2 Pre-modelling conditionsUncertainty in dataHandle by assigning pick uncertainty 10-200msPick heavily where arrivals are clearFit measured by Chi2 Normalised (observed –expected)2

Clear arrivals – smalluncertainty, lots of picks

Weak arrivals – largeuncertainty, few picks

Fit measured by Chi2 Aim to get this equal to 1Normalised (observed –expected)2 Called objective function

Aim is not to over-fit or under-fit the data

Starting model Two extremes:1D or lateral homogeneousOr include a priori informationTest more than one

Section 3 Modelling

Disadvantage forward modelling With a large complex dataset there is almost no possibility of deriving a model without introducing unnecessary structure

Advantage inverse modellingIt is possible to avoid this problem

GoalObtain minimum parameter or minimum structure modelOccam’s razor analogy – obtain the simplest model that fits the data.

Solutions:Node spacing in model ~ twice shot or receiver spacing (whichever is the largest)Restrict model perturbations by altering objective function so that it penalizes against model roughness.This is usually referred to as regularization

Chi2 = Normalised (observed –expected)2 + regularization term

4 Model assessment

Ray coverage

Gives indication of areasin the model that arewell constrained

4 Model assessment

g and h = resolution plots identify areas of model that are well resolved (dark shading)

Checkerboards

Add checkerboardof high and lowvelocity anomaliesto final model

Use inversion torecover checkerboard

Determine how well checkerboard isrecovered (semblance)

Identify areas of good recovery (dark)

Use to identify areas of model that are poorly constrained – coloured grey

Uncertainties in parameters

Get absolute errors

e.g. V = 5 ± 0.2 km/s

or depth to boundaryis 3.2 ± 0.1 km

And can see how “smeared” the perturbation is

3.07

Schedule and course outline will be us by the beginning of term

Please check it

My availability

Away 11th-18th March

12 – 1 Mon-Wed 20-22nd March My office 2.38b

Any queries on course