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A2.4VF2 Applied Environmental Geoscience

Lecture 2

SEISMIC REFRACTION METHODS

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Contents

• Introduction• Theory of the seismic method• Refraction surveys• Interpretation of refraction results

– Horizontal interfaces– Dipping interfaces– Irregular interfaces

• Conclusions

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INTRODUCTION

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• Seismic methods are those that rely on the transmission of elastic waves through the subsurface.

• These waves are generated by an energy source and are detected by an array of geophones.

• The raw data consists of the time-series response (‘wiggle trace’) at each geophone, which is processed to give the underground structure.

• The term shallow seismics is used for the detection of structures at less than ~100m depth. Arrival times are typically measured in milliseconds (mS).

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THEORY OF THE SEISMIC METHOD

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• There are two types of elastic body wave in a solid:– P-Waves: compression waves– S-waves: shear waves

• P-waves are the faster and are usually the ones studied in simple seismic methods.

• Other waves (surface waves) also exist but are much slower. It is these waves that do the damage in earthquakes.

• We will focus our attention on P-waves from now on.

7P-waves in an elastic solid

8S-waves in an elastic solid

9Surface waves in an elastic solid

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• Elastic waves behave in an analogous way to light rays in optics.

• At an underground interface (an elastic contrast), a wave is refracted and/or reflected.

• Both events may occur. Their relative importance is determined by the elastic contrast, measured by the change of elastic impedance (z).

Z = elastic velocity x density

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• To measure the strength of the impedance contrast we use a coefficient R, termed the coefficient of reflection.

• The larger is R, the more energy is reflected and the less refracted.

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12

zz

zzR

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• The progress of a seismic wave is followed by a ray-path. This is analogous to a light ray.

• At an elastic contrast a ray-path will obey the laws of geometrical optics.– The refracted ray obeys Snell’s Law. – This leads to the concept of a critical angle of refraction and a

critical distance.– The reflected ray obeys the law of reflection.

• This leads to a division into refraction surveys and reflection surveys, depending on which ray is studied.

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REFRACTION SURVEYS

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• Refraction surveys study the critical refracted ray.• Such a ray can only exist if, at an interface, the lower

layer has a higher impedance than the overlying layer, which usually implies a higher velocity.

• In practice this is often the case, for example if unconsolidated sediment overlies bedrock.

• If it is not true, then there is no critical ray and any layer beneath the interface is hidden. It can then only be revealed by a reflection survey.

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Seismic method usingmulti-channel geophone array

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• The critical ray follows the line of the interface and sends a return ray back to the surface. This is detected by the geophones.

• The critical ray (or head wave) moves in layer 2 at the (higher) layer 2 velocity. It thus sends a progressive series of return rays along its path.

• These are detected in turn by each geophone.• Both the downgoing and return rays meet the

interface at the critical angle of refraction.

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INTERPRETATION OF REFRACTION RESULTS

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• The interpretation of underground structure from refraction results relies on ray-path analysis.

• The ray path is identified from a travel-time graph of arrival times vs distance from source. This sometimes called a T-X diagram.

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• The technique is basically to inspect the T-X diagram and identify (?guess) the most likely underground structure from which it arises.

• Values are then picked off the T-X diagram and converted into structure parameters such as depth, etc using the assumed geometry of the ray path.

• Thus we need to know how T-X diagrams arise.

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• A refraction T-X diagram is based on the first arrival at each geophone.

• This is either picked off the geophone output (manually or in software) or is automatically recorded by a cut-off timer.

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Geophone positions

Tim

e (m

Sec

s)

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• The T-X diagram is thus a graph of first arrival times against distance from source.

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Horizontal Interfaces

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• Horizontal interfaces provide a simple introduction to the construction of T-X diagrams.

• Close to the source, the first arrival is due to the direct ray travelling in layer 1.

• This plots as a straight line on the T-X diagram.• The slope of the line is the reciprocal of the layer 1

velocity (assuming distance is on the X-axis).• The intercept is zero.

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• When the critical distance is exceeded, refraction occurs and some energy enters layer 2. A refracted ray then travels at V2 sending return rays back to the surface as it does so.

• At some point (the cross-over distance) the refracted ray (being the faster) will overtake the direct ray and the return rays will become the first arrivals, despite their longer travel distance.

• It is these that are now plotted on the T-X diagram

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• The T-X diagram thus develops an upper branch due to the refracted ray.

• This is again a straight line, whose slope is the reciprocal of V2 .

• There is now an intercept time (T1) whose value is determined by the layer 1 thickness and the two velocities

• The intercept time is an example of a delay time sum, composed of the separate times taken by the signal to descend to the interface and then to return to the surface.

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• The intercept time is given by

• Since, in this case, the ray path is symmetrical, the intercept time is the sum of two equal delay times

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222VV

VVzT

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• By a similar argument, a third layer introduces a third branch into the T-X diagram.

• The slope is the reciprocal of V3 and the intercept is a composite of the layer 1 and layer 2 delay times.

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213

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12 22VV

VVz

VV

VVzT

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Dipping Interfaces

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• The presence of a dipping interface is recognised if the reversed profile is not the mirror image of the forward profile

• The analysis of a dipping interface introduces three new issues:– There is an additional unknown (the dip angle)– The T-X diagram is no longer symmetrical and so the updip

and downdip intercepts are not equal– The updip and downdip velocities in layer 2 are not equal

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• The asymmetry arises because the return ray has a successively shorter (updip) or longer (downdip) path as the distance from the shot point increases.

• This is expressed by saying that the apparent velocity in layer 2 (the reciprocal slope of the upper branch) is greater (flatter slope) in the updip than than in the downdip directions.

• It is necessary to analyse both the forward and the reverse profiles to solve for V1, V2, Z and (dip angle)

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• Since it is not known in advance whether or not an interface is dipping - and most usually are! - the procedure is always to shoot a profile in both forward and reverse directions (i.e. interchange the shot position with the last geophone and leave the rest in place).

• The dip will very probably be an apparent dip in the geological sense, since the profile is unlikely to follow the line of true dip. Thus a second, perpendicular, profile is required to allow the true dip to be found.

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Irregular Interfaces

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• The T-X method smooths off interfaces by fitting a straight line through the data and so irregularies are not analysed.

• They are however visible as deviations from the best fit line and can be analysed using a different method.

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• It is possible to analyse these deviations by using the so-called plus-minus method. This simply uses the previously-measured arrival times: a new survey is not required.

• We return to the idea of a delay time.

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Z

The delay time is the timetaken to reach the lower layerminus the time taken to travelthe horizontal distance

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VV

VVZD

Hence if we know the delay time at a given station, we can find Z

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• We now state that the arrival time between any two stations (say A and B) is the horizontal transit time at the fastest velocity plus the sum of all the delay times along the ray path

• For the simple two-layer example

2V

xDDT ABBAAB

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• If we now take the sum of the forward and reverse times to any intermediate geophone and subtract the overall travel time, we can find the delay time at the intermediate geophone and hence the local depth.

• Since we have used both the forward and reverse profiles, the value obtained is an average depth around the position (approx smoothed over a distance of one-third depth)

50ABBIAI

IABBIAI

ABBAAB

BIIBBI

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xxx

because

DTTT

Thus

V

xDDT

V

xDDT

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2

2

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The method takes each intermediateposition in turn and forms the sumof the forward time plus the reversetime minus the overall time.

Hence it is called the plus-minus method.

It is also known as the intermediate geophone method

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FINAL REMARKS

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• Seismic refraction is a useful tool for the general investigation of bedrock structure, particularly at depth.

• The T-X method averages out depth variations, although the plus-minus method will show them from the same data

• It is incapable of fine detail, especially if the bedrock is irregular or lacks internal elastic contrasts.

• It assumes that the velocity increases in each successive layer. If it doesn’t, the lower velocity layer is missed.

• The velocity can be obtained from the T-X plot but is often measured in the field.

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Summary

• Introduction• Theory of the seismic method• Refraction surveys• Interpretation of refraction results

– Horizontal interfaces– Dipping interfaces– Irregular interfaces

• Conclusions

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THE END

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