Seismic Refraction Method

Overview (2)

Prepared byDr. Amin Khalil

Overview

Types and Properties of seismic waves

Seismic waves at an interface

Basic laws for seismic refraction

T-X graph (travel time distance curve)

Interpretation & Modeling

Travel time distance graph

T-x graph is made by picking the first onset of the first arrival seismic phases. The picked phase should be defined with great care. For refraction, which is an active source method, the first onset should generally be compressional, hence the polarity of the onset should be positive. We must take care because under certain circumstances the onset is masked due to noise and we may pick later arrivals that may be of –ve polarity.

Travel time curve

When the picked data is plotted, it will be time versus distances, that’s why we call it T-X or travel time distance curve.

Horizontal FlatInterface

• 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.

• 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

• 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.

11 /VxT

1212

Vdf

Vcd

VacT

)cos( cihdfac

)tan( cihdebc

)tan(2 cihxdebcxcd

2)(12

)tan(2cos2

Vihx

iVhT c

c

22)(12

)tan(2cos2

Vx

Vih

iVhT c

c

22)(12

)cos()sin(

cos12

Vx

iVi

iVhT

c

c

c

Using Seismic Refraction to Map the Subsurface

Depth{

12

12

2 VVVVXcDepth

Interpretation using intercept time• 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

12

21

222VVVV

zT

15

3 layer case

• 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.

12

21

22

213

21

23

12 22VVVV

zVVVV

zT

Delay Time Method• Allows Calculation of Depth Beneath Each Geophone

• Requires refracted arrival at each geophone from opposite directions

• Requires offset shots

• Data redundancy is important

Delay Time Methodx

V1

V2

x

V1

V2

)cos()tan()tan(

)cos( 12221 c

BcBcA

c

AAB

iVh

Vih

Vih

VAB

iVhT

Delay Time Methodx

)cos()tan()tan(

)cos( 12221 c

PcPcB

c

BBP

iVh

Vih

Vih

VBP

iVhT

)cos()tan()tan(

)cos( 12221 c

PcPcA

c

AAP

iVh

Vih

Vih

VAP

iVhT

)cos()tan()tan(

)cos( 12221 c

BcBcA

c

AAB

iVh

Vih

Vih

VAB

iVhT

V1

V2

Delay Time Methodx

t T T TAP BP AB0

Definition:

V1

V2

(7)

ABBPAP TTTt 0

)cos(

)tan()tan()cos( 12221

0c

PcPcA

c

A

iVh

Vih

Vih

VAP

iVht

)cos(

)tan()tan()cos( 12221 c

PcPcB

c

B

iVh

Vih

Vih

VBP

iVh

)cos(

)tan()tan()cos( 12221 c

BcBcA

c

A

iVh

Vih

Vih

VAB

iVh

2120

)tan(2)cos(

2V

ihiV

hV

ABBPAPt cP

c

p

But from figure above, BPAPAB . Substituting, we get

2120

)tan(2)cos(

2V

ihiV

hV

BPAPBPAPt cP

c

p

or

210

)tan(2)cos(

2V

ihiV

ht cP

c

p

)cos(

)sin()cos(

1221

0c

c

cp

iVi

iVht

)cos(

)sin()cos(

221

1

21

20

c

c

cp

iVViV

iVVVht

)cos(

)sin()cos(

22121

1

2

10c

c

cp

iVVi

iVVVV

Vht

2

1sinVVicSubstituting from Snell’s Law,

)cos(

)sin()cos(

sin1

22121

10c

c

c

cp

iVVi

iVViVht

)cos(

)sin()cos(

sin1

22121

10c

c

c

cp

iVVi

iVViVht

Multiplying top and bottom by sin(ic)

)cos()sin(

)(sin)cos()sin(

1221

2

2110

cc

c

ccp

iiVVi

iiVVVht

)cos()sin(

)(cos221

2

10cc

cp

iiVViVht

)sin(

)cos(22

0c

cp

iViht

)sin(

)cos(22

0c

cp

iViht

2

1sinVVic

Substituting from Snell’s Law,

10

)cos(2V

iht cp (8)

We get

11

)cos(2

)cos(22

Ppoint at Delay timeVih

VihtD cpcpo

TP (9)