Teori Dan Tugas 2 Geofisika

7/28/2019 Teori Dan Tugas 2 Geofisika

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METODA SEISMIK I [ GF 3231 ]

Program Studi Fisika

Fakultas Matematika dan Ilmu Pengetahuan Alam

Universitas Riau

Dosen :Dr. Muhammad Edisar, MT

SEISMIC REFRACTION


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r

fi

Snells Law

V1

V2


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r

fiV1

V2


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What happens if r = 90o

V1

V2

i1

r

21

1 sinsin

v

r

v

i

Boundary

interface


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r

i

Critical refraction When r = 90o

sin ic = V1/V2

V1

V2


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measure times of arrival of the initial ground movement generatedby a source recorded at a variety of distances.

Refraction Seismology :


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- one strike and multiple geophones

Refraction Seismology


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Later arriving complications in the recorded ground motion are

discarded.

Thus, the data set consists of a series of times of first arriving

energy versus distance.

Refraction Seismology


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TUGAS 2 GEOFISIKA HITUNG KECEPATAN MASING-MASING KECEPATAN

GELOMBANG SETIAP LAPISAN DATA SEISMIK BIAS BERIKUT DAN HITUNG

KETEBALAN MASING LAPISAN SERTA JENIS BATUAN LAPISAN TERSEBUT


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Travel Time Curve


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Interpret depths to subsurface interfaces and the

seismic wave velocities for each layer.

Refraction Seismology Objective


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Direct Arrivals


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Reflected Arrivals


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Refracted Arrivals


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Critical distance?

Crossover distance?

Time

Distance


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Model Calculation

Simple, Horizontal Two Layers


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Travel Time Calculations for Two-Layer Case

1

2

/( cos )

( 2 tan ) /

SG SA AB BG

SA BG c

AB c

T T T T

where

T T z V i

T x z i V

1 2 1

2 1

/( cos ) ( 2 tan ) / /( cos )

:

(1/ ) 2 (cos ) /

SG c c c

SG c

T z V i x z i V z V i

which simplifies to

T V x z i V


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Slope-Intercept Form of a Line

Y = mx + bPlot T vs. X

Slope of Line = 1/V2

Y Intercept = 2z(cos ic)/V1

2 1(1/ ) 2 (cos ) /SG cT V x z i V


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1 2

2 2 1/ 2 2 2

1 2

Re sin / ( ' ), :cos (1 / ) sin cos 1

c

c

member that i V V Snell s Law and hencei V V from


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12

2

1

2

2

2

2vv

vvhVxtT


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The Use of Crossover Distance to Calculate

Refractor Depth

Travel time of direct ray at the crossover

distance is xcross/V1

Travel time of critically refracted ray at thecrossover distance is given by:

21

2/12

1

2

2

2

)(2

VV

vvz

v

xT cross


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Model Calculation


Direct Wave?


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Model Calculation


Reflected Wave?


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Model Calculation


Head Wave or Critically Refracted?


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All Three Arrivals


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Time

Distance

?


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Time

Distance

Direct


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Time

Distance

?


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Time

Distance

Reflected


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Time

Distance

?


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Time

Distance

Refracted or Head Wave


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Time

Distance

Direct

Reflected



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?

Time

Distance

Direct



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Crossover distanceT

ime

Distance

Direct

Reflected



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Refracted Arrivals

2 1(1/ ) 2 (cos ) /SG cT V x z i V


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Slope-Intercept Form of a Line

Y = mx + b

where

Slope of Head Wave Line = 1/V2

Y Intercept or ti = 2z(cos ic)/V1

2 1(1/ ) 2 (cos ) /SG cT V x z i V


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Using Snells Law and Trig. Identity

2 22 1

2 2 1

2T

z V VxtV V V


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Setting x = 0

21

22

21

21

2

1

2

2

(2

(2

vv

vvtz

vv

vvzt

i

i


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Crossover distance?

Time

Distance

Direct

Reflected


ti

Wh t i l ti hi f di t d h d


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For direct wave at crossover distance

T = xcross/V1

For critically refracted wave at crossover distance

T = xcross/V2 + 2z(V22- V12)1/2/ V22 V12

What is relationship of direct and headwave at crossover distance?

Tdirect = Thead


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xcross/V1 = xcross/V2 + 2z(V22- V1

2)1/2/ V22

V12


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Dipping Layer Case


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Dipping Layer Case


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Dipping Layer Case

(ic = c)

12 /cos/cos vizzvxT cbaABCD


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td

Dipping Layer Case

Apparent Velocities


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Apparent Velocities

How can you determine dip direction?


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2 ( ) / 2d uV V V

An approximate relationship between true and apparent velocities

for shallow angles of dip ( < 10) is given by:

How Can We Calculate V


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How Can We Calculate V2

when dip > 10o?

Remember (ic = c)

c= [sin-1 (V1/Vd) + sin-1 (V1/Vu)]

2

How Can We Calculate V


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How Can We Calculate V2

when dip > 10o?

V2

=V1/sin

c

Wh t b t th di ?


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What about the dip?

Remember (ic = c)

= [sin-1 (V1/Vu) sin-1 (V1/Vd)]

2


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V2 and dip when dip > 10o?

Remember (ic = c)

c= [sin-1 (V1/Vd) + sin

-1 (V1/Vu)]

= [sin-1 (V1/Vu) sin-1 (V1/Vd)]

2

2


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Lets Next Determine Depth Z at each end

12 /cos/cos vizzvxT cbaABCD


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Review Dipping Layer Case

td


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Knowing ta,tb ,V2 , V1 , andc we can determine our z valuesat each end of profile

acd tVxt 1/)sin(

1/)(cos2 Vzt caa

The down dip travle time td is given by:

where

Solving for z where t is intercept


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Solving for za where ta is intercept

for down-dip traveltime curve

za = taV1/(2cos c)

Relationship of za to da ?

1/)(cos2 vzt caa


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za = taV1/(2cosc)

da = za cos


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What about up-dip profile?

bcu tVxt 1/)sin(

1/)(cos2 Vzt cbb

where

Solving for zb where tb is intercept for up-dip


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Solving for zb where tb is intercept for up dip

traveltime curve

zb = tbV1/(2cos c)

Relationship of zb to db ?

1/)(cos2 vzt cbb


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zb = tbV1/(2cos c)

db = zb cos


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Santa Teresa Hills Experiment

T = 0.332x

R2 = 0.8731

T = 0.0705x + 18.367

R2 = 0.9849

T = 0.0954x + 10.985

R2 = 0.9913

T = 0.3033x

R2 = 0.9792

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0 30 60 90 120 150 180 210 240 270 300 330 360

Distance (feet)

Traveltime(milliseconds)

Direct Wave Forw ard

Head Wave Forw ard

Direct Wave Reverse

Head Wave ReverseLinear (Direct Wave Forw ard)

Linear (Head Wave Forw ard)

Linear (Head Wave Reverse)

Linear (Direct Wave Reverse)

Interpreted Plot

Include T intercepts and crossover distances

D t i Sl d I t t V l


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Determine Slopes and Intercept Values

y = 0.0954x + 10.985

R2

= 0.9913

y = 0.3187xR

2= 0.975

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

0 30 60 90 120 150 180 210 240 270 300 330 360


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M lti l Di i L C


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Multiple Dipping Layer Case


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Can layers exist in the subsurface that are not observable


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y

from first arrival times? Hidden Layers

N h d i t d t V /V b d


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No head wave is generated at V1/V2 boundary

Thickness of V Layer is too high and no V layer


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Thickness of V1 Layer is too high and no V2 layer

Thin Large Velocity Contrast Layers


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Thin, Large Velocity Contrast Layers


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Head waves are produced at both interfaces.Head wave coming from the top boundary is never observed as

a first arrival!!


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Existence of the hidden layer can not be determined from thetravel-time observations you probably will never know that

hidden layers existed under your survey.

That is, until the client begins to excavate or drill!!

Di ti it C


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Discontinuity Case


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Discontinuity Case


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Discontinuity Case

Checking between Multiple layer vs. Discontinuity

Identical single, end-on forward profile

Try off-end shot forward profile

Forward and Reversed Profiles


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Forward and Reversed Profiles

Spread

End-on Shots

Off-end shot Split Spread Shot

Discontinuity Case


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Discontinuity Case

Shift in Crossover Point


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Vertical Shift

2-layer case Horizontal shift multiple layer

Irregular Interface & Travel time Anomalies


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Irregular Interface & Travel time Anomalies

Isolated spurious travel time of a first arrival, due to amispick the first arrival or a mis-plot of the correct travel

time value

Changes in velocity or thickness in the near-surface region

Changes in surface topography

Zones of different velocity within the intermediate deprh

range

Localized topographic features on an otherwise planar

refractor

Lateral changes in refractor velocity

Irregular Interface & Traveltime Anomalies


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