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Multichannel Analysis of Surface Wave

Theory and Applications

_______________________________________

Presented at China University of Geosciences, Wuhan, PRCChengdu University of Technology, Chengdu, PRC

China University of Geosciences, Beijing, PRCNorth China Institute of Water Conservancyand Hydroelectric Power, Zhengzhou, PRC

June 5, 2000 June 15, 2000

Presented by

Jianghai Xia

Prepared byJianghai Xia, Richard D. Miller,

and Choon B. Park

Kansas Geological Survey

The University of Kansas

1930 Constant Avenue

Lawrence, KS 66047, USA

KGS Open-file Report 2000-25

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Theory and ApplicationsTheory and ApplicationsTheory and ApplicationsTheory and ApplicationsTheory and ApplicationsTheory and ApplicationsTheory and ApplicationsTheory and Applications

Multichannel Analysis of Surface WavesMultichannel Analysis of Surface WavesMultichannel Analysis of Surface WavesMultichannel Analysis of Surface WavesMultichannel Analysis of Surface WavesMultichannel Analysis of Surface WavesMultichannel Analysis of Surface WavesMultichannel Analysis of Surface Waves

(MASW)(MASW)(MASW)(MASW)(MASW)(MASW)(MASW)(MASW)

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Part 2

Verifications

Real World Examples

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A Pitfall in Shallow Shear-waveRefraction Surveying

An Interesting Real-World Example

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Construction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveConstruction of 2-D Vertical Shear-waveVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel AnalysisVelocity Field by the Multichannel Analysis

of Surface Wave Techniqueof Surface Wave Techniqueof Surface Wave Techniqueof Surface Wave Techniqueof Surface Wave Techniqueof Surface Wave Techniqueof Surface Wave Techniqueof Surface Wave Technique

Part 3

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Part 4

Future Study

1. Higher Modes

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Advantages of Calculating

Shear-wave Velocity fromSurface Waves with Higher Modes

Why Use Higher Modes?

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Outline

Introduction

Modeling ResultsA Real-World Example

Discussion and Conclusions

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Introduction

What are higher modes?

More than one phase velocity can be associated with a given

frequency of Rayleigh wave simply because these waves

can travel at different velocities for a given frequency.

The lowest velocity for any given frequency is called the

fundamental-modevelocity (or the first mode). The next

higher velocity above the fundamental-mode phase

velocity is called the second-modevelocity, and so on.

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Why do we need higher modes?

In some situations, highermodes take more energy

than the fundamental mode

in a higher frequency

range, which means thefundamental-mode data

may not be available in the

higher frequency range and

higher modes are the only

choice.

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An Example of Higher Modes

Data acquired in San Jose, California, in 1998

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Modeling Results

1. the sensitivity of

higher modes ofsurface waves,

2. investigation depth,

3. stability duringinversion.

The six layer model isused to analyze

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Selected papers on surface wave techniques (as of June 1, 2000)

1.Xia, J., Miller, R.D., and Park, C.B., 1999, Estimation of near-surface shear-wave velocity byinversion of Rayleigh wave: Geophysics, 64, 691-700.

2.Park, C.B., Miller, R.D., and Xia, J., 1999, Multi-channel analysis of surface waves:

Geophysics, 64, 800-808.3. Miller, R.D., Xia, J., Park, C.B., Ivanov, J., 1999, Multichannel analysis of surface waves to

map bedrock: The Leading Edge, 18, 1392-1396.

4. Xia, J., Miller, R.D., Park, C.B., Hunter, J.A., and Harris, J.B., 2000, Comparing shear-wavevelocity profiles from MASW with borehole measurements in unconsolidated sediments,

Fraser River Delta, B.C., Canada: September 2000 issue ofJournal of Environmental andEngineering Geophysics.

5. Park, C.B., Miller, R.D., and Xia, J., 1998, Imaging dispersion curves of surface waves onmulti-channel record: Technical Program with Biographies, SEG, 68th Annual Meeting,

New Orleans, Louisiana, 1377-1380.

6. Xia, J., Miller, R.D., Park, C.B., Wightman, E. and Nigbor, R., 1999, A pitfall in shallowshear-wave refraction surveying: Technical Program with Biographies, SEG, 69th

Annual Meeting, Houston, TX, 508-511.

7. Xia, J., Miller, R.D., Park, C.B., and Ivanov, J., 2000, Construction of 2-D vertical shear-wavevelocity field by the multichannel analysis of surface wave technique: Proceedings of the

Symposium on the Application of Geophysics to Engineering and Environmental

Problems (SAGEEP 2000), Arlington, Va., February 20-24, 2000, 1197-1206 .

8.Miller, R.D., Xia, J., Park, C.B., Shefchik W.T., and Moore, L., 1999, Seismic techniques todelineate dissolution features in the upper 1000 ft at a power plant site: Technical

Program with Biographies, SEG, 69th Annual Meeting, Houston, TX, 492-495.

9.Xia, J. Miller, R.D., Park, C.B., in review, Advantage of calculating shear-wave velocity fromsurface waves with higher modes: submitted to the 70th SEG Annual Meeting, Calgary,

Canada.

10. Xia, J., Miller, R.D., and Park, C.B., 1997, Estimation of shear wave velocity in acompressible Gibson half-space by inverting Rayleigh wave phase velocity: Technical

Program with Biographies, SEG, 67th Annual Meeting, Dallas, TX, 1927-1930.

11. Park, C.B., Miller, R.D., and Xia, J., 1999, Detection of near-surface voids using surface

wave: Proceedings of the Symposium on the Application of Geophysics to Engineering

and Environmental Problems (SAGEEP 99), Oakland, CA, March 14-18, 281-286.12. Park, C.B., Miller, R.D., and Xia, J., Hunter, J.A., and Harris, J. B., 1999, Higher mode

observation by the MASW method:Technical Program with Biographies, SEG, 69thAnnual Meeting, Houston, TX, 524-527.

13.Park, C.B., Miller,R.D, Xia, J., Ivanov, I., Hunter, J.A., Good, R.L., and Burns., R.A.,

Multichannel analysis of underwater surface waves: submitted to the 70th SEG Annual

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Sensitivity of Higher Modes

Second mode Third mode

Contribution to the higher-mode Rayleigh-wave phase

velocity by a 25% change in each earth parameter.

200

400

600

800

1000

1200

10 15 20 25 30 35 40

Frequency (Hz)

Second-modephasevelocity(m/s)

Model

S-wave

P-wave

Density

Thickness

400

500

600

700

800

900

1000

25 30 35 40 45

Frequency (Hz)

Third-modep

hasevelocity(m/s)

Model

S-wave

P-wave

Density

Thickness

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Penetrating Depth of Higher Modes

Experimental analysis indicates that energy ofhigher modes tends to become more dominant

as the source distance increases.

The Jacobian matrix of the higher-mode

Rayleigh-wave data suggests higher-mode data

have deeper investigation depths than do the

fundamental-mode data.

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Penetrating Depth

The open circles are therow vectors of theJacobian matrix associated

with the shortest wave-

length data.

A wavelength of 8.7 m

reaches zero at a depth of

13 m for the fundamental-mode data

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Rowve

ctor

134

63.6

20.7

12.3

8.7

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Penetrating Depth Comparison

Fundamental mode Second mode

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Rowvector

134

63.6

20.7

12.3

8.7

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Rowvector

93.2

40.8

17.9

13.6

10.9

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Penetrating Depth Comparison

Second mode Third mode

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Row

vector

93.2

40.8

17.9

13.6

10.9

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Row

vector

27.9

21.7

16.9

10.7

6

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Conclusion on Penetrating Depth

Higher-mode Rayleigh-wave data cansee deeper when compared to the

same wavelength components of the

fundamental-mode Rayleigh-wave data.

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Stability of Inversion with Higher Modes

The most significant result is that higher-mode data stabilizes the inversion process

and increases the resolution of inverted

S-wave velocities.

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Stability of Inversion

A difference of more than 100% in S-wave velocity models at

depths of 6 m and 7 m only result in a standard deviation of4.6m/s in the fundamental-mode data,

33.5m/s in second-mode data, and

27.3m/s in the third-mode data.

Differences in phase velocity S-wave velocity models

-50

0

50

100

150

0 10 20 30 40 50 60 70

Frequency (Hz)

Difference(m/s)

Fundamental

Second

Third

0

100

200

300

400

500

600

700

800

0 5 10 15 20

Depth (m)

Vsvelocity(m/s)

Model 1

Model 2

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A 100% difference in S-wave velocity models at depths of 6 m

and 7 m and 9 m and 10 m only result in a standard deviation of59m/s in the fundamental-mode data,

113m/s in second-mode data, and

110m/s in the third-mode data.


-50

0

50

100

150

200

250

300

350

0 10 20 30 40 50 60 70 80

Frequency (Hz)

Difference(m/s)

Fundamental

Second

Third

0

200

400

600

800

1000

1200

0 5 10 15 20

Depth (m)

Vsvelocity(m/s)

Model 1

Model 2

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A 80% difference in S-wave velocity models at depths of 6 m and

7 m and 9 m and 10 m only result in a standard deviation of13m/s in the fundamental-mode data,

45m/s in second-mode data, and



0

200

400

600

800

1000

0 5 10 15 20

Vs velocity (m/s)

Depth(m)

Model 1

Model 2-40

-20

0

20

40

60

80

100

120

140

160

180

0 10 20 30 40 50 60 70 80

Frequency (Hz)

Difference(m/s)

Fundamental

Second

Third

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80% difference in S-wave velocity models at depths from 3 m

to 6 m only result in a standard deviation of17m/s in the fundamental-mode data

66m/s in second-mode data



0100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20

Depth (m)

VsVelocity(m/s)

Model 1

Model 2-100

-50

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80

Frequency (Hz)

Difference(m/s)

Fundamental

Second

Third

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Conclusion on Stability

An inversion with higher mode data can

reject irrational model 2 due to itshigher RMS error. Model 2 may be

accepted by an inversion only with the

fundamental mode data due to its lower

RMS error.

A stabilized inversion can be achievedby including higher mode data in an

inversion process.

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A Real-world Example

San Jose, California, Fall of 1998

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Field Layout

To determine S-wave velocity in near-surface materials up to

10 m deep.

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Layered Model

A fourteen-layermodel with each

layer 1 m in

thickness.

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Shot gather and its image in F-K domain

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Fundamental Mode Data(Set One)

100

150

200

250

300

350

5 10 15 20 25

Frequency (Hz)

Phas

evelocity(m/s)

MEASURED

INITIAL

FINAL

100

150

200

250

300

350

400

450

0 5 10 15 20

Depth (m)

Shearwavevelocity(m/s)

INITIAL

INVERTED

Pink lines present results of inversion of fundamental mode of

surface wave data with errors.

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Fundamental Mode Data with Errors(Set Two)

0

100

200

300

400

500

600

0 5 10 15 20

Depth (m)

S-w

avevelocity(m/s)

Fundamental with e rror

Fundamental

Fundamental with error

plus s econd mode

Pink lines present results of inversion of fundamental mode of

surface wave data with errors.

100

150

200

250

300

350

5 10 15 20 25

Frequency (Hz)

Phasevelocity(m/s)

Measured

Initial

Final

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Fundamental Mode Data with Errors

Plus the Second Mode Data(Set Three)

0

100

200

300

400

500

600

0 5 10 15 20

Depth (m)

S-wa

vevelocity(m/s)

Fund amental with error

Fundamental

Fundamental with error

plus second mode

Yellow lines present results of inversion of fundamental mode

of surface wave data with errors plus the second mode data.

100

150

200

250

300

350

5 10 15 20 25 30

Frequency (Hz)

Phas

evelocity(m/s)

MEASURED

INITIAL

FINAL

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Discussion

In the real world, we normally make achoice between error and resolution of a

model. The instability that we see in the

inverted S-wave velocities of data set twois error in the inverted model, which can

be reduced by reducing the resolution of

the model.

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Trade off BetweenResolution and Error

100

200

300

400

500

0 5 10 15 20

Depth (m)

S-

wavevelocity(m/s)

INITIAL Vs

INVERTED Vs

NO ERROR

100

200

300

400

5 10 15 20 25

Frequency (Hz)

Ph

asevelocity(m/s)

MEASURED

INITIAL

FINAL

Resolution is reduced by one half (layer thickness is increased

to 2 m) to obtain a stable result (less model errors).

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Acknowledgments

The authors thank Geometrics, Inc. for itssupport in acquiring data used in this paper.

The authors also thank Rob Huggins, Craig

Lippus, Ming-Wen Sung, and Mark Prouty ofGeometrics for their assistance in acquiring

the seismic data. The authors also appreciate

the efforts of Mary Brohammer in manuscriptpreparation and submission.

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Future Study (continuation)

2. Accuracy of phase velocity

To extract phase velocity from higher

resolution image in the f-k domain and/orin the wavelet domain.

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3. Group Velocity and Attenuation

To extract S-wave velocity from groupvelocity and/or attenuation curve.

Both group velocity and attenuation arerelated to derivatives of phase velocity.

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4. Wave equation modeling andlaboratory modeling

To model cases such as a dipping layered earthmodel, voids in layered earth models, layered

model with S-wave velocity inversion (higher

velocity on the top of lower velocity layer).

To verify if there are any surface wave

reflections and/or refractions. If yes, in whatsituations they will occur.

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5. Resolution

Horizontal resolution of inverted S-wavevelocity changes with depth due difference

wavelengths.

Vertical resolutionstudy by modeling?

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6. Surface Wave Tomography

New 3-D near-surface technology

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Introduction

The Method Examples

Mapping bed rock, Olathe, Kansas

Imaging a steam tunnel, Lawrence, Kansas Mapping bed rock, Joplin, Missouri

Mapping dissolution features, Damascus, Alabama

Locating a pit site, Raleigh, North Carolina

Conclusions

Acknowledgements

2-D Vertical S-wave Velocity Map2-D Vertical S-wave Velocity Map2-D Vertical S-wave Velocity Map2-D Vertical S-wave Velocity Map

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INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONA Three-phase Research ProjectA Three-phase Research Project

1) acquisition of high-frequency broad band

ground roll

2) creation of efficient and accurate algorithmsto extract Rayleigh wave dispersion curves

from ground roll

3) development of stable and efficient inversionalgorithms to obtain near-surface S-wave

velocity profiles

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INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTION (continued)(continued)(continued)(continued)

A 2-D S-wave Velocity Section2-D S-wave Velocity Section2-D S-wave Velocity Section2-D S-wave Velocity Section2-D S-wave Velocity Section2-D S-wave Velocity Section2-D S-wave Velocity Section2-D S-wave Velocity Section

A combination of inverted S-wave velocity and

the standard CDP roll-along acquisition format

to generate a two-dimensional S-wave velocity

section

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THE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHOD

Acquiring data in CDP acquisition format

Extracting phase velocities of ground roll from

each shot gather

Generating a 1-D S-wave profile for each shot

Contouring a 2-D section of S-wave velocity field

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THE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHOD (continued)(continued)(continued)(continued)

75

100

125150

175

200

0 5 10 15

Frequency (Hz)

Phasevelo

city(m/s)

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THE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHODTHE METHOD (continued)(continued)(continued)(continued)

0

50

100

150

200

250

0 5 10 15 20 25 30

Depth (m)

120 140 160 180 200 220 240 260 280 300 320 340

120

100

80

60

40

20

0

Source station number

D

h

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THE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLESTHE REAL WORLD EXAMPLES

1. Mapping Bedrock (

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Olathe ExampleOlathe ExampleOlathe ExampleOlathe Example

Traces per shot:Traces per shot:Traces per shot:Traces per shot: 48484848

Sampling Rayleigh waves:Sampling Rayleigh waves:Sampling Rayleigh waves:Sampling Rayleigh waves:

2 to 94 ft2 to 94 ft2 to 94 ft2 to 94 ft

Length of four lines:Length of four lines:Length of four lines:Length of four lines: 1400 ft1400 ft1400 ft1400 ft

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GeophonesGeophonesGeophonesGeophones with spikes,with spikes,with spikes,with spikes, baseplatesbaseplatesbaseplatesbaseplates, or, or, or, orbaseplatesbaseplatesbaseplatesbaseplates with sandbagswith sandbagswith sandbagswith sandbags

Geophones with spikes andbaseplates

Geophones with baseplatesand baseplates with

sandbags

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GeophonesGeophonesGeophonesGeophones with spikes,with spikes,with spikes,with spikes, baseplatesbaseplatesbaseplatesbaseplates, or, or, or, orbaseplatesbaseplatesbaseplatesbaseplates with sandbagswith sandbagswith sandbagswith sandbags

spikes baseplates baseplates with sandbags

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GeophonesGeophonesGeophonesGeophones with spikes,with spikes,with spikes,with spikes, baseplatesbaseplatesbaseplatesbaseplates, or, or, or, or

baseplatesbaseplatesbaseplatesbaseplates with sandbagswith sandbagswith sandbagswith sandbags

Dispersion curves Inverted S-wave velocities

15 0

20 0

25 0

30 0

35 0

40 0

25 30 35 40 45 50 55 60

Freq ue nc y (Hz)

Sandbag

Plate

Spike

0

100

200

300

400

500

600

0 2 4 6 8 10

Depth (m)

S-w

avevelocity(m/s)

Sandbag

Plate

Spike

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OlatheOlatheOlatheOlathe (continued)(continued)(continued)(continued)

4.5 Hz geophone

with baseplate

12 lb hammer and

1 ft by 1 ft steel plate

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Observed frequency ofObserved frequency ofObserved frequency ofObserved frequency ofRayleigh waves:Rayleigh waves:Rayleigh waves:Rayleigh waves:

20 to 60 Hz20 to 60 Hz20 to 60 Hz20 to 60 Hz

Observed wavelength ofObserved wavelength ofObserved wavelength ofObserved wavelength of

Rayleigh waves:Rayleigh waves:Rayleigh waves:Rayleigh waves:


A ten-layer model

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Line 1, on asphalt parking lotLine 1, on asphalt parking lotLine 1, on asphalt parking lotLine 1, on asphalt parking lot

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1030 1040 1050 1060 1070 1080 1090 1100 1110 1120 1130 1140 1150 1160 1170 1180 1190 1200 1210

Station Number

30

25

20

15

10

5

0

Dep

th(ft)

0 800 1200 1600 2000 2400 2800

0 20 40 60 80

Contour interval is 200 ft/s.

ft/s

ft

S N

A 2-D S-wave velocity map of line 1, Olathe, KansasA 2-D S-wave velocity map of line 1, Olathe, KansasA 2-D S-wave velocity map of line 1, Olathe, KansasA 2-D S-wave velocity map of line 1, Olathe, Kansas

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Line 2, on asphalt parking lotLine 2, on asphalt parking lotLine 2, on asphalt parking lotLine 2, on asphalt parking lot

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2030 2040 2050 2060 2070 2080 2090 2100 2110 2120 2130 2140 2150 2160 2170 2180 219030

25

20

15

10

5

0

0 800 1200 1600 2000 2400 2800

0 20 40 60 80

ft/sft

Station Number

Depth(ft)

W E


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4030 4040 4050 4060 4070 4080 4090 4100 4110 4120 4130 4140 4150 4160 4170 4180 4190

Station number

30

25

20

15

10

5

0

Depth(ft)

0 800 1200 1600 2000 2400 2800ft/s

Contour interval is 200 ft/s.

W E


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EXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLES (continued)(continued)(continued)(continued)

2.2.2.2.2.2.2.2. Imaging a Steam Tunnel (

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Steam Tunnel Testing SiteSteam Tunnel Testing SiteSteam Tunnel Testing SiteSteam Tunnel Testing Site

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Steam TunnelSteam TunnelSteam TunnelSteam Tunnel (continued)(continued)(continued)(continued)

Traces per shot:Traces per shot:Traces per shot:Traces per shot: 30303030

Sampling Rayleigh waves:Sampling Rayleigh waves:Sampling Rayleigh waves:Sampling Rayleigh waves:


76 shots along a line76 shots along a line76 shots along a line76 shots along a line

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IVIIVIIVIIVI MinivibMinivibMinivibMinivib

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The observed frequencyThe observed frequencyThe observed frequencyThe observed frequency

of Rayleigh waves:of Rayleigh waves:of Rayleigh waves:of Rayleigh waves:

10 to 50 Hz

The observed wavelengthThe observed wavelengthThe observed wavelengthThe observed wavelengthof Rayleigh waves:of Rayleigh waves:of Rayleigh waves:of Rayleigh waves:

4 to 65 ft

Thickness of the layersThickness of the layersThickness of the layersThickness of the layersFirst four layers:First four layers:First four layers:First four layers: 3.3 ft each

Last five layers:Last five layers:Last five layers:Last five layers: 6.6 ft each

A ten-layer model


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At beginning of line At top of tunnel

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The difference between the twodispersion curves indicates the

existence of an anomalous

subsurface.

Relatively lower phase velocity

(pink line) in lower frequencies

(< 17 Hz) suggests low S-wave

velocity at a relatively deeper

depth. Relatively higher phasevelocity in a range (> 20 Hz)

suggests very shallow materials

are compacted.

700

800

900

1000

1100

1200

13 17 21 25 29 33

Frequency (Hz)

Phasevelocity(ft/

s)

Station 1001

Station 1060

Dispersion curves for imaging beginning of line and top of tunnelDispersion curves for imaging beginning of line and top of tunnelDispersion curves for imaging beginning of line and top of tunnelDispersion curves for imaging beginning of line and top of tunnel

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1010 1020 1030 1040 1050 1060 107030

25

20

15

10

5

0

Depth(ft)

Station Number

200 500 700 900 1100 1300 1500

0 20 40 60 80 Feet

S-wave velocity map, Steam Tunnel at KUS-wave velocity map, Steam Tunnel at KUS-wave velocity map, Steam Tunnel at KUS-wave velocity map, Steam Tunnel at KU

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1010 1020 1030 1040 1050 1060 1070

30

25

20

15

10

5

0

-350 -250 -150 -50 50 150 250

Depth

(ft)

Station Number

ft/s0 20 40 60 80 Feet

Residual S-wave velocity, first-order trend removed,Residual S-wave velocity, first-order trend removed,Residual S-wave velocity, first-order trend removed,Residual S-wave velocity, first-order trend removed,

Steam Tunnel, KUSteam Tunnel, KUSteam Tunnel, KUSteam Tunnel, KU

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3. Mapping Bedrock Surface (

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Joplin ExampleJoplin ExampleJoplin ExampleJoplin Example

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JoplinJoplinJoplinJoplin (continued)(continued)(continued)(continued)

Traces per shot: 34

Sampling Rayleigh waves:

4 to 132 ft

Observed frequency of

Rayleigh waves: 10 to 25 Hz

Observed wavelength ofRayleigh waves: 40 to 100 ft

A five-layer model

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Shot for imaging station 1050 Shot for imaging station 1326

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Dispersion curves for imaging stations 1050 and 1326

800

900

1000

1100

1200

1300

17 19 21 23 25 27 29

Frequency (Hz)

Phasevelocity(ft/s)

Station 1050

Station 1326

200 ft/s difference

between these two

dispersion curves:

station 1050 is at thebeginning of the line,

and station 1326 is at

the location of the

second well.

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1050 1100 1150 1200 1250 1300 1350100

80

60

40

20

0

0 800 1200 1600 2000 2400 2800 3200 3600

Well, 70 ft to bedrock Well, 40 ft to bedrockFill Gravel road

Depth(ft)

Station number

0 50 100 150 200 ftft/s

A 2-D S-wave velocity map of line 1, Joplin, MissouriA 2-D S-wave velocity map of line 1, Joplin, MissouriA 2-D S-wave velocity map of line 1, Joplin, MissouriA 2-D S-wave velocity map of line 1, Joplin, Missouri

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Feet

50 100 150 200 250 300

100

80

60

40

20

0

Well, 36 ft to bedrock Well, 51 ft to bedrock

0 50 100 150 200

Depth(f

t)

Station number

0 800 1200 1600 2000 2400 2800 3200 3600ft/s

A 2-D S-wave velocity map of line 2, Joplin, MissouriA 2-D S-wave velocity map of line 2, Joplin, MissouriA 2-D S-wave velocity map of line 2, Joplin, MissouriA 2-D S-wave velocity map of line 2, Joplin, Missouri

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EXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLES (continued)(continued)(continued)(continued)4. Mapping Dissolution Feature (

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Line LocationLine LocationLine LocationLine Location

MapMapMapMap

13 lines13 lines13 lines13 lines

2,500 shots2,500 shots2,500 shots2,500 shots

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Working SiteWorking SiteWorking SiteWorking Site

Damascus ExampleDamascus ExampleDamascus ExampleDamascus Example (continued)(continued)(continued)(continued)

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A rubber band accelerated weight dropperA rubber band accelerated weight dropperA rubber band accelerated weight dropperA rubber band accelerated weight dropper

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DamascusDamascusDamascusDamascus (continued)(continued)(continued)(continued)

A survey lineA survey lineA survey lineA survey line

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224 shots along line 1

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Traces per shot: 48

Sampling Rayleigh waves:

4 to 188 ft

Observed frequency of

Rayleigh: 5 to 22 Hz

Observed wavelength ofRayleigh waves:

25 to 200 ft

A fourteen-layer model


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A 2-D S-wave velocity map of line 1A 2-D S-wave velocity map of line 1A 2-D S-wave velocity map of line 1A 2-D S-wave velocity map of line 1

Two distinguished S-wave velocity lows are around stations 1050 and 1270 from 40 to 100 ft

depth. The weathered limestone surface is interpreted along the 1,200 ft/s contour line.

Depth(ft)

Station Number

ft

W E

1030 1050 1070 1090 1110 1130 1150 1170 1190 1210 1230 1250 1270 1290 1310 1330 1350 1370 1390 1410 1430 1450

120

100

80

60

40

20

0

0 80 160 240 3200 200 400 600 800 1000 1200 1400 1600 ft/s

DamascusDDDamascus (continued)(continued)(continued)(continued)

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DamascusDamascus

2050 2070 2090 2110 2130 2150 2170 2190 2210 2230 2250 2270 2290 2310 2330 2350 2370 2390 2410 2430 2450 2470

120

100

80

60

40

20

0

N S

0 80 160 240 320

Station Number

Dept

h(ft)

0 200 400 600 800 1000 1200 1400 1600ft/s

ft

A 2-D S-wave velocity map of line 2A 2-D S-wave velocity map of line 2A 2-D S-wave velocity map of line 2A 2-D S-wave velocity map of line 2

EXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLES ( ti d)( ti d)( ti d)( ti d)

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5. Pit site location (< 40 ft), Raleigh, North Carolina5. Pit site location (< 40 ft), Raleigh, North Carolina5. Pit site location (< 40 ft), Raleigh, North Carolina5. Pit site location (< 40 ft), Raleigh, North Carolina

(250 shots acquired along two lines)

Source: one ground impacts from 8 lb. hammer

Source spacing: 2 ft

Geophone: Single 4.5 Hz vertical component geophone

Geophone spacing: 2 ft

Nearest source-geophone offset: 24 ft

48-channel48-channel48-channel48-channel Geometrics StrataViewGeometrics StrataView

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8888 lblblblb Hammer and 1 ft by 1 ft plate (DELRIN)Hammer and 1 ft by 1 ft plate (DELRIN)Hammer and 1 ft by 1 ft plate (DELRIN)Hammer and 1 ft by 1 ft plate (DELRIN)

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4 5 Hz vertical component4 5 Hz vertical component4 5 Hz vertical component4 5 Hz vertical component geophonegeophonegeophonegeophone

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4.5 Hz vertical component4.5 Hz vertical component4.5 Hz vertical component4.5 Hz vertical component geophonegeophonegeophonegeophone

Raleigh, North CarolinaRaleigh, North CarolinaRaleigh, North CarolinaRaleigh, North Carolina

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1040 1060 1080 1100 1120 1140 1160 1180 1200 1220 1240 126030

25

20

15

10

5

0

0 20 40 60 80Station Number

Depth(ft)

200 600 1000 1400 2000 2400 2800 ft/s

S-wave velocity section of line 1


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2110 2120 2130 2140 2150 2160 2170 2180 2190 2200 2210 2220 2230 224030

25

20

15

10

5

0

200 600 1000 1400 2000 2400 2800

Station Number

Depth(ft)

ft/s0 10 20 30 40 ft

S-wave velocity section of line 2

CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS

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CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS1. Shallower target investigationShallower target investigationShallower target investigationShallower target investigation

High-frequency (>2 Hz) ground roll

Investigation depth from 5 to 100 feet

2. Feasibility in noisy environmentsFeasibility in noisy environmentsFeasibility in noisy environmentsFeasibility in noisy environments

Ground roll, high signal-to-noise ratio, allowing 2-D

images to be obtained in noisy environments

3.EfficiencyEfficiencyEfficiencyEfficiency

The standard CDP roll-along acquisition methodprovides an efficient way to acquire large quantities of

broadband surface wave data along a line

CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS (continued)(continued)(continued)(continued)

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CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS (continued)(continued)(continued)(continued)4.ReliabilityReliabilityReliabilityReliability

The redundancy of the CDP acquisition method providesa reliable way to verify inverted S-wave velocities so that

it reduces the ambiguity of inverted S-wave velocities

5. SimplicitySimplicitySimplicitySimplicity

A contouring software: from a 1-D S-wave velocity profile

to a 2-D S-wave velocity map

6. Anomaly enhancementAnomaly enhancementAnomaly enhancementAnomaly enhancement

2-D data processing techniques can be applied to a 2-D

S-wave velocity section to enhance local anomalies

ACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTS

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ACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTS

The authors would like to thank Brett Bennett, David

Laflen, Joe Anderson, Tom Weis, and Chad Gratton for their

assistance during the field tests.

The authors appreciate the efforts of Mary Brohammer,

John Charlton, and Amy Stillwell in manuscript and slide

preparations.

Outline

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OutlineIntroduction

A Real World Example

SH-wave Refraction Survey

P-wave Refraction Survey

Explanation

MASWAn Alternative for Determining

S-wave Velocity

S-wave Velocity from Suspension LoggingConclusions

Introduction

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Introduction

For a ser ies of

hor izontal layers,

a pure, plane SH

wave refracts andreflects only SH

waves. There is

no wave-typeconversion.

Introduction (continued)

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However, complex near-surface geology

may not fit into the assumption of a ser ies

of horizontal layers. That a plane SH waveundergoes wave-type conversion along an

interface in an area of non-horizontal layers

is theoretically inevitable.


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Can we recognize converted waves?

How do we find true S-wave velocities ifwave-type conversion really occurs?

A Real-World Example

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A Real World Example

A shallow SH-wave refraction survey wasconducted in Wyoming during the fall of

1998 to determine shear-wave velocities in

near-surface materials up to 7 m deep.

SH-wave Source

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Field Layout for SH-wave Refraction Survey

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y y

SH-wave Refraction Data

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A Layer Model from SH-wave Data

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Compared

with the SH-

wave velocityof the first

layer, the SH-

wave velocity

of the second

layer is more

than double.

Are velocities of the second and thirdlayers the true SH-wave velocities, or

are they converted P-wave velocities?

Field Layout for P-wave Refraction Survey

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y y

P-wave Refraction Data

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A Layer Model from SH-wave Data

P wave

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P-wave

velocities of

the second

and third

layers are

almost the

same as therelevant

SH-wave

velocities.

Velocities from SH-wave refractionsurvey actually are converted P-wave

velocities.

Explanation

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p

Field Layout for MASW Survey

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Surface Wave Data

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Dispersion C r e S a e Velocit Model

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Dispersion Curve S-wave Velocity Model

150

200

250

300

350

400

450

10 15 20 25 30Frequency (Hz)

Measured (E)

Final (E)

Measured (W)

Final (W)

0

100

200

300

400

500

600

0 5 10 15 20

Dep th (m)

Inverted (E)

Inverted (W)

S-wave Velocities from

SH-wave Refraction and MASW

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S-wave Velocity from Suspension Logging

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To confirm

the inverted

S-wavevelocity, a

borehole was

drilled on the

site andsuspension

logging was

conducted.

Be CarefulWhen Doing SH-wave Refraction Surveys

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When Doing SH-wave Refraction Surveys

In a case of a

dipping layer, SH-P

conversion will

occur if a surveyline is not parallel to

Yaxis.

Conclusions

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Shallow shear-wave refraction survey may not provide the

true S-wave velocity because of wave-type conversion in

an area of non-horizontal layers.

To verify if velocities based on shear-wave refraction

surveys are velocities of converted waves, an additional

P-wave refraction survey is necessary.

The best alternative at this time is MASW, which can

provide reliable S-wave velocities, even in an area of

velocity inversion (a higher velocity layer underlain bya lower velocity layer).

Acknowledgments

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The authors wish to thank Blackhawk Geometrics for

their permission to publish the seismic data presentedherein. Authors extend their thanks to Bart Hoekstra

of Blackhawk Geometrics for acquiring seismic data

and to Julian Ivanov for constructive discussions onthis topic. The authors also appreciate the efforts of

Mary Brohammer and Amy Stillwell in manuscript

preparation.

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Comparing Shear-Wave Velocity Profiles

from MASW with Borehole Measurementsin Lawrence, Kansas

One Detailed Real-World Example

Testing SiteKGS Front Yard

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Field Layout

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Raw Data

Seismograph:

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Seismograph:

Geometr ics StrataView

Seismic Source: I VI M inivib

Geophone:

10 Hz vertical component

Acquisition filter:

No

Recording length:

1024 mil l iseconds

Sample interval:

1 mil l isecond

Layered Model for Inversion

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A ten-layer model

with a one meterthick top layer

gradually increasing

to a 6 meter layeron the bottom.

Dispersion Curves S-wave Velocity Models

1000

M d

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0

100

200

300

400

500

600

700

800

900

15 20 25 30 35 40 45 50 55 60 65 70 75 80

Frequency (Hz)

Phasevelocity(m/s

)

Measured

Initial A

Final A

Initial B

Final B

Three-component borehole data were acquired. Overall error in S-wave

velocity of the borehole survey is 10%.

Effects of Initial Models

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0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35 40

Depth (m)

S-wavevelocity(m/s)

100

200

300

400

500

600

700

800

900

Borehole

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35 40

Depth (m)

S-wavevelocity(m/s)

half

Quarter

half-h

Inverted B

Borehole

Initial models are blindly selected as a uniform half-space with a

constant S-wave velocity from 100 m/s to 1,800 m/s.

Effect of the Number of Data Points

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Half (solid diamonds):

33 points from 15 to 47 Hz;Quarter (solid squares):

17 points from 15 to 31 Hz;

Half-h (solid tr iangles):17 points from 15 to 47 Hz

at 2 Hz interval, and

Inverted B (Solid circles):

66 points from 15 to 80 Hz.

0

200

400

600

800

1000

1200

1400

1600

0 5 10 15 20 25 30 35 40

Depth (m)

S-wavevelocity(m/s)

half

Quarter

half-hInverted B

Borehole

Summary

The proposed inversion is stable. 1. Inverted

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The proposed inversion is stable. 1. Inverted

models do not seem to be too sensitive to

initial models; 2. The inversion is continuously

improving inverted modes during inversion

processing.Inverted S-wave velocities are reliable. A 15%

difference can be expected between inverted

S-wave velocities and borehole measurements.

Comparing Shear-Wave Velocity Profilesfrom MASW with Borehole Measurements

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in the Fraser River Delta,

Vancouver, Canada

Eight Real-World Examples

Testing Site

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Common Parameters

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Seismograph: Geometr ics StrataView

Seismic Source: Weight dropper (bui l t by KGS)

Geophone: 4.5 Hz vertical component

Acquisition filter: NoRecording length: 2048 mil l iseconds

Sample interval: 1 mil l isecond

Field Layout

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Field Layout for Borehole FD95-2

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Borehole FD95-2140

150

160

170

ocity(m/s)

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100

110

120

130

5 10 15 20 25

Frequency (Hz)

Phasevelo

Measured

Final

0

50

100

150

200

250

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s)

Borehole FD95-2

Inverted

Borehole FD95-2

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Wavelength Range: 6 - 23 m

Phase Velocity Range: 130 - 158 m/s

Frequency Range: 7 - 23 Hz

Depth Studied: 30 m

Inverted S-wave Velocity Range: 111 - 206 m/s

Average Relative Difference: 10%

Average Difference: 19 m/s


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Borehole FD97-2

140

150

160

170

180

evelocity(m/s)

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100

110

120

130

0 5 10 15 20

Frequency (Hz)

Phase

Measured

Final

0

50

100

150

200

250

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s)

Borehole FD97-2

Inverted

Borehole FD97-2

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Depth Studied: 30 m





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120

140

160

180

200

evelocity(m/s) Measured

FinalBorehole FD92-11

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60

80

100

0 5 10 15 20 25 30

Frequency (Hz)

Phase

0

50

100

150

200

250

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s)

Borehole FD92-11

Inverted

Cross hole

Borehole FD92-11

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Depth Studied: 30 m





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Borehole FD92-3

100

150

200

250

300

350

Phasevelocity(m/s)

Measured

Final

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0

50

100

0 5 10 15 20

Frequency (Hz)

0

100

200

300

400

500

600

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s)

Borehole FD92-3

Inverted

Borehole FD92-3

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Depth Studied: 30 m

Inverted S-wave Velocity Range:82 - 404 m/s



Field Layout for Borehole Unknown

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Borehole Unknown

100

150

200

250

Phasevelocity(m/s)

M d

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50

10 15 20 25

Frequency (Hz)

Measured

Final

0

50

100

150

200

250

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity

(m/s)

Inverted Vs

Borehole

Borehole Unknown

W l th R 7 60

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Depth Studied: 30 m





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Borehole FD86-5

100

110

120

130

140

150

Phasevelocity(m/

s)

Measured

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80

90

0 5 10 15 20 25 30

Frequency (Hz)

Final

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s)

Borehole FD86-5

Inverted

Borehole FD86-5

Wavelength Range: 4 29 m

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Depth Studied: 30 m





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Borehole FD92-4

100

150

200

250

Phasevelocity(m/s)

Measured

Final

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500 5 10 15 20 25 30

Frequency (Hz)

0

50

100

150

200

250

300

350

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s

)

Borehole FD92-4

Inverted

Borehole FD92-4


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Frequency Range: 3.5 - 25 Hz

Depth Studied: 30 mInverted S-wave Velocity Range: 92 - 311 m/s




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Borehole FD97-7

30

40

50

60

70

Phasevelocity(m/s)

Measured

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20

0 2 4 6 8

Frequency (Hz)

Final

0

20

40

60

80

100

120

0 2 4 6 8

Depth (m)

S-wavevelocity(m/s)

Borehole FD97-7

Inverted

Borehole FD97-7


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Wavelength Range: 4 31 m



Depth Studied: 7 mInverted S-wave Velocity Range: 29 - 67 m/s



Reasons for differences

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Body waves and/orhigher-mode

Rayleigh waves.

Sharpness of

dispersion curve in

the F-K domain.


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Heterogeneity of thenear-surface materials.

Borehole measurement is

in vertical direction and

the MASW S-wave

velocity is is horizontal

direction.


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Random noise and/or reflected ground roll.

Non-uniqueness in the inversion of Rayleigh wave

data and a local minimum search of the inverse

algorithm.

The first arrival picking on borehole data.

Conclusions

The overall difference between S-wave velocities from the

MASW method and borehole measurements is 15%.

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Most errors can be associated with random and coherentnoise and accuracy of borehole measurements.

Differences between S-wave velocities from the MASW

method and borehole measurements appear to berandom.

This comparison demonstrates the reliability and accuracy

of S-wave velocities estimated from the MASW methodin unconsolidated sediments.

Acknowledgments The authors would like to thank Brett Bennett,

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David Laflen, Ron Good, Jim Droddy, andChad Gratton for their assistance during the

field tests.

The authors appreciate the efforts ofMary Brohammer, John Charlton, and

Amy Stillwell in manuscript preparations.

Presented atPresented at

China University of Geosciences, Wuhan

Chengdu University of Technology, Chengdu

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China University of Geosciences, BeijingNorth China Institute of Water Conservancyand Hydroelectric Power, Zhengzhou

June 5, 2000 June 15, 2000

ByBy Jianghai Xia

[email protected]

Prepared byPrepared byPrepared byPrepared byPrepared byPrepared byPrepared byPrepared by

Jianghai XiaJianghai XiaJianghai XiaJianghai XiaJianghai XiaJianghai XiaJianghai XiaJianghai Xia

Richard D. MillerRichard D. MillerRichard D. MillerRichard D. MillerRichard D. MillerRichard D. MillerRichard D. MillerRichard D. Miller

Choon B. ParkChoon B. ParkChoon B. ParkChoon B. ParkChoon B. ParkChoon B. ParkChoon B. ParkChoon B. Park

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Kansas Geological SurveyKansas Geological SurveyKansas Geological SurveyKansas Geological SurveyKansas Geological SurveyKansas Geological SurveyKansas Geological SurveyKansas Geological Survey

The University of KansasThe University of KansasThe University of KansasThe University of KansasThe University of KansasThe University of KansasThe University of KansasThe University of Kansas

I would like to thank the following people who made this trip

successful.

Prof. Jiaying Wang, Vice President of China University of

AcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgments

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Geosciences, Wuhan;

Prof. Yixian Xu, Chairman of Department of Geophysics, CUG;

Prof. Zhenhua He, President of Chengdu University of Technology;

Prof. Xuben Wang, Chairman of Department of Geophysics, CUT;Prof. Qinfan Yu and Prof. Xiaohong Meng, China University of

Geosciences, Beijing; and

Prof. Xujin Sun, North China Institute of Water Conservancy andHydroelectric Power.

I greatly appreciate Prof. Richard Miller, Chief of Exploration

Services, Kansas Geological Survey, for his motivation

AcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgments

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and support of this trip.

I would also like to thank the Kansas Geological Survey for

the continuous support to this project during the last fiveyears.

TheoryTheory

OutlineOutlineOutlineOutlineOutlineOutlineOutlineOutline

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VerificationsVerifications

2-D S-wave Velocity Sections2-D S-wave Velocity Sections

Future StudiesFuture Studies

Part 1Part 1Part 1Part 1Part 1Part 1Part 1Part 1

TheoryTheory

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From field shot gather toS-wave velocity profile

MultichannelMultichannelrecording systemrecording system

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Raw Field DataRaw Field Data

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Surface wave background

TheoryOutlineTheoryOutlineTheoryOutlineTheoryOutlineTheoryOutlineTheoryOutlineTheoryOutlineTheoryOutline

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Calculation of dispersion curve

Inversion of dispersion curve

Parameters of a layered earth model Equipment and data acquisition

parameters

TheorySurface waveTheorySurface waveTheorySurface waveTheorySurface waveTheorySurface waveTheorySurface waveTheorySurface waveTheorySurface wave

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TheoryPenetrating depthTheoryPenetrating depthTheoryPenetrating depthTheoryPenetrating depthTheoryPenetrating depthTheoryPenetrating depthTheoryPenetrating depthTheoryPenetrating depth

Penetrating depth is

about one wavelength.

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Longer wavelengths

can see deeper than

shorter wavelengths.

In a homogeneous

half-space, Rayleigh

wave velocity is about

0.92Vs if Poissonsratio = 0.25.

TheoryModel responseTheoryModel responseTheoryModel responseTheoryModel responseTheoryModel responseTheoryModel responseTheoryModel responseTheoryModel response A B S-wave velocity

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TheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curve

1.

U(x,t) is a shot gather in the offset-time domain

= dtetxuwxUiwt),(),(

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U(x,w) isa shot gather in the offset-frequency domain after applied the

Fourier transform to U(x,t).

U(x,w)can be expressed as the multiplication of phase and amplitudespectrum

),(),( wxAewxU xi= wcw /=

wis frequency in radian and cwis phase velocity for frequency w.

TheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curveTheoryCalculation of dispersion curve

2. Applying integral transformation toU(x,t)

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dxwxUwxUewVxi ]),(/),([),( =

( )dxwxAwxAe

xi ]),(/),([ =

Because A(x,w)is both real and positive, will have a

maximum if

=

),( wV

Example of dispersion curve imageExample of dispersion curve imageExample of dispersion curve imageExample of dispersion curve imageExample of dispersion curve imageExample of dispersion curve imageExample of dispersion curve imageExample of dispersion curve image

FD97-1

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TheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curve

OutlineOutlineOutlineOutlineOutlineOutlineOutlineOutline

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Forward calculation

Partial derivatives of phase velocity function

Sensitivity of earth model parameters

Inversion algorithms

TheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curveTheoryInversion of dispersion curve

Layered earth model, four parametersLayered earth model, four parametersLayered earth model, four parametersLayered earth model, four parameters Free surfaceFree surface

___________________________________

vs1 vp1 1 h1

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_____________________________________________

vs2 vp2 2 h2

_____________________________________________

.

.

.

_____________________________________________

vsi vpi i hi

_____________________________________________

.

.

.

_____________________________________________

vsn vpn n infinite

Forward calculationForward calculationForward calculationForward calculationForward calculationForward calculationForward calculationForward calculation

Fj(fj, cRj, vs, vp, d, h) = 0, (j= 1, 2, ..., m)

m: the number of data points

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m: the number of data points,

fj: the frequency,

cRj: the Rayleigh wave phase velocity,

vs= (vs1, vs2, ..., vsn)T: the S-wave velocity vector,

vp= (vp1, vp2, ..., vpn)T: the P-wave velocity vector,

d = (d1, d2, ..., dn)T: the density vector, andh = (h1, h2, ..., hn-1)

T: the thickness vector

Partial derivatives of the phasePartial derivatives of the phasePartial derivatives of the phasePartial derivatives of the phasePartial derivatives of the phasePartial derivatives of the phasePartial derivatives of the phasePartial derivatives of the phasevelocity functionvelocity functionvelocity functionvelocity functionvelocity functionvelocity functionvelocity functionvelocity function

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The Jacobian matrix calculated by

Ridders methodone numericalmethod.

Sensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parameters

The six-layer model is

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The six-layer model isused to analyze

the sensitivity of

higher modes ofsurface waves.

Sensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parametersSensitivity of earth model parameters

Why only S-wave velocity?

Model Parameters model (%) data (%)

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P-wave Velocity 25 3

Density 25 10

S-wave Velocity 25 39

Thickness 25 16

S-wave velocity is the dominant property for the fundamental mode of

high-frequency Rayleigh wave dispersion data.

Based on the sensitivity analysis of four groups of earth

model parameters: S-wave velocity, P-wave velocity,

density, and thickness of layers, S-wave velocity is

dominant. If we can get good estimates of P-wave velocity

Why only S-wave velocity?

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do a t. we ca get good est ates o wave ve oc tyand density, we can only invert S-wave velocity from phase

velocities of surface waves.

The following discussion assumes P-wave velocity and

density are known. Only S-wave velocities are updated

during the inversion procedure based on the layered earth

model.

Inversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithms

Objective function:

2

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2

222xbJxWbJx +=

SolutionSolutionSolutionSolutionSolutionSolutionSolutionSolution

( ) dUIVxT

1

2

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Where dis the vector of difference between modeled

and measured data, V, , and U are the SVD matrixesof the weighted Jacobian matrix A.

( ) dUIVx += 2

TheoryTheoryTheoryTheoryTheoryTheoryTheoryTheory

Parameters of a layered earth modelParameters of a layered earth modelParameters of a layered earth modelParameters of a layered earth modelParameters of a layered earth modelParameters of a layered earth modelParameters of a layered earth modelParameters of a layered earth model

1. Initial values of S-wave velocities:

v = c (high)/A (for the first layer)

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vs1= cR(high)/A, (for the first layer)

vsn= cR(low)/A, (for the half space)

vsi = cR(i)/A, (i = 2, 3, ..., n-1)

A = 0.88

Initial values of S-wave velocities are

determined based on dispersion curve data.



Based on analysis of sensitivity of earth model

parameters, the other three groups of

parametersP-wave velocities, densities, and

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p , ,

thickness of layersare not changed during

inversion procedure.

2. P-wave velocities can be determined from the

first arrivals of surface wave data. The first

arrivals are refraction information on P-wave

velocities.



3. Densities can be chosen from 1.62.2 g/cc for

shallow sedimentary geology. Based on our

experience, this range of density gives enough

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p , g y g g

accuracy for inverted S-wave velocities up to

100 ft depth.



4. The depth to the top of the half-space is

determined by your investigation depth. Ten tofifteen layers is a good place to start with testing

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y y g pfifteen layers is a good place to start with testing.

After determining the number of layers, the

thickness of each layer can easily be defined.

Make sure the maximum wavelength is greater

than the investigation depth.



Trade-off between resolution and accuracy

The thickness of layers basically is a measurement

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y y

of the vertical resolution. The vertical resolution

is limited by accuracy of the dispersion curve. In

the case of low accuracy of dispersion curve data,

you should reduce the number of layers (increase

thickness of each layer) to reduce uncertainty of

the inverted S-wave velocities (stabilize inversion).

SummarySummarySummarySummarySummarySummarySummarySummary

From shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profileFrom shot gather to S-wave velocity profile

160

170250

f-k transformation Inversion

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100

110

120

130

140

150

5 10 15 20 25

Frequency (Hz)

Phasevelocity(m/s)

Measured

Final

0

50

100

150

200

0 5 10 15 20 25 30

Depth (m)

S-wavevelocity(m/s)

Borehole FD95-2

Inverted

Multichannel raw data Dispersion curve S-wave velocity

Synthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic Examples

Two-layer modelsTwo-layer modelsTwo-layer modelsTwo-layer models

500600

700

(m/s)

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0

100

200

300

400

5 15 25 35 45 55 65 75

Frequency (Hz)

Phasevelocity

Measured

Initial

Final

Thickness of top layer: 2 m



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Why use two-layer models?

One direct application of a two-layer model is

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static correction in S-wave reflection and

refraction survey in oil industry.


A multilayer modelEffects of P-wave velocity and density

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25% change (1) in S; (2) in S and P; (3) in S and density; and

(4) in S, P, and density.

Data Acquisition Equipment:Data Acquisition Equipment:

Seismic SourcesSeismic SourcesA surface impact source

can generate surfacewave enriched

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wave e c ed

records. Enriched

means wavelengths of

surface waves evenly

cover the range of

investigation depth.

Seismic SourcesSeismic Sources

1. Industrial Vehicle International (IVI) MinivibDownward weight 6,000 lb.

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Investigation depth: 1 to 30 meters


2. KGS-built weight dropper

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Investigation depth: 2 to 30 meters


3. Sledgehammer and plate

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Investigation depth: 0.5 to 15 meters

Seismograph48 to 60 channelsSeismograph48 to 60 channels

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60-channel Geometrics StrataView

GeophonesGeophones4.5 to 10 Hz vertical4.5 to 10 Hz vertical

componentcomponent geophonegeophone

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Geophone with spike Geophone with baseplate

GeophonesGeophones4.5 to 10 Hz vertical4.5 to 10 Hz vertical

componentcomponentgeophonegeophone

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Geophone on tiles Geophone on carpet

Data Acquisition ParametersData Acquisition Parameters

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A. Nearest source-receiver offset

B. Receiver spacing

C. Receiver spread: distance between the firstreceiver and the last receiver


Nearest source-receiver offsetNearest source-receiver offset

Near-offset effect: Lower frequency components are

not fully developed as plane waves.

Plane-wave propagation of surface waves occurs

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when the nearest source-receiver offset is greater

than half the maximum desired wavelength.The maximum desired wavelength is about equal to

the maximum investigation depth so that the

nearest source-receiver offset is about equal to themaximum investigation depth.


Receiver spacingReceiver spacing

Receiver spacing should follow the Nyquist sampling

theorem. Receiver spacing determines the shortest

wavelength in recorded data, which is a guideline

f d t i i thi k f l d l d i

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for determining thickness of a layer model and is

also a limit in the inverted S-wave velocity model.


Receiver spreadReceiver spread

Receiver spread should also follow the Nyquist

sampling theorem. Receiver spread determines the

longest wavelength in recorded data, which is aguideline for determining total thickness of layers

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guideline for determining total thickness of layers

on the top of the half-space.

The receiver spread is limited by far-offset effect.

Far-offset effect: Higher frequency components of

surface waves are contaminated by body wavesdue to high-frequency attenuation.

Near-offset effectsNear-offset effects

Nearest offset: 1.8 m.

Receiver spacing: 1 m.Receiver spread: 40 m.

10 Hz 16 Hz 22 Hz 28 Hz 34 Hz 40 Hz 46 Hz

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Lower frequencycomponents are not

fully developed as

plane waves.

1.5 s 3.0 s 4.5 s 6.0 s 7.5 s 9.0 s 10.5 s 12.0 s

Far-offset effectsFar-offset effects

Nearest offset: 89 m.

Receiver spacing: 1 m.

Receiver spread: 40 m.

10 Hz 16 Hz 22 Hz 28 Hz 34 Hz 40 Hz 46 Hz

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Higher frequencycomponents arecontaminated by bodywaves due toattenuation of high

frequency componentsof surface waves.

1.5 s 3.0 s 4.5 s 6.0 s 7.5 s 9.0 s 10.5 s 12.0 s

Optimum offsetOptimum offset

Nearest offset: 27 m.

Receiver spacing: 1 m.Receiver spread: 40 m.

10 Hz 16 Hz 22 Hz 28 Hz 34 Hz 40 Hz 46 Hz

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Linearity of surfacewave is clearly

improved from

4 Hz to 35 Hz.1.5 s 3.0 s 4.5 s 6.0 s 7.5 s 9.0 s 10.5 s 12.0 s

00

2000 2000

00

2000 2000

How to check near-

offset effects or

far-offset effects onimpulsive data?

Impulsive data to

swept data:

Convolution

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40004000 40004000

Swept data to

impulsive data

(frequency

decomposition):

Correlation

SummaryRule of thumbSummaryRule of thumb

The nearest source-receiver offset = 1/3

to 1/2 of the maximum investigation

depth.

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Receiver spacing = the thinnest layer of

the layer model.

Receiver spread = 1 to 2 times of the

maximum investigation depth.

KGS-00-25.pdf

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