Multichannel Analysis of Surface Wave - Exploration Services et al...velocity field by the multichannel analysis of surface wave technique: Proceedings of the Symposium on the Application

Multichannel Analysis of Surface WaveTheory 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 byJianghai Xia

Prepared byJianghai Xia, Richard D. Miller,

and Choon B. Park

Kansas Geological SurveyThe University of Kansas

1930 Constant AvenueLawrence, KS 66047, USA

KGS Open-file Report 2000-25

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)

Part 2

Verifications

Real World Examples

A Pitfall in Shallow Shear-waveRefraction Surveying

An Interesting Real-World Example

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 Analysisof 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

Part 4

Future Study

1. Higher Modes

Advantages of CalculatingShear-wave Velocity fromSurface Waves with Higher Modes

Why Use Higher Modes?

Outline

❧ Introduction❧ Modeling Results❧ A Real-World Example❧ Discussion and Conclusions

IntroductionWhat are higher modes?

More than one phase velocity can be associated with a givenfrequency of Rayleigh wave simply because these wavescan travel at different velocities for a given frequency.

The lowest velocity for any given frequency is called thefundamental-mode velocity (or the first mode). The nexthigher velocity above the fundamental-mode phasevelocity is called the second-mode velocity, and so on.

Why do we need higher modes?

In some situations, highermodes take more energythan the fundamental modein a higher frequencyrange, which means thefundamental-mode datamay not be available in thehigher frequency range andhigher modes are the onlychoice.

An Example of Higher Modes

Data acquired in San Jose, California, in 1998

Modeling Results

1. the sensitivity ofhigher modes of surface waves,

2. investigation depth,3. stability during

inversion.

The six layer model isused to analyze

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 tomap 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 of Journal 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, 69thAnnual 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 theSymposium on the Application of Geophysics to Engineering and EnvironmentalProblems (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: TechnicalProgram 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: TechnicalProgram 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 surfacewave: Proceedings of the Symposium on the Application of Geophysics to Engineeringand 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 modeobservation 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 AnnualMeeting, Calgary, Canada.

14. Ivanov, J., Park, C.B., Miller, R.D., and Xia, J., 2000, Mapping Poisson’s Ratio ofunconsolidated materials from a joint analysis of surface-wave and refraction events:Proceedings of the Symposium on the Application of Geophysics to Engineering andEnvironmental Problems (SAGEEP 2000), Arlington, Va., February 20-24, 2000, 11-20.

Additional papers are available on this topic. They are not included here because they did notexist at the time this open-file report was prepared.

Sensitivity of Higher Modes

Second mode Third mode

Contribution to the higher-mode Rayleigh-wave phasevelocity by a 25% change in each earth parameter.

200

400

600

800

1000

1200

10 15 20 25 30 35 40

Frequency (Hz)

Seco

nd-m

ode p

hase

velo

city

(m/s

)

ModelS-waveP-waveDensityThickness

400

500

600

700

800

900

1000

25 30 35 40 45

Frequency (Hz)Th

ird-m

ode

phas

e ve

loci

ty (m

/s)

Model

S-wave

P-wave

Density

Thickness

Penetrating Depth of Higher Modes

❧ Experimental analysis indicates that energy ofhigher modes tends to become more dominantas the source distance increases.

❧ The Jacobian matrix of the higher-modeRayleigh-wave data suggests higher-mode datahave deeper investigation depths than do thefundamental-mode data.

Penetrating Depth

The open circles are therow vectors of theJacobian matrix associatedwith the shortest wave-length data.

A wavelength of 8.7 mreaches zero at a depth of13 m for the fundamental-mode data

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Row

vec

tor

134

63.6

20.7

12.3

8.7

Penetrating Depth Comparison

Fundamental mode Second mode

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Row

vec

tor

134

63.6

20.7

12.3

8.7

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)Ro

w v

ecto

r

93.2

40.8

17.9

13.6

10.9

Penetrating Depth Comparison

Second mode Third mode

Wavelength

0.001

0.01

0.1

1

0 5 10 15 20

Depth (m)

Row

vec

tor

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)Ro

w v

ecto

r

27.9

21.7

16.9

10.7

6

Conclusion on Penetrating Depth

❧ Higher-mode Rayleigh-wave data can“see” deeper when compared to thesame wavelength components of thefundamental-mode Rayleigh-wave data.

Stability of Inversion with Higher Modes

❧ The most significant result is that higher-mode data stabilizes the inversion processand increases the resolution of invertedS-wave velocities.

Stability of Inversion

A difference of more than 100% in S-wave velocity models atdepths of 6 m and 7 m only result in a standard deviation of4.6 m/s in the fundamental-mode data,33.5 m/s in second-mode data, and27.3 m/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)

Diff

eren

ce (m

/s)

Fundamental

Second

Third

0

100

200

300

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500

600

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800

0 5 10 15 20

Depth (m)

Vs v

eloc

ity (m

/s)

Model 1Model 2


A 100% difference in S-wave velocity models at depths of 6 mand 7 m and 9 m and 10 m only result in a standard deviation of59 m/s in the fundamental-mode data,113 m/s in second-mode data, and110 m/s in the third-mode data.


-50

0

50

100

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0 10 20 30 40 50 60 70 80Frequency (Hz)

Diff

eren

ce (m

/s)

FundamentalSecondThird

0

200

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600

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1000

1200

0 5 10 15 20

Depth (m)

Vs v

eloci

ty (m

/s)

Model 1Model 2


A 80% difference in S-wave velocity models at depths of 6 m and7 m and 9 m and 10 m only result in a standard deviation of13 m/s in the fundamental-mode data,45 m/s in second-mode data, and37 m/s in the third-mode data.


0

200

400

600

800

1000

0 5 10 15 20

Vs velocity (m/s)

Dep

th (m

)

Model 1Model 2

-40-20

0204060

80100120140

160180

0 10 20 30 40 50 60 70 80

Frequency (Hz)

Diff

eren

ce (m

/s)



80% difference in S-wave velocity models at depths from 3 mto 6 m only result in a standard deviation of17 m/s in the fundamental-mode data66 m/s in second-mode data35 m/s in the third-mode data.


0100200300400500600700800900

1000

0 5 10 15 20Depth (m)

Vs V

elocit

y (m

/s)

Model 1Model 2

-100

-50

0

50

100

150

200

250

0 10 20 30 40 50 60 70 80Frequency (Hz)

Diff

eren

ce (m

/s)


Conclusion on Stability

❧ An inversion with higher mode data canreject “irrational” model 2 due to itshigher RMS error. Model 2 may beaccepted by an inversion only with thefundamental mode data due to its lowerRMS error.

❧ A stabilized inversion can be achievedby including higher mode data in aninversion process.

A Real-world ExampleSan Jose, California, Fall of 1998

Field Layout

To determine S-wave velocity in near-surface materials up to10 m deep.

Layered Model

❧ A fourteen-layermodel with eachlayer 1 m inthickness.

Shot gather and its image in F-K domain

Fundamental Mode Data(Set One)

100

150

200

250

300

350

5 10 15 20 25

Frequency (Hz)

Phas

e ve

locit

y (m/

s)

MEASUREDINITIALFINAL

100

150

200

250

300

350

400

450

0 5 10 15 20

Depth (m)Sh

ear w

ave

velo

city

(m/s)

INITIAL INVERTED

Pink lines present results of inversion of fundamental mode ofsurface wave data with errors.

Fundamental Mode Data with Errors(Set Two)

0

100

200

300

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500

600

0 5 10 15 20

Depth (m)S-

wav

e ve

loci

ty (m

/s)

Fundamental with error

Fundamental

Fundamental with errorplus second mode

Pink lines present results of inversion of fundamental mode ofsurface wave data with errors.

100

150

200

250

300

350

5 10 15 20 25

Frequency (Hz)

Phas

e velo

city (

m/s)

MeasuredInitialFinal

Fundamental Mode Data with ErrorsPlus the Second Mode Data

(Set Three)

0

100

200

300

400

500

600

0 5 10 15 20

Depth (m)S-

wav

e ve

loci

ty (m

/s)

Fundamental with error

Fundamental

Fundamental with errorplus second mode

Yellow lines present results of inversion of fundamental modeof surface wave data with errors plus the second mode data.

100

150

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250

300

350

5 10 15 20 25 30

Frequency (Hz)

Phas

e velo

city (

m/s)


Discussion

❧ In the real world, we normally make achoice between error and resolution of amodel. The instability that we see in theinverted S-wave velocities of data set twois error in the inverted model, which canbe reduced by reducing the resolution ofthe model.

Trade off BetweenResolution and Error

100

200

300

400

500

0 5 10 15 20

Depth (m)S-

wav

e ve

loci

ty (m

/s)

INITIAL Vs INVERTED Vs NO ERROR

100

200

300

400

5 10 15 20 25

Frequency (Hz)

Phas

e ve

loci

ty (m

/s)


Resolution is reduced by one half (layer thickness is increasedto 2 m) to obtain a stable result (less model errors).

AcknowledgmentsThe authors thank Geometrics, Inc. for itssupport in acquiring data used in this paper.The authors also thank Rob Huggins, CraigLippus, Ming-Wen Sung, and Mark Prouty ofGeometrics for their assistance in acquiringthe seismic data. The authors also appreciatethe efforts of Mary Brohammer in manuscriptpreparation and submission.

Future Study (continuation)

2. Accuracy of phase velocity

To extract phase velocity from higherresolution image in the f-k domain and/orin the wavelet domain.

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.

4. Wave equation modeling andlaboratory modeling

To model cases such as a dipping layered earthmodel, voids in layered earth models, layeredmodel with S-wave velocity inversion (highervelocity on the top of lower velocity layer).

To verify if there are any surface wavereflections and/or refractions. If yes, in whatsituations they will occur.

5. Resolution

Horizontal resolution of inverted S-wavevelocity changes with depth due differencewavelengths.

Vertical resolution—study by modeling?

6. Surface Wave Tomography

New 3-D near-surface technology

❂ 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

INTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONINTRODUCTIONA Three-phase Research ProjectA Three-phase Research Project

1) acquisition of high-frequency broad band ground roll

2) creation of efficient and accurate algorithms to extract Rayleigh wave dispersion curves from ground roll

3) development of stable and efficient inversion algorithms to obtain near-surface S-wave velocity profiles

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 andthe standard CDP roll-along acquisition formatto generate a two-dimensional S-wave velocitysection

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

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

75100125150175200

0 5 10 15Frequency (Hz)

Phas

e velo

city

(m/s

)

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

0

50

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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

Dep

th

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 (<30 ft) in Olathe, Kansas1. Mapping Bedrock (<30 ft) in Olathe, Kansas1. Mapping Bedrock (<30 ft) in Olathe, Kansas1. Mapping Bedrock (<30 ft) in Olathe, Kansas

SourceSourceSourceSource: a 12 lb hammer and a 1 ft by 1 ft plate

Source spacingSource spacingSource spacingSource spacing: 4 ft

GeophoneGeophoneGeophoneGeophone: single, 4.5 Hz vertical component geophone

Geophone spacingGeophone spacingGeophone spacingGeophone spacing: 2 ft

Nearest source-geophone offsetNearest source-geophone offsetNearest source-geophone offsetNearest source-geophone offset: 8 ft

Olathe ExampleOlathe ExampleOlathe ExampleOlathe Example

Traces per shot:Traces per shot:Traces per shot:Traces per shot: 48 48 48 48

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 ft 1400 ft 1400 ft 1400 ft

Geophones Geophones Geophones Geophones with spikes, with spikes, with spikes, with spikes, baseplatesbaseplatesbaseplatesbaseplates, or, or, or, orbaseplates baseplates baseplates baseplates with sandbagswith sandbagswith sandbagswith sandbags

Geophones with spikes andbaseplates

Geophones with baseplatesand baseplates withsandbags


spikes baseplates baseplates with sandbags


Dispersion curves Inverted S-wave velocities

150

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400

25 30 35 40 45 50 55 60Fre que nc y (Hz)

SandbagPlateSpike

0

100

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600

0 2 4 6 8 10Depth (m)

S-w

ave

velo

city

(m/s

)

SandbagPlateSpike

Olathe Olathe Olathe Olathe (continued)(continued)(continued)(continued)

4.5 Hz geophonewith baseplate

12 lb hammer and1 ft by 1 ft steel plate



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 ofRayleigh waves:Rayleigh waves:Rayleigh waves:Rayleigh waves: 9 to 50 ft9 to 50 ft9 to 50 ft9 to 50 ft

A ten-layer model

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


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

Station Number

30

25

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15

10

5

0

Dep

th (f

t)

0 800 1200 1600 2000 2400 2800

0 20 40 60 80Contour 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

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


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

25

20

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10

5

0

0 800 1200 1600 2000 2400 28000 20 40 60 80

ft/sft

Station Number

Dep

th (f

t)

W E



A 2-D S-wave velocity map of line 3, Olathe, KansasA 2-D S-wave velocity map of line 3, Olathe, KansasA 2-D S-wave velocity map of line 3, Olathe, KansasA 2-D S-wave velocity map of line 3, Olathe, KansasS N

Station Number

Dep

th (f

t)

ft/s

3150 3140 3130 3120 3110 3100 3090 3080 3070 3060 3050 3040 303030

25

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5

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0 800 1200 1600 2000 2400 28000 20 40 60 80 ft


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

Station number

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0

Dep

th (f

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Contour interval is 200 ft/s.

W E



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

2. 2. 2. 2. 2. 2. 2. 2. Imaging a Steam Tunnel (<20 ft), Lawrence, KansasImaging a Steam Tunnel (<20 ft), Lawrence, KansasImaging a Steam Tunnel (<20 ft), Lawrence, KansasImaging a Steam Tunnel (<20 ft), Lawrence, Kansas

SourceSourceSourceSource: an IVI minivib with a 10 second linear up-sweep (10 to 150 Hz)

Source spacingSource spacingSource spacingSource spacing: 4 ft

GeophoneGeophoneGeophoneGeophone: three 10 Hz vertical component geophones wired in series

Geophone spacingGeophone spacingGeophone spacingGeophone spacing: 4 ft

Nearest source-geophone offsetNearest source-geophone offsetNearest source-geophone offsetNearest source-geophone offset: 80 ft

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

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

Traces per shot:Traces per shot:Traces per shot:Traces per shot: 30 30 30 30

Sampling Rayleigh waves:Sampling Rayleigh waves:Sampling Rayleigh waves:Sampling Rayleigh waves:4 to 116 ft4 to 116 ft4 to 116 ft4 to 116 ft

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

IVIIVIIVIIVI Minivib Minivib Minivib Minivib



The observed frequencyThe observed frequencyThe observed frequencyThe observed frequencyof 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 eachLast five layers:Last five layers:Last five layers:Last five layers: 6.6 ft each

A ten-layer model


At beginning of line At top of tunnel


The difference between the twodispersion curves indicates theexistence of an anomaloussubsurface.

Relatively lower phase velocity(pink line) in lower frequencies(< 17 Hz) suggests low S-wavevelocity at a relatively deeperdepth. Relatively higher phasevelocity in a range (> 20 Hz)suggests very shallow materialsare compacted.

700

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1100

1200

13 17 21 25 29 33

Frequency (Hz)

Phas

e ve

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t/s)

Station 1001Station 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


1010 1020 1030 1040 1050 1060 107030

25

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0

Dep

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t)

Station Number

200 500 700 900 1100 1300 15000 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


1010 1020 1030 1040 1050 1060 107030

25

20

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10

5

0

-350 -250 -150 -50 50 150 250

Dep

th (f

t)

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


3. Mapping Bedrock Surface (<100 ft), Joplin, Missouri3. Mapping Bedrock Surface (<100 ft), Joplin, Missouri3. Mapping Bedrock Surface (<100 ft), Joplin, Missouri3. Mapping Bedrock Surface (<100 ft), Joplin, Missouri(Two parallel lines total 364 shots)

Source:Source:Source:Source: an IVI minivib with a 10 second linear down- sweep (100 to 10 Hz)

Source spacing:Source spacing:Source spacing:Source spacing: 4 ft Geophone:Geophone:Geophone:Geophone: three 10 Hz vertical component geophones

wired in series Geophone spacing:Geophone spacing:Geophone spacing:Geophone spacing: 4 ft Nearest source-geophone offset:Nearest source-geophone offset:Nearest source-geophone offset:Nearest source-geophone offset: 40 ft

Joplin ExampleJoplin ExampleJoplin ExampleJoplin Example

Joplin Joplin Joplin Joplin (continued)(continued)(continued)(continued)

Traces per shot: 34

Sampling Rayleigh waves:4 to 132 ft

Observed frequency ofRayleigh waves: 10 to 25 Hz

Observed wavelength ofRayleigh waves: 40 to 100 ft

A five-layer model


Shot for imaging station 1050 Shot for imaging station 1326


Dispersion curves for imaging stations 1050 and 1326

800

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1300

17 19 21 23 25 27 29

Frequency (Hz)

Phas

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t/s)

Station 1050Station 1326

200 ft/s differencebetween these twodispersion curves:station 1050 is at thebeginning of the line,and station 1326 is atthe location of thesecond well.


1050 1100 1150 1200 1250 1300 1350100

80

60

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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


Feet

50 100 150 200 250 300100

80

60

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0

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

0 50 100 150 200

Dep

th (f

t)

Station number

0 800 1200 1600 2000 2400 2800 3200 3600 ft/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

EXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLESEXAMPLES (continued)(continued)(continued)(continued)4. Mapping Dissolution Feature (<100 ft), Damascus, Alabama4. Mapping Dissolution Feature (<100 ft), Damascus, Alabama4. Mapping Dissolution Feature (<100 ft), Damascus, Alabama4. Mapping Dissolution Feature (<100 ft), Damascus, Alabama

(2,500 shots acquired along thirteen lines)

Source: three ground impacts from a rubber band accelerated weight drop

Source spacing: 4 ft

Geophone: Single 4.5 Hz vertical component geophone

Geophone spacing: 4 ft

Nearest source-geophone offset: 40 ft

Site MapSite MapSite MapSite Map

Line LocationLine LocationLine LocationLine LocationMapMapMapMap

13 lines13 lines13 lines13 lines2,500 shots2,500 shots2,500 shots2,500 shots

Working SiteWorking SiteWorking SiteWorking Site

Damascus Example Damascus Example Damascus Example Damascus Example (continued)(continued)(continued)(continued)A rubber band accelerated weight dropperA rubber band accelerated weight dropperA rubber band accelerated weight dropperA rubber band accelerated weight dropper

Damascus Damascus Damascus Damascus (continued)(continued)(continued)(continued)

A survey lineA survey lineA survey lineA survey line


224 shots along line 1


Traces per shot: 48

Sampling Rayleigh waves:4 to 188 ft

Observed frequency ofRayleigh: 5 to 22 Hz

Observed wavelength ofRayleigh waves: 25 to 200 ft

A fourteen-layer model


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

Dep

th (f

t)

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


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

0N S

0 80 160 240 320Station Number

Dep

th (f

t)

0 200 400 600 800 1000 1200 1400 1600 ft/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


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

8 8 8 8 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)

4.5 Hz vertical component 4.5 Hz vertical component 4.5 Hz vertical component 4.5 Hz vertical component geophonegeophonegeophonegeophone

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


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

25

20

15

10

5

0

0 20 40 60 80Station Number

Dep

th (f

t)

200 600 1000 1400 2000 2400 2800 ft/s

S-wave velocity section of line 1


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

Dep

th (f

t)

ft/s0 10 20 30 40 ft

S-wave velocity section of line 2

CONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONSCONCLUSIONS1. Shallower target investigationShallower target investigationShallower target investigationShallower target investigation

High-frequency (> 2 Hz) ground rollInvestigation depth from 5 to 100 feet

2. Feasibility in noisy environmentsFeasibility in noisy environmentsFeasibility in noisy environmentsFeasibility in noisy environmentsGround roll, high signal-to-noise ratio, allowing 2-Dimages to be obtained in noisy environments

3. EfficiencyEfficiencyEfficiencyEfficiencyThe standard CDP roll-along acquisition method provides an efficient way to acquire large quantities ofbroadband surface wave data along a line

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

4. ReliabilityReliabilityReliabilityReliabilityThe redundancy of the CDP acquisition method providesa reliable way to verify inverted S-wave velocities so thatit reduces the ambiguity of inverted S-wave velocities

5. SimplicitySimplicitySimplicitySimplicityA contouring software: from a 1-D S-wave velocity profileto a 2-D S-wave velocity map

6. Anomaly enhancementAnomaly enhancementAnomaly enhancementAnomaly enhancement2-D data processing techniques can be applied to a 2-DS-wave velocity section to enhance local anomalies

ACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTS

The authors would like to thank Brett Bennett, DavidLaflen, Joe Anderson, Tom Weis, and Chad Gratton for theirassistance during the field tests.

The authors appreciate the efforts of Mary Brohammer,John Charlton, and Amy Stillwell in manuscript and slidepreparations.

Outline❧ Introduction❧ A Real World Example

SH-wave Refraction SurveyP-wave Refraction SurveyExplanation

❧ MASW—An Alternative for DeterminingS-wave Velocity

❧ S-wave Velocity from Suspension Logging❧ Conclusions

Introduction

For a series ofhorizontal layers,a pure, plane SHwave refracts andreflects only SHwaves. There isno wave-typeconversion.

Introduction (continued)

However, complex near-surface geologymay not fit into the assumption of a seriesof horizontal layers. That a plane SH waveundergoes wave-type conversion along aninterface in an area of non-horizontal layersis theoretically inevitable.

Introduction (continued)

Can we recognize converted waves?

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

A Real-World Example

A shallow SH-wave refraction survey wasconducted in Wyoming during the fall of1998 to determine shear-wave velocities innear-surface materials up to 7 m deep.

SH-wave Source

Field Layout for SH-wave Refraction Survey

SH-wave Refraction Data

A Layer Model from SH-wave Data

Comparedwith the SH-wave velocityof the firstlayer, the SH-wave velocityof the secondlayer is morethan double.

Are velocities of the second and thirdlayers the true SH-wave velocities, orare they converted P-wave velocities?

Field Layout for P-wave Refraction Survey

P-wave Refraction Data

A Layer Model from SH-wave DataP-wavevelocities ofthe secondand thirdlayers arealmost thesame as therelevant“SH-wave”velocities.

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

Explanation

Field Layout for MASW Survey

Surface Wave Data

Dispersion Curve S-wave Velocity Model

150

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450

10 15 20 25 30Frequency (Hz)

Measured (E)

Final (E)

Measured (W)

Final (W)

0

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500

600

0 5 10 15 20

De pth (m)

Inverted (E)Inverted (W)

S-wave Velocities fromSH-wave Refraction and MASW

S-wave Velocity from Suspension Logging

To confirmthe invertedS-wavevelocity, aborehole wasdrilled on thesite andsuspensionlogging wasconducted.

Be CarefulWhen Doing SH-wave Refraction Surveys

In a case of adipping layer, SH-Pconversion willoccur if a surveyline is not parallel toY axis.

Conclusions❧ Shallow shear-wave refraction survey may not provide the

true S-wave velocity because of wave-type conversion inan area of non-horizontal layers.

❧ To verify if velocities based on shear-wave refractionsurveys are velocities of converted waves, an additionalP-wave refraction survey is necessary.

❧ The best alternative at this time is MASW, which canprovide reliable S-wave velocities, even in an area ofvelocity inversion (a higher velocity layer underlain bya lower velocity layer).

Acknowledgments

The authors wish to thank Blackhawk Geometrics fortheir permission to publish the seismic data presentedherein. Authors extend their thanks to Bart Hoekstraof Blackhawk Geometrics for acquiring seismic dataand to Julian Ivanov for constructive discussions onthis topic. The authors also appreciate the efforts ofMary Brohammer and Amy Stillwell in manuscriptpreparation.

Comparing Shear-Wave Velocity Profilesfrom MASW with Borehole Measurements

in Lawrence, Kansas

One Detailed Real-World Example

Testing Site—KGS Front Yard

Field Layout

Raw DataSeismograph: Geometrics StrataViewSeismic Source: IVI MinivibGeophone: 10 Hz vertical componentAcquisition filter:

NoRecording length: 1024 millisecondsSample interval:

1 millisecond

Layered Model for Inversion

❧ A ten-layer modelwith a one meterthick top layergradually increasingto a 6 meter layeron the bottom.

Dispersion Curves S-wave Velocity Models

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

Frequency (Hz)

Phas

e ve

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ty (m

/s)

MeasuredInitial AFinal AInitial BFinal B

Three-component borehole data were acquired. Overall error in S-wavevelocity of the borehole survey is 10%.

Effects of Initial Models

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0 5 10 15 20 25 30 35 40

Depth (m)

S-w

ave

velo

city

(m/s

)

100200300400500600700800900Borehole

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1600

0 5 10 15 20 25 30 35 40

Depth (m)S-

wav

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loci

ty (m

/s)

halfQuarterhalf-hInverted BBorehole

Initial models are blindly selected as a uniform half-space with aconstant S-wave velocity from 100 m/s to 1,800 m/s.

Effect of the Number of Data Points

Half (solid diamonds):33 points from 15 to 47 Hz;

Quarter (solid squares):17 points from 15 to 31 Hz;

Half-h (solid triangles):17 points from 15 to 47 Hzat 2 Hz interval, and

Inverted B (Solid circles):66 points from 15 to 80 Hz.

0

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0 5 10 15 20 25 30 35 40

Depth (m)S-

wav

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/s)

halfQuarterhalf-hInverted BBorehole

Summary❧ The proposed inversion is stable. 1. Inverted

models do not seem to be too sensitive toinitial models; 2. The inversion is continuouslyimproving inverted modes during inversionprocessing.

❧ Inverted S-wave velocities are reliable. A 15%difference can be expected between invertedS-wave velocities and borehole measurements.

Comparing Shear-Wave Velocity Profilesfrom MASW with Borehole Measurements

in the Fraser River Delta,Vancouver, Canada

Eight Real-World Examples

Testing Site

Common Parameters

❧ Seismograph: Geometrics StrataView❧ Seismic Source: Weight dropper (built by KGS)❧ Geophone: 4.5 Hz vertical component❧ Acquisition filter: No❧ Recording length: 2048 milliseconds❧ Sample interval: 1 millisecond

Field Layout

Field Layout for Borehole FD95-2

Borehole FD95-2

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5 10 15 20 25

Frequency (Hz)

Phas

e ve

loci

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/s)

MeasuredFinal

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0 5 10 15 20 25 30

Depth (m)

S-w

ave

velo

city

(m/s

)Borehole FD95-2

Inverted

Borehole FD95-2

❧ 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


Borehole FD97-2

100

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0 5 10 15 20

Frequency (Hz)

Phas

e ve

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/s)

MeasuredFinal

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Depth (m)

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(m/s

)Borehole FD97-2Inverted

Borehole FD97-2



60

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200

0 5 10 15 20 25 30

Frequency (Hz)

Phas

e ve

loci

ty (m

/s) Measured

Final

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0 5 10 15 20 25 30

Depth (m)

S-w

ave

velo

city

(m/s

)Borehole FD92-11InvertedCross hole

Borehole FD92-11

Borehole FD92-11



Borehole FD92-3

0

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Frequency (Hz)

Phas

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MeasuredFinal

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Depth (m)

S-wa

ve v

eloc

ity (m

/s)

Borehole FD92-3 Inverted

Borehole FD92-3


Field Layout for Borehole Unknown

Borehole Unknown

50

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10 15 20 25

Frequency (Hz)

Phas

e ve

loci

ty (m

/s)

MeasuredFinal

0

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0 5 10 15 20 25 30

Depth (m)

S-w

ave

velo

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(m/s

)Inverted VsBorehole

Borehole Unknown



Borehole FD86-5

80

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0 5 10 15 20 25 30

Frequency (Hz)

Phas

e ve

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/s)

MeasuredFinal

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Depth (m)

S-w

ave

velo

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(m/s

)Borehole FD86-5Inverted

Borehole FD86-5



Borehole FD92-4

50

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250

0 5 10 15 20 25 30

Frequency (Hz)

Phas

e ve

loci

ty (m

/s)

MeasuredFinal

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0 5 10 15 20 25 30

Depth (m)

S-w

ave

velo

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(m/s

)Borehole FD92-4

Inverted

Borehole FD92-4

❧ Wavelength Range: 4 - 68 m❧ Phase Velocity Range: 96 - 239 m/s❧ Frequency Range: 3.5 - 25 Hz❧ Depth Studied: 30 m❧ Inverted S-wave Velocity Range: 92 - 311 m/s❧ Average Relative Difference: 10%❧ Average Difference: 19 m/s


Borehole FD97-7

20

30

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0 2 4 6 8

Frequency (Hz)

Phas

e ve

loci

ty (m

/s)

MeasuredFinal

0

20

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120

0 2 4 6 8

Depth (m)

S-w

ave

velo

city

(m/s

)

Borehole FD97-7Inverted

Borehole FD97-7


Reasons for differences

❧ Body waves and/orhigher-modeRayleigh waves.

❧ Sharpness ofdispersion curve inthe F-K domain.


❧ Heterogeneity of thenear-surface materials.Borehole measurement isin vertical direction andthe MASW S-wavevelocity is is horizontaldirection.


❧ Random noise and/or reflected ground roll.❧ Non-uniqueness in the inversion of Rayleigh wave

data and a local minimum search of the inversealgorithm.

❧ The first arrival picking on borehole data.

ConclusionsThe overall difference between S-wave velocities from the

MASW method and borehole measurements is 15%.

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

Differences between S-wave velocities from the MASWmethod and borehole measurements appear to berandom.

This comparison demonstrates the reliability and accuracyof S-wave velocities estimated from the MASW methodin unconsolidated sediments.

Acknowledgments The authors would like to thank Brett Bennett,

David Laflen, Ron Good, Jim Droddy, andChad Gratton for their assistance during thefield tests.

The authors appreciate the efforts ofMary Brohammer, John Charlton, andAmy Stillwell in manuscript preparations.

Presented atPresented atChina University of Geosciences, Wuhan

Chengdu University of Technology, ChengduChina 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

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 tripsuccessful.

Prof. Jiaying Wang, Vice President of China University ofGeosciences, 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; andProf. Xujin Sun, North China Institute of Water Conservancy and

Hydroelectric Power.

AcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgments

I greatly appreciate Prof. Richard Miller, Chief of ExplorationServices, Kansas Geological Survey, for his motivationand support of this trip.

I would also like to thank the Kansas Geological Survey forthe continuous support to this project during the last fiveyears.

AcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgmentsAcknowledgments

❂❂ TheoryTheory❂❂ VerificationsVerifications❂❂ 2-D S-wave Velocity Sections2-D S-wave Velocity Sections❂❂ Future StudiesFuture Studies

OutlineOutlineOutlineOutlineOutlineOutlineOutlineOutline

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

TheoryTheory

From field shot gather to

S-wave velocity profile

MultichannelMultichannel recording system recording system

Raw Field DataRaw Field Data

❂ Surface wave background❂ Calculation of dispersion curve❂ Inversion of dispersion curve❂ Parameters of a layered earth model❂ Equipment and data acquisition

parameters

Theory—OutlineTheory—OutlineTheory—OutlineTheory—OutlineTheory—OutlineTheory—OutlineTheory—OutlineTheory—Outline

Theory—Surface waveTheory—Surface waveTheory—Surface waveTheory—Surface waveTheory—Surface waveTheory—Surface waveTheory—Surface waveTheory—Surface wave

Theory—Penetrating depthTheory—Penetrating depthTheory—Penetrating depthTheory—Penetrating depthTheory—Penetrating depthTheory—Penetrating depthTheory—Penetrating depthTheory—Penetrating depth❂ Penetrating depth is

about one wavelength.❂ Longer wavelengths

can “see” deeper thanshorter wavelengths.

❂ In a homogeneoushalf-space, Rayleighwave velocity is about0.92Vs if Poisson’sratio = 0.25.

Theory—Model responseTheory—Model responseTheory—Model responseTheory—Model responseTheory—Model responseTheory—Model responseTheory—Model responseTheory—Model response A B S-wave velocity

Theory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curve

1.

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

U(x,w) is a shot gather in the offset-frequency domain after applied theFourier transform to U(x,t).

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

∫= dtetxuwxU iwt),(),(

),(),( wxAewxU xiΦ−= wcw /=Φw is frequency in radian and cw is phase velocity for frequency w.

Theory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curveTheory—Calculation of dispersion curve

2. Applying integral transformation to U(x,t)

dxwxUwxUewV xi ]),(/),([),( ∫= φφ

( ) dxwxAwxAe xi ]),(/),([∫ −Φ−= φ

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

φ=Φ

),( wV φ

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

Theory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curve

OutlineOutlineOutlineOutlineOutlineOutlineOutlineOutline

❂ Forward calculation❂ Partial derivatives of phase velocity function❂ Sensitivity of earth model parameters❂ Inversion algorithms

Theory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveTheory—Inversion of dispersion curveLayered earth model, four parametersLayered earth model, four parametersLayered earth model, four parametersLayered earth model, four parameters

Free surfaceFree surface___________________________________

vs1 vp1 1 h1

_____________________________________________vs2 vp2 2 h2

_____________________________________________...

_____________________________________________vsi vpi i hi

_____________________________________________.

.

._____________________________________________

vsn vpn n infiniteρ

ρ

ρ

ρ

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

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

The Jacobian matrix calculated byRidder’s method—one 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 isused to analyzethe sensitivity ofhigher 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 parametersWhy only S-wave velocity?

Model Parameters model (%) data (%)

P-wave Velocity 25 3Density 25 10S-wave Velocity 25 39Thickness 25 16

S-wave velocity is the dominant property for the fundamental mode ofhigh-frequency Rayleigh wave dispersion data.

Based on the sensitivity analysis of four groups of earthmodel parameters: S-wave velocity, P-wave velocity,density, and thickness of layers, S-wave velocity isdominant. If we can get good estimates of P-wave velocityand density, we can only invert S-wave velocity from phasevelocities of surface waves.

The following discussion assumes P-wave velocity anddensity are known. Only S-wave velocities are updatedduring the inversion procedure based on the layered earthmodel.

Why only S-wave velocity?

Inversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithmsInversion algorithms

Objective function:

2

222xbJxWbJx λ+−−=Φ

SolutionSolutionSolutionSolutionSolutionSolutionSolutionSolution

Where d is the vector of difference between modeledand measured data, V, , and U are the SVD matrixesof the weighted Jacobian matrix A.

Λ

( ) dUIVx TΛ+Λ= −12 λ

Theory—Theory—Theory—Theory—Theory—Theory—Theory—Theory—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:

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 aredetermined based on dispersion curve data.


Based on analysis of sensitivity of earth modelparameters, the other three groups ofparameters—P-wave velocities, densities, andthickness of layers—are not changed duringinversion procedure.

2. P-wave velocities can be determined from thefirst arrivals of surface wave data. The firstarrivals are refraction information on P-wavevelocities.


3. Densities can be chosen from 1.6–2.2 g/cc forshallow sedimentary geology. Based on ourexperience, this range of density gives enoughaccuracy for inverted S-wave velocities up to100 ft depth.


4. The depth to the top of the half-space isdetermined by your investigation depth. Ten tofifteen layers is a good place to start with testing.After determining the number of layers, thethickness of each layer can easily be defined.

Make sure the maximum wavelength is greaterthan the investigation depth.


Trade-off between resolution and accuracy

The thickness of layers basically is a measurementof the vertical resolution. The vertical resolutionis limited by accuracy of the dispersion curve. Inthe case of low accuracy of dispersion curve data,you should reduce the number of layers (increasethickness of each layer) to reduce uncertainty ofthe inverted S-wave velocities (stabilize inversion).

Summary—Summary—Summary—Summary—Summary—Summary—Summary—Summary—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

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Frequency (Hz)

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MeasuredFinal

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(m/s

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Borehole FD95-2

Inverted

Multichannel raw data Dispersion curve S-wave velocity

f-k transformation Inversion

Synthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic Examples

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

0

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Frequency (Hz)

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MeasuredInitialFinal

Thickness of top layer: 2 m








Why use two-layer models?

One direct application of a two-layer model isstatic correction in S-wave reflection andrefraction survey in oil industry.

Synthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesSynthetic ExamplesA multilayer model—Effects of P-wave velocity and density

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”records. “Enriched”means wavelengths ofsurface waves evenlycover the range ofinvestigation depth.

Seismic SourcesSeismic Sources1. Industrial Vehicle International (IVI) Minivib

Downward weight 6,000 lb.

Investigation depth: 1 to 30 meters

Seismic SourcesSeismic Sources2. KGS-built weight dropper

Investigation depth: 2 to 30 meters

Seismic SourcesSeismic Sources3. Sledgehammer and plate

Investigation depth: 0.5 to 15 meters

Seismograph—48 to 60 channelsSeismograph—48 to 60 channels

60-channel Geometrics StrataView

GeophonesGeophones——4.5 to 10 Hz vertical4.5 to 10 Hz verticalcomponent component geophonegeophone

Geophone with spike Geophone with baseplate

GeophonesGeophones——4.5 to 10 Hz vertical4.5 to 10 Hz verticalcomponentcomponent geophone geophone

Geophone on tiles Geophone on carpet

Data Acquisition ParametersData Acquisition Parameters

A. Nearest source-receiver offsetB. Receiver spacingC. Receiver spread: distance between the first

receiver and the last receiver

Data Acquisition ParametersData Acquisition ParametersNearest source-receiver offsetNearest source-receiver offset

Near-offset effect: Lower frequency components arenot fully developed as plane waves.

Plane-wave propagation of surface waves occurswhen the nearest source-receiver offset is greaterthan half the maximum desired wavelength.

The maximum desired wavelength is about equal tothe maximum investigation depth so that thenearest source-receiver offset is about equal to themaximum investigation depth.

Data Acquisition ParametersData Acquisition ParametersReceiver spacingReceiver spacing

Receiver spacing should follow the Nyquist samplingtheorem. Receiver spacing determines the shortestwavelength in recorded data, which is a guidelinefor determining thickness of a layer model and isalso a limit in the inverted S-wave velocity model.

Data Acquisition ParametersData Acquisition ParametersReceiver spreadReceiver spread

Receiver spread should also follow the Nyquistsampling theorem. Receiver spread determines thelongest wavelength in recorded data, which is aguideline for determining total thickness of layerson the top of the half-space.

The receiver spread is limited by far-offset effect.

Far-offset effect: Higher frequency components ofsurface 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.

Lower frequencycomponents are notfully developed asplane waves.

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

Far-offset effectsFar-offset effects

Nearest offset: 89 m.Receiver spacing: 1 m.Receiver spread: 40 m.

Higher frequencycomponents arecontaminated by bodywaves due toattenuation of highfrequency componentsof surface waves.

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

Optimum offsetOptimum offset

Nearest offset: 27 m.Receiver spacing: 1 m.Receiver spread: 40 m.

Linearity of surfacewave is clearlyimproved from4 Hz to 35 Hz.

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

40004000

00

2000 2000

40004000

How to check near-offset effects orfar-offset effects onimpulsive data?

Impulsive data toswept data:

Convolution

Swept data toimpulsive data(frequencydecomposition):

Correlation

Summary—Rule of thumbSummary—Rule of thumb❂ The nearest source-receiver offset = 1/3

to 1/2 of the maximum investigationdepth.

❂ Receiver spacing = the thinnest layer ofthe layer model.

❂ Receiver spread = 1 to 2 times of themaximum investigation depth.

Documents

Multichannel Analysis of Surface Wave - Exploration Services et al...velocity field by the multichannel analysis of surface wave technique: Proceedings of the Symposium on the Application