Improving the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion Data

Supranata, Yosep E.; Kalinski, Michael E.; Ye, Qiang

doi:10.1061/(asce)1532-3641(2007)7:5(333)

Cited by 14 publications

(15 citation statements)

References 9 publications

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“…Shear‐wave velocity error and thickness error are a measure of the cumulative difference between the true and inverted

V_{S}

profiles and thicknesses and are defined as (Supranata et al . )

E_{s} = \frac{\sqrt{\sum_{i = 1}^{M} {(V_{i}^{i n v e r t e d} - V_{i}^{t r u e})}^{2}}}{\sqrt{\sum_{i = 1}^{M} {(V_{i}^{t r u e})}^{2}}} \times 100 %, E_{H} = \frac{\sqrt{\sum_{i = 1}^{M} {(H_{i}^{i n v e r t e d} - H_{i}^{t r u e})}^{2}}}{\sqrt{\sum_{i = 1}^{M} {(H_{i}^{t r u e})}^{2}}} \times 100 %,

where

V_{i}^{i n v e r t e d} = inverted shear‐wave velocity

and

V_{i}^{t r u e} = inverted thickness

H_{i}^{i n v e r t e d} = inverted thickness

and

H_{i}^{t r u e} = inverted thickness

of the i th layer, respectively. The variable

M = number of shear‐wave velocities

(i.e., number of layers).…”

Section: Inversion By Genetic Algorithmmentioning

confidence: 99%

“…Rayleigh dispersion curve and Love dispersion curve errors are defined as (Supranata et al . )

E_{R} = \sqrt{\frac{\sum_{i = 1}^{N} {(V_{R, i}^{i n v e r t e d} - V_{R, i}^{t r u e})}^{2}}{N}} (m / s) E_{L} = \sqrt{\frac{\sum_{i = 1}^{N} {(V_{L, i}^{i n v e r t e d} - V_{L, i}^{t r u e})}^{2}}{N}} (m / s)

where

V_{R, i}^{i n v e r t e d} = Rayleigh dispersion curve

and

V_{L, i}^{^{i n v e r t e d}} = Love dispersion curve

obtained from the forward modelling of the inverted

V_{S}

profiles and

V_{R, i}^{t r u e} = Rayleigh dispersion curve

and

V_{L, i}^{t r u e} = Love dispersion curve

obtained from the forward modelling of the true

V_{S}

profiles. The variable

N = amount of Rayleigh

or Love phase velocities (i.e., dispersion data) used in the inversion, which is used to normalize error with respect to

N

due to the varying number of dispersion data used in each inversion.…”

Section: Inversion By Genetic Algorithmmentioning

confidence: 99%

“…To appraise the value of the accuracy of each inversion approach, differences between the true and inverted V S profiles and differences between the true and inverted thicknesses are quantified in terms of shear-wave velocity error (E S ) and thickness error (E H ), respectively. Shear-wave velocity error and thickness error are a measure of the cumulative difference between the true and inverted V S profiles and thicknesses and are defined as (Supranata et al 2007) (3)…”

Section: Numerical Errormentioning

confidence: 99%

“…Rayleigh dispersion curve and Love dispersion curve errors are a measure of the difference between the experimental dispersion data and the theoretical dispersion data derived from forward modelling of the inverted profile. Rayleigh dispersion curve and Love dispersion curve errors are defined as (Supranata et al 2007) (5) where V R,i inverted = Rayleigh dispersion curve and V L,i inverted = Love dispersion curve obtained from the forward modelling of the is z = 0. A spread of 48 geophones at 1 m spacing with 5 m nearoffset has been used.…”

Section: Generating Experimental Dispersion Curvesmentioning

confidence: 99%

See 3 more Smart Citations

Improving the accurate assessment of a shear‐wave velocity reversal profile using joint inversion of the effective Rayleigh wave and multimode Love wave dispersion curves

Hamimu

Safani

Nawawi

2010

Near Surface Geophysics

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Joint inversion codes of the effective Rayleigh wave and multimode Love wave dispersion curves based on modified GA have been developed. We focus on the attempt to improve the estimated shear‐wave velocity profile for a reversal subsurface structure. Two different profiles representing the high‐velocity layer (HVL) and low‐velocity layer (LVL) cases are used. Effective Rayleigh wave and multimode Love wave dispersion curves are synthesized from these profiles using full P‐SV waveform and full SH‐waveform reflectivity, respectively. The dispersion curves are then inverted using a modified genetic algorithm with two different inversion approaches, namely single inversion of Love/Rayleigh dispersion curves and joint inversion of Love and Rayleigh dispersion curves. To asses the accuracy of each inversion approach, differences between the true and inverted shear‐wave velocity profile are quantified in terms of shear‐wave velocity error, ES. Our numerical modelling showed that the shear‐wave velocity errors of the joint inversion approach are relatively smaller than the single inversion approach. These errors indicate that the accuracy of shear‐wave velocity reversal can be improved by jointly inverting Rayleigh wave and Love wave dispersion curves. All of these approaches have been applied on the real data acquired at a site in Niigata prefecture, Japan. In this field example, our inversion results show good agreement between the calculated and experimental dispersion curves and can well detect LVL targets.

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“…Shear‐wave velocity error and thickness error are a measure of the cumulative difference between the true and inverted

V_{S}

profiles and thicknesses and are defined as (Supranata et al . )

E_{s} = \frac{\sqrt{\sum_{i = 1}^{M} {(V_{i}^{i n v e r t e d} - V_{i}^{t r u e})}^{2}}}{\sqrt{\sum_{i = 1}^{M} {(V_{i}^{t r u e})}^{2}}} \times 100 %, E_{H} = \frac{\sqrt{\sum_{i = 1}^{M} {(H_{i}^{i n v e r t e d} - H_{i}^{t r u e})}^{2}}}{\sqrt{\sum_{i = 1}^{M} {(H_{i}^{t r u e})}^{2}}} \times 100 %,

where

V_{i}^{i n v e r t e d} = inverted shear‐wave velocity

and

V_{i}^{t r u e} = inverted thickness

H_{i}^{i n v e r t e d} = inverted thickness

and

H_{i}^{t r u e} = inverted thickness

of the i th layer, respectively. The variable

M = number of shear‐wave velocities

(i.e., number of layers).…”

Section: Inversion By Genetic Algorithmmentioning

confidence: 99%

“…Rayleigh dispersion curve and Love dispersion curve errors are defined as (Supranata et al . )

E_{R} = \sqrt{\frac{\sum_{i = 1}^{N} {(V_{R, i}^{i n v e r t e d} - V_{R, i}^{t r u e})}^{2}}{N}} (m / s) E_{L} = \sqrt{\frac{\sum_{i = 1}^{N} {(V_{L, i}^{i n v e r t e d} - V_{L, i}^{t r u e})}^{2}}{N}} (m / s)

where

V_{R, i}^{i n v e r t e d} = Rayleigh dispersion curve

and

V_{L, i}^{^{i n v e r t e d}} = Love dispersion curve

obtained from the forward modelling of the inverted

V_{S}

profiles and

V_{R, i}^{t r u e} = Rayleigh dispersion curve

and

V_{L, i}^{t r u e} = Love dispersion curve

obtained from the forward modelling of the true

V_{S}

profiles. The variable

N = amount of Rayleigh

or Love phase velocities (i.e., dispersion data) used in the inversion, which is used to normalize error with respect to

N

due to the varying number of dispersion data used in each inversion.…”

Section: Inversion By Genetic Algorithmmentioning

confidence: 99%

Section: Numerical Errormentioning

confidence: 99%

Section: Generating Experimental Dispersion Curvesmentioning

confidence: 99%

See 2 more Smart Citations

Improving the accurate assessment of a shear‐wave velocity reversal profile using joint inversion of the effective Rayleigh wave and multimode Love wave dispersion curves

Hamimu

Safani

Nawawi

2010

Near Surface Geophysics

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show abstract

“…Xia et al, 2000;Supranata et al, 2007) have already proposed inversion methods including higher modes of Rayleigh waves. They introduced an inversion method that assigns mode number to each observed phase velocity data and compares the assigned phase velocity with each mode of theoretical phase velocity.…”

Section: Inversion Using Genetic Algorithmmentioning

confidence: 99%

Analysis of Surface-Wave Data Including Higher Modes Using the Genetic Algorithm

Hayashi¹

2012

GeoCongress 2012

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Analysis of surface wave data generally assumes that a dispersion curve mainly consists of a fundamental mode. Higher modes may dominate in several types of velocity structures, such as a model in which a high-velocity layer overlays on a low-velocity layer or a model in which a high-velocity layer is embedded in lowvelocity layers. In these types of complex velocity structures, higher modes may dominate in particular frequency range and observed dispersion curves look very complex. It is generally difficult to separate the fundamental mode and the higher modes correctly and traditional inversion methods based on the Jacobiam matrix cannot be applied. In order to overcome these difficulties, we have developed a new inversion method using a genetic algorithm (GA). In this new method, phase velocities and relative amplitude for the fundamental and higher modes are calculated. For each frequency, residual between observed and theoretical phase velocities is defined as the difference of an observed phase velocity and a synthetic phase velocity that has maximum relative amplitude in all modes. The GA is applied to obtain a velocity model that provides minimum residual. In this paper, we describe typical examples of dispersion curves in which higher modes dominate. Secondly, the theory of the new inversion method and numerical examples are shown. Finally, application of the new method to an engineering site investigation is demonstrated.

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Joint inversion of Rayleigh and Love wave dispersion curves for improving the accuracy of near-surface S-wave velocities

Xiaofei

et al. 2020

Journal of Applied Geophysics

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Improving the Uniqueness of Surface Wave Inversion Using Multiple-Mode Dispersion Data

Cited by 14 publications

References 9 publications

Improving the accurate assessment of a shear‐wave velocity reversal profile using joint inversion of the effective Rayleigh wave and multimode Love wave dispersion curves

Improving the accurate assessment of a shear‐wave velocity reversal profile using joint inversion of the effective Rayleigh wave and multimode Love wave dispersion curves

Analysis of Surface-Wave Data Including Higher Modes Using the Genetic Algorithm

Joint inversion of Rayleigh and Love wave dispersion curves for improving the accuracy of near-surface S-wave velocities

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