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Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data.

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Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data. / Cordua, Knud S.; Nielsen, Lars; Looms, Majken C. et al.
In: Journal of Applied Geophysics, Vol. 68, No. 1, 05.2009, p. 71-84.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

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Cordua KS, Nielsen L, Looms MC, Hansen TM, Binley A. Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data. Journal of Applied Geophysics. 2009 May;68(1):71-84. doi: 10.1016/j.jappgeo.2008.12.002

Author

Cordua, Knud S. ; Nielsen, Lars ; Looms, Majken C. et al. / Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data. In: Journal of Applied Geophysics. 2009 ; Vol. 68, No. 1. pp. 71-84.

Bibtex

@article{a494c3f179b74c35b63edcdaa0aa2963,
title = "Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data.",
abstract = "Unknown borehole irregularities and small-scale velocity fluctuations near transmitter and receiver antennae positions may cause relatively strong travel time effects on cross-borehole ground penetrating radar (GPR) data. Previous studies have demonstrated that such effects may severely contaminate cross-borehole GPR tomographic images of radar wave velocity if they are not properly accounted for prior to, or during, inversion. In this paper we calculate the travel time effect of cavities in the borehole walls and small-scale velocity anomalies near the antennae positions using a full waveform modeling algorithm. We define covariance matrices for static-like errors which approximately capture the overall correlation properties of these effects. In synthetic tests, we investigate to which extent the resolution of least-squares-based tomographic inversion is affected by the calculated error types under different assumptions made about the statistical properties of the data errors. We find that the effects of the correlated data errors may be significantly suppressed if static-like errors are accounted for during inversion, even though the errors are not strictly static. Furthermore, we demonstrate that when static-like errors are accounted for, model resolution does not decline significantly, even when the expectation to the standard deviation of the data errors is increased above the level of the correlated errors. We implement this approach of accounting for correlated data errors in a sequential simulation algorithm, which we use to solve the inverse tomographic problem in order to obtain multiple realizations of the fine-scale GPR velocity distribution between the boreholes. Synthetic tests show that the assumptions made about the error correlation properties are significant for obtaining reliable images of the fine-scaled velocity distribution between the boreholes, even in cases where the correct prior knowledge about model correlation properties are available. We observe that the static-like data errors may introduce artifacts in the velocity distributions near the borehole walls if they are not properly accounted for during the conditioned simulation process. We apply the sequential simulation algorithm to a real data set from Arren{\ae}s, Denmark and demonstrate that accounting for correlated data errors has a significant effect on the interpretation of the field data. In comparison to the standard approach in which errors are considered to be uncorrelated, higher resolution images with stronger contrasts between high- and low-velocity anomalies are produced when correlation of the data errors are accounted for.",
keywords = "Ground penetrating radar (GPR), Cross-borehole, Tomography, Resolution analysis, Correlated data errors, Sequential simulation",
author = "Cordua, {Knud S.} and Lars Nielsen and Looms, {Majken C.} and Hansen, {Thomas M.} and Andrew Binley",
year = "2009",
month = may,
doi = "10.1016/j.jappgeo.2008.12.002",
language = "English",
volume = "68",
pages = "71--84",
journal = "Journal of Applied Geophysics",
issn = "0926-9851",
publisher = "Elsevier",
number = "1",

}

RIS

TY - JOUR

T1 - Quantifying the influence of static-like errors in least-squares-based inversion and sequential simulation of cross-borehole ground penetrating radar data.

AU - Cordua, Knud S.

AU - Nielsen, Lars

AU - Looms, Majken C.

AU - Hansen, Thomas M.

AU - Binley, Andrew

PY - 2009/5

Y1 - 2009/5

N2 - Unknown borehole irregularities and small-scale velocity fluctuations near transmitter and receiver antennae positions may cause relatively strong travel time effects on cross-borehole ground penetrating radar (GPR) data. Previous studies have demonstrated that such effects may severely contaminate cross-borehole GPR tomographic images of radar wave velocity if they are not properly accounted for prior to, or during, inversion. In this paper we calculate the travel time effect of cavities in the borehole walls and small-scale velocity anomalies near the antennae positions using a full waveform modeling algorithm. We define covariance matrices for static-like errors which approximately capture the overall correlation properties of these effects. In synthetic tests, we investigate to which extent the resolution of least-squares-based tomographic inversion is affected by the calculated error types under different assumptions made about the statistical properties of the data errors. We find that the effects of the correlated data errors may be significantly suppressed if static-like errors are accounted for during inversion, even though the errors are not strictly static. Furthermore, we demonstrate that when static-like errors are accounted for, model resolution does not decline significantly, even when the expectation to the standard deviation of the data errors is increased above the level of the correlated errors. We implement this approach of accounting for correlated data errors in a sequential simulation algorithm, which we use to solve the inverse tomographic problem in order to obtain multiple realizations of the fine-scale GPR velocity distribution between the boreholes. Synthetic tests show that the assumptions made about the error correlation properties are significant for obtaining reliable images of the fine-scaled velocity distribution between the boreholes, even in cases where the correct prior knowledge about model correlation properties are available. We observe that the static-like data errors may introduce artifacts in the velocity distributions near the borehole walls if they are not properly accounted for during the conditioned simulation process. We apply the sequential simulation algorithm to a real data set from Arrenæs, Denmark and demonstrate that accounting for correlated data errors has a significant effect on the interpretation of the field data. In comparison to the standard approach in which errors are considered to be uncorrelated, higher resolution images with stronger contrasts between high- and low-velocity anomalies are produced when correlation of the data errors are accounted for.

AB - Unknown borehole irregularities and small-scale velocity fluctuations near transmitter and receiver antennae positions may cause relatively strong travel time effects on cross-borehole ground penetrating radar (GPR) data. Previous studies have demonstrated that such effects may severely contaminate cross-borehole GPR tomographic images of radar wave velocity if they are not properly accounted for prior to, or during, inversion. In this paper we calculate the travel time effect of cavities in the borehole walls and small-scale velocity anomalies near the antennae positions using a full waveform modeling algorithm. We define covariance matrices for static-like errors which approximately capture the overall correlation properties of these effects. In synthetic tests, we investigate to which extent the resolution of least-squares-based tomographic inversion is affected by the calculated error types under different assumptions made about the statistical properties of the data errors. We find that the effects of the correlated data errors may be significantly suppressed if static-like errors are accounted for during inversion, even though the errors are not strictly static. Furthermore, we demonstrate that when static-like errors are accounted for, model resolution does not decline significantly, even when the expectation to the standard deviation of the data errors is increased above the level of the correlated errors. We implement this approach of accounting for correlated data errors in a sequential simulation algorithm, which we use to solve the inverse tomographic problem in order to obtain multiple realizations of the fine-scale GPR velocity distribution between the boreholes. Synthetic tests show that the assumptions made about the error correlation properties are significant for obtaining reliable images of the fine-scaled velocity distribution between the boreholes, even in cases where the correct prior knowledge about model correlation properties are available. We observe that the static-like data errors may introduce artifacts in the velocity distributions near the borehole walls if they are not properly accounted for during the conditioned simulation process. We apply the sequential simulation algorithm to a real data set from Arrenæs, Denmark and demonstrate that accounting for correlated data errors has a significant effect on the interpretation of the field data. In comparison to the standard approach in which errors are considered to be uncorrelated, higher resolution images with stronger contrasts between high- and low-velocity anomalies are produced when correlation of the data errors are accounted for.

KW - Ground penetrating radar (GPR)

KW - Cross-borehole

KW - Tomography

KW - Resolution analysis

KW - Correlated data errors

KW - Sequential simulation

U2 - 10.1016/j.jappgeo.2008.12.002

DO - 10.1016/j.jappgeo.2008.12.002

M3 - Journal article

VL - 68

SP - 71

EP - 84

JO - Journal of Applied Geophysics

JF - Journal of Applied Geophysics

SN - 0926-9851

IS - 1

ER -