Q factor estimation based on the method of logarithmic spectral area difference

Wang, Shoudong; Yang, Dengfeng; Li, Jingnan; Song, Huijuan

doi:10.1190/geo2014-0257.1

Cited by 52 publications

(11 citation statements)

References 24 publications

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“…The Q estimation based on equation is known as the LSAD method, which was proposed by Wang et al . (). The noise robustness of the Q estimation is improved considerably when the logarithmic spectrum frequency integration is applied.…”

Section: Theorymentioning

confidence: 97%

“…Wang et al . () defined the logarithmic spectral area, which is the definite integral of the function of logarithmic spectrum

\ln S_{i} false(f false)

with a given frequency interval [

f_{L}

f_{H}

], at depth h i as

A_{i} = \int_{f_{L}}^{f_{H}} \ln S_{i} ((), f) d f .

Therefore, we can obtain the logarithmic spectral area difference (LSAD) between the two receivers as follows:

Δ A_{i} = \int_{f_{L}}^{f_{H}} \ln S_{i} ((), f) d f - \int_{f_{L}}^{f_{H}} \ln S_{i + 1} ((), f) d f = \int_{f_{L}}^{f_{H}} \ln \frac{S_{i} ((), f)}{S_{i + 1} (f)} d f .

…”

Section: Theorymentioning

confidence: 99%

“…For the zero‐offset VSP data, Wang et al . () calculated the transmission coefficient p i of the i th impedance interface using the formula as follows:

p_{i} = \frac{2 ρ_{i} {boldv}_{i}}{ρ_{i + 1} {boldv}_{i + 1} + ρ_{i} {boldv}_{i}},

where the interval velocity v i can be calculated from the first arrivals, the density ρ i can also be obtained by the Gardner, Gardner and Gregory () empirical equation,

ρ_{i} = 0.31 \times {v_{i}}^{\frac{1}{4}}

. The total transmission coefficient P i is equivalent to the continuous product of the transmission coefficients at each impedance interface, that is,

P_{i} = \prod_{j}^{i - 1} p_{j}

.…”

Section: Theorymentioning

confidence: 99%

“…Assuming that the data have been corrected by geometric diffusion, in terms of equations and of LSAD, a formula for Q estimation called the LSAD method is expressed as (Wang et al . )

Q_{i} = \frac{Δ t_{i}}{Δ A_{i} + \int_{f_{L}}^{f_{H}} \ln P_{i} d f} \int_{f_{L}}^{f_{H}} π fdf

in order to archive the layer quality factors, Q n ( n = 1, …, N ). Assuming that the record of the first receiver on the ground is taken as the reference trace, a series of average‐ Q factors can be obtained by the formula (Wang et al .…”

Section: Theorymentioning

confidence: 99%

“…Wang et al . () proposed a new logarithmic spectral area difference (LSAD) method based on logarithmic spectral frequency integration, and by applying the Q ‐value estimation to vertical seismic profile (VSP) data achieved a considerable improvement in the anti‐noise and stability of Q ‐value estimation results. However, it is necessary to know the transmission coefficients of each transmission interface, and the accuracy of the Q ‐value estimation is often affected by estimation errors in the transmission coefficients.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Estimation of near‐surface Q factor under constraint of layered velocity based on uphole survey data

Zhao

Meihou

et al. 2020

Near Surface Geophysics

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To improve the resolution of seismic data, it is important to accurately estimate the near‐surface quality factor, Q, which provides a measure of seismic wave attenuation. In view of the unique advantages provided by uphole surveys when investigating near‐surface structures, they are widely employed to estimate the near‐surface Q factor. However, the Q factor estimated using the traditional spectral ratio method is not always precise and provides larger oscillations in the estimated Q factors due to errors associated with first‐break picking and velocity estimation. Following on the traditional logarithmic spectral ratio method, a new method called the logarithmic spectral ratio integral method was proposed to estimate the layer Q factor using uphole survey data. It calculates first the weighted integral of the logarithmic spectral ratio in an effective frequency interval between non‐adjacent traces, then makes a linear regression between the inter‐trace travel moveout and the weighted integral of logarithmic spectral ratio under the constraint of velocity stratification. The result of model analysis shows that under an ideal condition (without first‐break picking errors), the layer Q values estimated by the logarithmic spectral ratio integral method are fairly consistent with the true layer‐specific Q values in the model. In addition, the Q values estimated from field‐measured data and data from forward modelling with 10% random noise added, both have smaller mean relative errors than the results using traditional spectral ratio method and the double‐linear regression method. A case study is employed and the results show that the layer Q factor estimated using the new method correlates well with the velocity stratification and is thus applicable for use with various uphole survey observation systems. Furthermore, all results indicate that the logarithmic spectral ratio integral method delivers a more precise and stable estimation of the layered Q than the other methods, and the anti‐noise characteristics are stronger.

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Section: Theorymentioning

confidence: 97%

“…Wang et al . () defined the logarithmic spectral area, which is the definite integral of the function of logarithmic spectrum

\ln S_{i} false(f false)

with a given frequency interval [

f_{L}

f_{H}

], at depth h i as

A_{i} = \int_{f_{L}}^{f_{H}} \ln S_{i} ((), f) d f .

Therefore, we can obtain the logarithmic spectral area difference (LSAD) between the two receivers as follows:

Δ A_{i} = \int_{f_{L}}^{f_{H}} \ln S_{i} ((), f) d f - \int_{f_{L}}^{f_{H}} \ln S_{i + 1} ((), f) d f = \int_{f_{L}}^{f_{H}} \ln \frac{S_{i} ((), f)}{S_{i + 1} (f)} d f .

…”

Section: Theorymentioning

confidence: 99%

“…For the zero‐offset VSP data, Wang et al . () calculated the transmission coefficient p i of the i th impedance interface using the formula as follows:

p_{i} = \frac{2 ρ_{i} {boldv}_{i}}{ρ_{i + 1} {boldv}_{i + 1} + ρ_{i} {boldv}_{i}},

where the interval velocity v i can be calculated from the first arrivals, the density ρ i can also be obtained by the Gardner, Gardner and Gregory () empirical equation,

ρ_{i} = 0.31 \times {v_{i}}^{\frac{1}{4}}

. The total transmission coefficient P i is equivalent to the continuous product of the transmission coefficients at each impedance interface, that is,

P_{i} = \prod_{j}^{i - 1} p_{j}

.…”

Section: Theorymentioning

confidence: 99%

“…Assuming that the data have been corrected by geometric diffusion, in terms of equations and of LSAD, a formula for Q estimation called the LSAD method is expressed as (Wang et al . )