Effects of low-pass filtering on the calculated structural index from magnetic data

Euler and extended Euler deconvolution applications use an assumed structural index (SI) or calculate the SI, respectively, for magnetic anomaly data within a specified window. The structural index depends on the source type: specifically, the rate at which the field produced by the source decays. We have examined the effects that the application of low-pass filtering to magnetic data has on estimating the SI. Using a simple low-pass filter, we derived the SI for filtered-field solutions directly over, and away from, a target based on the magnetic potential of a vertical dipole [Formula: see text]. We validated this approach by applying extended Euler deconvolution to synthetic and field examples. In general, filtered magnetic data will decrease the numerically determined SI to a value lower than the theoretical one. The slope and cutoff wavelength of the filter directly affect the estimated SI solutions. The results prove that one must take into account filtering for the application of Euler deconvolution to locate dipole anomalies for unexploded ordnance detection.

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Statistics of fine-scale velocity in turbulent plane and circular jets

Journal of Fluid Mechanics ◽

10.1017/s0022112082001268 ◽

1982 ◽

Vol 119 ◽

pp. 55-89 ◽

Cited By ~ 90

Author(s):

R. A. Antonia ◽

B. R. Satyaprakash ◽

A. K. M. F. Hussain

Keyword(s):

Streamwise Velocity ◽

Higher Order ◽

Pass Filter ◽

Low Pass Filter ◽

A Value ◽

Circular Jets ◽

Low Pass ◽

Number Variation ◽

Turbulent Plane ◽

Velocity Derivative

Higher-order statistics of the streamwise velocity derivative have been measured on the centre-line of turbulent plane and circular jets. The instrumentation and sources of error are discussed to establish the accuracy of the data and convergence of statistics. The optimum setting for the low-pass filter cut-off was found to be 1·75 times the Kolmogorov frequency fK, in contrast with the majority of previous investigations where it was set equal to fK. The magnitude of the constant μ in Kolmogorov's revised hypothesis is obtained using statistics derived from the instantaneous velocity derivative or its squared value. The correlation and spectrum of fluctuations of the squared velocity derivative and the Reynolds-number variation of the skewness and flatness factors of the velocity derivative are consistent with μ ≃ 0·2, while the most popular value used is 0·5. Second-order moments of the locally averaged dissipation, assumed proportional to the squared streamwise velocity derivative, and breakdown coefficients also suggest a value of μ of about 0·2. Higher-order correlations and spectra of the dissipation are in closer agreement with the Novikov-Stewart or β-model than with Kolmogorov's lognormal model. Higher-order moments of locally averaged values of the dissipation rate are more closely represented by the lognormal than the β-model.

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On the estimation of the structural index from low-pass filtered magnetic data

Geophysics ◽

10.1190/geo2013-0421.1 ◽

2014 ◽

Vol 79 (6) ◽

pp. J67-J80 ◽

Cited By ~ 20

Author(s):

Giovanni Florio ◽

Maurizio Fedi ◽

Roman Pašteka

Keyword(s):

Magnetic Data ◽

Main Task ◽

Euler Deconvolution ◽

Structural Index ◽

Potential Field Data ◽

Upward Continuation ◽

Physically Based ◽

Low Pass ◽

Butterworth Filters ◽

Low Pass Filters

The estimation of the structural index and of the depth to the source is the main task of many popular methods used to analyze potential field data, such as Euler deconvolution. However, these estimates are unstable even in the presence of a weak amount of noise, and Euler deconvolution of noisy data leads to an underestimation of structural index and depth. We have studied how the structural index and depth estimates are affected by applying low-pass filtering to the data. Physically based low-pass filters, such as upward continuation and integration, have been shown to be the best choice over a range of altitudes (upward continuation) or orders (integration filters), mainly because their outputs have a well-defined physical meaning. In contrast, mathematical low-pass filters require that the filter parameters be tuned carefully by means of several trial tests to produce optimally smoothed fields. The C-norm criterion is a reliable strategy to produce a stabilized vertical derivative, and we discourage Butterworth filters because they tend to a vertical integral filter, for a high cutoff wavenumber, thus complicating the interpretation of the estimated structural index. We found that the estimated structural index and depth to source increase proportionally with the amount of smoothing, unless in the case of overfiltering. In that case, the severe distortion of the original field may cause a decrease of the estimated structural index and depth to source.

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