On: “Mineral discrimination and removal of inductive coupling with multifrequency IP” by W. H. Pelton, S. H. Ward, P. G. Hallof, W. R. Sill, and P. H. Nelson (GEOPHYSICS, 43, 588–609).

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1556-1557
Author(s):  
Heikki Soininen
Keyword(s):  
Apparent Resistivity ◽  
Dispersion Model ◽  
Constant Factor ◽  
Constant Independent ◽  
Real Constant ◽  
Frequency Range ◽  
Dilution Factor ◽  
Amplitude Spectra ◽  
Polarizable Body ◽  
Phase Spectra

The authors discussed the behavior of the resistivity spectra by means of the Cole‐Cole dispersion model. They also discussed the corrections with which the petrophysical resistivity spectrum can be reduced into an apparent resistivity spectrum caused by a polarizable body embedded in an unpolarizable environment. The application of the Cole‐Cole dispersion model is a marked step forward in spectral IP analysis. However, closer attention must be paid to the assumptions and approaches on which the authors base the relations between the petrophysical and apparent spectra. The authors based their relations between the true and apparent spectra on the use of the dilution factor [Formula: see text]. In accordance with the definition by Seigel (1959), they assumed that [Formula: see text] is a real constant (independent of frequency) over the whole frequency range under consideration. First consider the justification for the assumption of the existence of a constant factor [Formula: see text] in the light of an example calculated for phase spectra. Similar considerations could also be made with the aid of amplitude spectra.

The behavior of the apparent resistivity phase spectrum in the case of a polarizable prism in an unpolarizable half‐space

Geophysics ◽  
1984 ◽  
Vol 49 (9) ◽  
pp. 1534-1540 ◽  
Author(s):  
Heikki Soininen
Keyword(s):  
Frequency Dependence ◽  
Half Space ◽  
Time Constant ◽  
Apparent Resistivity ◽  
Dispersion Model ◽  
Three Dimensional ◽  
Phase Spectrum ◽  
True Time ◽  
Polarizable Body ◽  
Lower Frequencies

In the application of the broadband induced polarization method, it is necessary to know how a petrophysical resistivity spectrum is transformed into an apparent spectrum measured in the field. Investigated in the present work was the forming of an apparent spectrum in the case of a polarizable three‐dimensional prism embedded in an unpolarizable half‐space for gradient and dipole‐dipole arrays. The computations were done numerically using the integral equation technique. The frequency dependence of the resistivity of the prism was depicted by means of the Cole‐Cole dispersion model. With this simple model geometry, the phase spectra of apparent resistivity resemble quite closely in functional form the original petrophysical phase spectrum of the Cole‐Cole dispersion model. The apparent spectra have shifted on the log‐log scale downward, owing to geometric attenuation, and toward lower frequencies. The apparent Cole‐Cole parameters have been inverted from the apparent spectra. The apparent chargeability is generally noticeably smaller, owing to the geometric attenuation, than the chargeability of the original petrophysical spectrum. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The shift of the apparent phase spectrum toward lower frequencies partly compensates for the decrease in the apparent time constant caused by attenuation of the spectrum. The apparent time constant is thus close to the true time constant of the petrophysical spectrum. It is therefore possible in principle to obtain by direct inversion from an apparent spectrum measured in the field a reasonable estimate of the frequency dependence and time constant of the true spectrum of a polarizable body.

Determination of crustal thickness from spectral behavior of SH waves

1969 ◽  
Vol 59 (3) ◽  
pp. 1247-1258
Author(s):  
Abou-Bakr K. Ibrahim
Keyword(s):  
Amplitude Spectrum ◽  
Body Waves ◽  
Multiple Reflections ◽  
Matrix Formulation ◽  
Sh Waves ◽  
Crustal Model ◽  
Amplitude Spectra ◽  
Phase Spectra ◽  
Zero Phase

abstract The amplitude spectrum obtained from Haskell's matrix formulation for body waves travelling through a horizontally layered crustal model shows a sequence of minima and maxima. It is known that multiple reflections within the crustal layers produce constructive and destructive interferences, which are shown as maxima and minima in the amplitude spectrum. Analysis of the minima in the amplitude spectra, which correspond to zero phase in the phase spectra, enables us to determine the thickness of the crust, provided the ratio of wave velocity in the crust to velocity under the Moho is known.

When the Hydrophone Works as an Accelerometer

2020 ◽  
Vol 92 (1) ◽  
pp. 365-377
Author(s):  
Giovanni Iannaccone ◽  
Giuseppe Pucciarelli ◽  
Sergio Guardato ◽  
Gian Paolo Donnarumma ◽  
Giovanni Macedonio ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Pressure ◽  
Vertical Component ◽  
Forced Oscillations ◽  
Campi Flegrei ◽  
Frequency Range ◽  
Ground Acceleration ◽  
Seismic Sensors ◽  
Wide Range ◽  
Amplitude Spectra

Abstract We show the equivalence of earthquake-induced ground acceleration and water-pressure waveforms for the case of collocated hydrophones and seafloor seismometers installed in shallow water. In particular, the comparison of the waveforms and amplitude spectra of the acceleration and water-pressure signals confirms the existence of a frequency range of “forced oscillations” in which the water-pressure variations are proportional to the vertical component of the ground acceleration. We demonstrate the equivalence of the acceleration and water-pressure signals for a set of local earthquakes (epicenter distance of a few tens of kilometers) and regional earthquakes with a wide range of magnitude (2.7<Mw<6.8), recorded by seismometers and hydrophones operating in shallow water (depth less than 80 m) in the Campi Flegrei caldera (southern Italy). We describe the “forced oscillations” theory, and we demonstrate the signals equivalence in the frequency range 0.1–10 Hz, thus extending the frequency range of application of the hydrophones as accelerometers. The high correlation between the ground acceleration, derived from the ground velocity, and hydrophone pressure signals in the mentioned frequency range enables the use of the hydrophone waveforms for standard seismological studies (i.e., earthquake source). The calibration of hydrophones by comparison with collocated accelerometers, or seismometers, is also enabled in a range of frequencies that is very difficult to reproduce in a laboratory. The results of our work also open the possibility of hydrophones being more extensively used in place of accelerometers in marine environments where accurate installation of seismic sensors is difficult or unaffordable.

True and apparent spectra of buried polarizable targets

Geophysics ◽  
1984 ◽  
Vol 49 (2) ◽  
pp. 171-176 ◽  
Author(s):  
D. Guptasarma
Keyword(s):  
Numerical Modeling ◽  
Phase Shift ◽  
Host Rock ◽  
Field Measurements ◽  
Phase Spectrum ◽  
Complex Frequency ◽  
Minimum Phase ◽  
Dilution Factor ◽  
Shift Type ◽  
Phase Spectra

If the chargeability of a buried target is not infinitesimal, the popularly used low chargeability approximation formulated by Seigel (1959) can produce large errors in the computation of apparent polarizability spectra. A more accurate alternative approximation, based on a complex, frequency dependent “dilution factor” is presented. It turns out that for dispersions of the minimum phase shift type this approximation can be somewhat simplified and that for targets with such a dispersion, buried in a nondispersive host rock, the apparent log‐phase spectrum is only slightly different from a vertically shifted version of the true phase spectrum of the target. These results should be useful for the computation of apparent polarizabilities in numerical modeling for IP, and in attempts for mineral discrimination through field measurements of phase spectra.

A RECORDING-BASED APPROACH FOR IDENTIFYING SEISMIC SITE LIQUEFACTION AND NONLINEARITY VIA HHT DATA ANALYSIS

2009 ◽  
Vol 01 (01) ◽  
pp. 89-123 ◽  
Author(s):  
RAY RUICHONG ZHANG
Keyword(s):  
Data Analysis ◽  
Instantaneous Frequency ◽  
Temporal Frequency ◽  
Site Investigation ◽  
Intermediate Frequency ◽  
Site Amplification ◽  
Reduction Factor ◽  
Nonlinear Phenomena ◽  
Frequency Range ◽  
Amplitude Spectra

This study proposes an approach to identify earthquake-induced site liquefaction and/or nonlinearity from Hilbert–Huang–Transformation- or HHT-based data analysis of seismic motion recordings. The proposed approach fully utilizes unique features of the HHT method in characterizing instantaneous frequency and damping as well as temporal-frequency motion from the recordings, so as to single out and quantify liquefaction- and/or nonlinear-soil-related nonlinear phenomena shown in the recordings. With post-earthquake, site investigation as a reference, this study shows that the proposed approach is effective in characterizing site nonlinearity, quantifying nonlinear influences in site amplification, and diagnosing site liquefaction. Major results from this study are listed below.1. Predominant instantaneous frequency of earthquake motion is defined as the frequency with the largest amplitude in Hilbert amplitude spectra of the motion at a time instant, and subsequently used together with other motion features for identifying site liquefaction conditions. Analysis of 29 sets of seismic recordings with different liquefaction conditions shows that the proposed approach is more effective in detecting site liquefaction than other Fourier-based methods.2. HHT-based site amplification is defined as the ratio of marginal Hilbert amplitude spectra, similar to the Fourier-based one that is the ratio of Fourier amplitude spectra. The HHT-based site amplification can be used for effectively quantifying site nonlinearity in terms of frequency downshift in the low-frequency range and amplification-reduction factor in intermediate-frequency range in comparison with the Fourier-based one.3. Instantaneous damping, and Hilbert and marginal Hilbert damping spectra are defined in way similar to instantaneous frequency, and Hilbert and marginal Hilbert amplitude spectra, respectively. Consequently, the HHT-based site damping is found as the difference of marginal Hilbert damping spectra, which can be used as an alternative, complementary index to measure influences of site nonlinearity in seismic ground responses.

Accurate dispersion model for microstrip line up to terahertz frequency range

2013 ◽  
Author(s):  
Ritu Bansal ◽  
Yogendra K. Awasthi ◽  
Paramjeet Singh ◽  
Anand K. Verma
Keyword(s):  
Microstrip Line ◽  
Dispersion Model ◽  
Terahertz Frequency ◽  
Frequency Range ◽  
Terahertz Frequency Range

scholarly journals Object Clusters or Spectral Energy? Assessing the Relative Contributions of Image Phase and Amplitude Spectra to Trypophobia

2019 ◽  
Author(s):  
R. Nathan Pipitone ◽  
Chris DiMattina
Keyword(s):  
Amplitude Spectrum ◽  
Spectral Energy ◽  
Visual Comfort ◽  
Visual Discomfort ◽  
Comfort Levels ◽  
Spatial Frequencies ◽  
Amplitude Spectra ◽  
Small Clusters ◽  
Full Factorial ◽  
Phase Spectra

Trypophobia refers to the visual discomfort experienced by some people when viewing clustered patterns (e.g., clusters of holes). Trypophobic images deviate from the 1/f amplitude spectra typically characterizing natural images by containing excess energy at mid-range spatial frequencies. While recent work provides partial support for the idea of excess mid-range spatial frequency energy causing visual discomfort when viewing trypophobic images, a full factorial manipulation of image phase and amplitude spectra has yet to be conducted. Here, we independently manipulated the phase and amplitude spectra of 31 Trypophobic images using a standard Fast Fourier Transform (FFT). Participants rated the four different versions of each image for levels of visual comfort, and completed the Trypophobia Questionnaire (TQ). Images having the original phase spectra intact (with either original or 1/f amplitude) explained the most variance in comfort ratings and were rated lowest in comfort. However, images with the original amplitude spectra but scrambled phase spectra were rated higher in comfort, with a smaller amount of variance in comfort attributed to the amplitude spectrum. Participant TQ scores correlated with comfort ratings only for images having the original phase spectra intact. There was no correlation between TQ scores and comfort levels when participants viewed the original amplitude / phase-scrambled images. Taken together, the present findings show that the phase spectrum of trypophobic images, which determines the pattern of small clusters of objects, plays a much larger role than the amplitude spectrum in determining visual comfort.

The behavior of the apparent resistivity phase spectrum in the case of two polarizable media

Geophysics ◽  
1985 ◽  
Vol 50 (5) ◽  
pp. 810-819 ◽  
Author(s):  
Heikki Soininen
Keyword(s):  
Frequency Dependence ◽  
Half Space ◽  
Time Constant ◽  
Apparent Resistivity ◽  
Dispersion Model ◽  
Phase Spectrum ◽  
The Body ◽  
Spectral Parameters ◽  
The Difference ◽  
True Time

I employed numerical modeling to examine the formation of the apparent resistivity phase spectrum first of a polarizable prism situated in a polarizable half‐space, and second of two polarizable prisms joined in an unpolarizable half‐space. The calculations were done using the integral equation technique. The frequency dependence of the resistivity of the polarizable medium is depicted by means of the Cole‐Cole dispersion model. The effect of a weakly polarizable half‐space may be handled by simply adding the phase angle of the half‐space to the apparent phase due to the body. The apparent spectral parameters can be inverted by fitting the sum of two Cole‐Cole dispersion model phase spectra to the apparent phase spectrum. Of the parameters describing the prism, the apparent chargeability is smaller than the chargeability of the original petrophysical spectrum because of geometric attenuation. The apparent frequency dependence, on the other hand, is very close to the value of the original frequency dependence. The apparent time constant is commonly also near the true time constant of the petrophysical spectrum. The values of the apparent spectral parameters of the polarizable half‐space are all close to their petrophysical or true values. The apparent spectrum of two polarizable prisms builds up in a complex fashion. Nevertheless, by measuring the spectra at a number of points along a profile crossing over two formations differing in time constant, the various components can be discriminated from the apparent spectrum even if the difference in time constant is small. As the conductivity contrast decreases, the share of the spectrum of the formation in the apparent spectrum increases. Similarly, the formation with the smaller time constant is in a more advantageous position than the body with the greater time constant.

scholarly journals The effects of fixational tremor on the retinal image

2018 ◽  
Author(s):  
Norick R. Bowers ◽  
Alexandra E. Boehm ◽  
Austin Roorda
Keyword(s):  
Adaptive Optics ◽  
High Frequency ◽  
Retinal Image ◽  
Frequency Range ◽  
Active Fixation ◽  
Amplitude Spectra ◽  
Eye Motion ◽  
Fixation Task ◽  
Optical Blur ◽  
High Frequency Oscillatory

AbstractThe study of fixational eye motion (FEM) has implications for the neural and computational underpinnings of vision. One component of FEM is tremor, a high-frequency oscillatory jitter reported to be anywhere from ∼5 to 60 seconds of arc in amplitude. In order to isolate the effects of tremor on the retinal image directly and in the absence of optical blur, high-frequency, high-resolution eye traces were collected in 6 subjects from videos recorded with an Adaptive Optics Scanning Laser Ophthalmoscope. Videos were acquired while subjects engaged in an active fixation task where they fixated on a tumbling E stimulus and reported changes in its orientation. Spectral analysis was conducted on isolated segments of optical drift. The resultant amplitude spectra showed a slight deviation from the traditional 1/f nature of optical drift in the frequency range of 50-100 Hz, which is indicative of tremor; however, the amplitude of this deviation rarely exceeded one second of arc, smaller than any magnitude previously reported.

Wide Frequency Characterization of Magnetic Properties of Commercial LTCC Ferrite Material

2011 ◽  
Vol 2011 (CICMT) ◽  
pp. 000224-000231
Author(s):  
Nelu Blaž ◽  
Andrea Marić ◽  
Goran Radosavljević ◽  
Nebojša Mitrović ◽  
Ibrahim Atassi ◽  
...  
Keyword(s):  
Dispersion Model ◽  
Low Frequency ◽  
Hysteresis Loops ◽  
Wide Frequency Range ◽  
Complex Permeability ◽  
Frequency Range ◽  
Dispersion Parameters ◽  
Simple Method ◽  
Microwave Engineering ◽  
Characterization Procedure

Complex magnetic permeability and hysteresis characteristic are key parameters that determine properties of ferrite components. This paper offers effective, accurate and simple method for complex permeability determination of LTCC (Low Temperature Co-fired Ceramic) ferrite sample at wide frequency range (up to 1 GHz). Presented research can be found to be of importance in fields of ferrite components design and application, as well as RF and microwave engineering. The characterization sample is a stack of LTCC tapes forming a toroidal shape structure. Commercially available ferrite tape ESL 40012 was used and standard LTCC processing applied for the sample fabrication. Permeability is determined in the frequency range from 10 kHz to 1 GHz and characterization procedure is divided in two segments - for low and high frequencies. Low frequency measurements (from 10 kHz to 1000 kHz) are performed using LCZ meter and discrete turns of wire, while a short coaxial sample holder and Vector Network Analyzer were used for the higher frequency range (from 1000 kHz to 1 GHz). Hysteresis properties of this material are also determined. B-H hysteresis loops were measured with BROCKHAUS Tester MPG 100D system using the maximum excitation of 2 kA/m and frequencies of 50 Hz, 500 Hz and 1000 Hz. In addition, we presented another important factor in the practical design, the temperature variation of the permeability dispersion parameters. Obtained results show good agreement with datasheet values given by the manufacturer at lower frequencies and are in good correlation with results extracted from developed dispersion model at higher frequencies.

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