On the determination of the apparent frequency-effect in the frequency-domain induced polarization method

Clay horizons and other clay‐bearing unconsolidated sediments are potential sources of induced‐polarization anomalies. If such anomalies may be detected above system noise, the induced‐polarization method may be of value for in‐situ classification of unconsolidated sediments encountered in hydrological projects. One such project exists in Santa Clara County where near‐surface unconsolidated sediments are frequently considered as potential recharge areas. Of four areas surveyed with induced‐polarization apparatus in Santa Clara County, only two yielded significant frequency‐effect anomalies, and in each of these two the frequency effects were of the order of 3 percent. These anomalous frequency effects may be related to clayey gravels. The dipole‐dipole array, with spreads of 10 ft and 20 ft, was typically used in the study.

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A COMPARISON OF THE VARIOUS PARAMETERS EMPLOYED IN THE VARIABLE‐FREQUENCY INDUCED‐POLARIZATION METHOD

Geophysics ◽

10.1190/1.1439376 ◽

1964 ◽

Vol 29 (3) ◽

pp. 425-433 ◽

Cited By ~ 18

Author(s):

Philip G. Hallof

Keyword(s):

Induced Polarization ◽

Frequency Effect ◽

Variable Frequency ◽

Transient Method ◽

Polarization Method ◽

Applied Current ◽

Frequency Method ◽

Pulse Transient Method ◽

Factor Data ◽

The Time Domain

The increased use of the induced‐polarization method in recent years has resulted in two methods of measurement. The measurements in the frequency domain (variable‐frequency method) rely on changes in the apparent resistivities measured as the frequency of the applied current is varied. The measurement in the time domain (pulse‐transient method) detects transients in the measured potentials when the applied current is interrupted. The “chargeability” is the parameter used in the pulse‐transient method, while both the “frequency effect” and the normalized parameter “metal factor” are used in the variable‐frequency method. The most useful parameter would be the one which best indicates the amount of metallic mineralization present. Eight sets of field results from variable‐frequency field surveys are shown. The cases are shown in pairs; in each pair, the geometry of the source is much the same. By comparing the resistivity, the frequency effect (chargeability), and metal‐factor data with the amount of mineralization indicated by the drilling results, the usefulness of these parameters can be evaluated.

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Error analyses of a Multi-Input-Multi-Output cantilever beam test

Journal of Vibration and Control ◽

10.1177/10775463211033733 ◽

2021 ◽

pp. 107754632110337

Author(s):

Arup Maji ◽

Fernando Moreu ◽

James Woodall ◽

Maimuna Hossain

Keyword(s):

Transfer Function ◽

Frequency Domain ◽

Cantilever Beam ◽

Transfer Functions ◽

Linear Superposition ◽

Transfer Function Matrix ◽

Error Analyses ◽

Pseudo Inverse ◽

Function Matrix

Multi-Input-Multi-Output vibration testing typically requires the determination of inputs to achieve desired response at multiple locations. First, the responses due to each input are quantified in terms of complex transfer functions in the frequency domain. In this study, two Inputs and five Responses were used leading to a 5 × 2 transfer function matrix. Inputs corresponding to the desired Responses are then computed by inversion of the rectangular matrix using Pseudo-Inverse techniques that involve least-squared solutions. It is important to understand and quantify the various sources of errors in this process toward improved implementation of Multi-Input-Multi-Output testing. In this article, tests on a cantilever beam with two actuators (input controlled smart shakers) were used as Inputs while acceleration Responses were measured at five locations including the two input locations. Variation among tests was quantified including its impact on transfer functions across the relevant frequency domain. Accuracy of linear superposition of the influence of two actuators was quantified to investigate the influence of relative phase information. Finally, the accuracy of the Multi-Input-Multi-Output inversion process was investigated while varying the number of Responses from 2 (square transfer function matrix) to 5 (full-rectangular transfer function matrix). Results were examined in the context of the resonances and anti-resonances of the system as well as the ability of the actuators to provide actuation energy across the domain. Improved understanding of the sources of uncertainty from this study can be used for more complex Multi-Input-Multi-Output experiments.

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