Showing papers in "Geophysical Prospecting in 1974"

An analysis of stacking, rms, average, and interval velocities over a horizontally layered ground *

Abstract: A correct derivation of rms, average and interval velocities from one another and from common depth point stacking velocities requires a clear understanding of the relationships between these velocities. We relate the average velocity to the rms velocity through a “heterogeneity factor” which is a quantity that gives a measure of the degree of velocity heterogeneity in the ground. The interval velocity is a quantity which varies according to the method of its derivation. The difference between rms and stacking velocities depends on the heterogeneity factor and on the length of the spread. Unless allowed for, this difference can reverse the advantages of long spreads and cause large errors in interval velocity determinations. It may be removed through a number of techniques. The accuracy of stacking velocities in the presence of random “noise” is independent of the heterogeneity factor. Relevant expressions can be broken down into simple formulae which give the accuracy quickly and with good precision.

Transient EM Response of a Large Loop on a Layered Ground

Abstract: The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle. The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t) ≃— ( Ib αμ/20 t ) (σμ 2 / t ) 3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t) ≃— Ib μ/2 t. When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described. The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer. Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer.

Two‐dimensional power spectral analysis of aeromagnetic fields *

Abstract: A study of probability distribution function and spectrum of the Airborne Total Intensity Map for an area of 3000 Squ. miles covered by the Bundelkhand granite in India has revealed a close correlation between the Gaussian or non-Gaussian nature of distribution and the shape of unite value contour on the spectrum plot. Further studies of radial spectrum plots suggest that the surface magnetic sources are mainly responsible for the non-Gaussian character of the distribution function and as well as for irregular spectrum shape. The histogram of depth values for magnetic sources obtained from radial spectrum plots show three horizons, namely (i) surface (ii) 410 m(1400′) and (iii) 1000 m (3400′). Based on these informations blocks with ferromagnetic composition at the surface can be identified from those which are non magnetic at the surface.

Estimation of the primary seismic pulse

Abstract: A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.

The Influence of Electrical Anisotropy on Mise a la Masse Surveys

Abstract: In a transversely electrically anisotropic rock mass of arbitrary dip, the potential distribution about an electrode at arbitrary depth is the sum of the whole-space potential about that electrode, plus the whole-space potential about a postulated image electrode displaced up-dip from the source position. Equipotential lines on the rock-air surface are ellipses, elongated parallel to strike, and with centers displaced up-dip from the surface projection of the electrode position. In metamorphosed rocks frequently encountered in mining geophysics, anisotropy is such that elongation is most marked in steeply dipping rocks, with displacement most evident in low to moderate dip. Graphs relating the anisotropy coefficient to displacement and elongation assist in separation of the anisotropy-related effects from those of a significant subsurface conductive body, particularly if surface resistivity sounding establishes the coefficient of anisotropy.

On the transformation of dipole to schlumberger sounding curves

Abstract: A method is described to transform a dipole sounding curve, obtained with any one of the common dipole arrays over a horizontally layered earth, to the form of a Schlumberger sounding curve. Starting from the general expression which relates the dipole apparent resistivity to the Schlumberger apparent resistivity and its derivative with respect to the spacing, it is possible with some approximations to derive an easy numerical computation procedure in order to perform the transformation. The applicability of the method is discussed briefly.

Related properties of minimum‐phase and zero‐phase time functions *

Abstract: In this paper properties of the discrete zero-phase time function are derived and compared with related properties of the discrete minimum-phase time function. The two-sided minimum-length signal is introduced and it is derived that, for any given amplitude spectrum, the two-sided minimum-length signal and the signal with zero-phase spectrum are identical signals. A comparison is made between the one-sided minimum-length signal (minimum-phase signal) and the two-sided minimum-length signal (zero-phase signal). A computational scheme is discussed which determines the zero-phase correspondent of a given signal. A method is proposed to compute zero-phase least-square inverse filters. The efficiency of minimum-phase and zero-phase least-square inverse filters is shown on signals with different phase properties. A criterion is derived which determines whether a symmetric time function has the zero-phase property. The close relationship with the minimum-phase criterion is discussed. Finally the relationship between signal length and resolving power is illustrated on numerical examples.

The determination of filter coefficients for the computation of standard curves for dipole resistivity sounding over layered earth by linear digital filtering

Abstract: The technique of linear digital filtering developed for the computation of standard curves for conventional resistivity and electromagnetic depth soundings is applied to the determination of filter coefficients for the computation of dipole curves from the resistivity transform function by convolution. In designing the filter function from which the coefficients are derived, a sampling interval shorter than the one used in the earlier work on resistivity sounding is found to be necessary. The performance of the filter sets is tested and found to be highly accurate. The method is also simple and very fast in application.

Transformation of dipole resistivity sounding measurements over layered earth by linear digital filtering

Abstract: The technique of linear digital filtering as developed for the direct interpretation of Schlumberger and Wenner soundings (Ghosh 1971) has been applied here for the derivation of the resistivity transform function from the field dipole measurements as the first step in directly interpreting dipole data. Filter coefficients for this transformation have been worked out for the radial-polar, perpendicular and parallel (30°) arrays of dipole sounding. The procedure combines speed with accuracy.

Depth of investigation in resistivity methods using linear electrodes

Abstract: Depths of investigation for normal (bipolar) and focusing (unipolar) linear electrode arrays have been computed following the method given earlier (Roy and Apparao 1971) both in homogeneous and layered earth. The focusing arrangement is found to be superior to normal arrangement both in regard to depth of investigation and zone of uniform depth of investigation. This analysis holds good in layered media too. Further, the depth of investigation increases with the increase in the length (2 M ) of the electrode and reaches a limit, 0.29 L for normal and 0.50 L for focusing, when the electrode attains an optimum length to satisfy the infinite condition. This optimum length of the electrode is six times the distance L of the observation point from the electrode for normal and about ten times for focusing. A contour diagram for contributions of individual ground elements to the total signal measured at the centre of focused system is also discussed.

Theoretical resistivity sounding results over a transition layer model

Abstract: An earth model with a transition layer (anisotropic inhomogeneous) is considered. The inhomogeneity in σv (vertical conductivity) of the transition layer is represented by a power law variation. Expressions for potential distribution in the upper layer, transition layer and bottom layer are obtained by solving appropriate differential equation for each layer. By utilizing the boundary conditions, expressions of apparent resistivity for Wenner and Schlumberger configurations are derived. Numerical analysis is performed for linear and quadratic variation of σv. The results are presented in the form of theoretical apparent resistivity curves for both configurations. Negative apparent resistivities are the interesting feature of this analysis.

A modified geoelectrical procedure using polardipole arrays—an example of application to deep exploration

Abstract: Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar-dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field. A special measurement technique is required since the dipole-dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.

A high resolution marine seismic survey

Abstract: Sub‐bottom profilers achieve high resolution but limited penetration beneath the seabed. Marine seismic surveys with long streamers and conventional sources suffer from an incomplete CDP stack and an unnecessarily low signal frequency in the early part of the section. Consequently there is a depth interval over which the optimum resolution of the seismic reflection method is not achieved. This paper describes the design, conduct, and results of an experimental survey made to obtain high resolution sections (predominant frequency about 200 Hz) with reflection times up to one second in the northern North Sea. The prime motivation for the experiment was to assess the possibility of mapping a shallow gas sand which had been encountered by the drillers. The design concept of the survey was to keep all the benefits of conventional marine seismic data gathering and processing, but to reduce their dimensions and time scales by a factor of five to ten. The survey in 1972 recorded a total of twenty‐four lines using twenty‐four fold cover with 5 m spacing between the reflector points, and a separation of 50 m between adjacent lines. Multi‐electrode sparkers were used with a shallow purpose‐built twenty‐four channel 240 m hydrophone streamer. The recording sample interval was 1 ms. The final sections, obtained after conventional data processing, were of good quality. The results of velocity analysis helped to distinguish primary and multiple energy. Reflections with large negative reflection coefficients were seen in some parts of the survey area, and these are thought to indicate thin gas sands.

Section Migration, Before Stack, after Stack, or Inbetween *

Abstract: Section migration after stack has been widely accepted by the industry. From a theoretical point of view, section migration before stack should provide superior results, the improvement warranting the drastically increased cost is not realized in most cases. There are a number of reasons that explain the discrepancy between actual and theoretically expected quality: Long period statics, refraction of rays, two-dimensional treatment of an actually three-dimensional problem. The section migration package subject to this paper allows (i) to take refraction into account, (ii) to discriminate against noise with a variety of statistical and geometrical criteria, (iii) to adapt processing time to problem complexity by a special process called SEMI-STACK. A number of examples will demonstrate the effects of section migration.

Mathematical Models of Conducting Ore Bodies for Direct Current Electrical Prospecting

Abstract: The authors generalize a method expounded in a previous paper (1971, Geoph. Prosp. 18, 786-799) to the case of a local conductivity σ(M) of the infinite medium satisfying the relation where the Ri's are the distances from the point M to n fixed points Si (i= 1,. n), k is a positive real constant and Ci, Cii are constants ensuring the condition α > O. The sub-surface conductivity distributions (half-spaces) complying with (1) provide a wide variety of conducting structures, which can fit quite successfully the rather complicated distributions of conductivity occurring in natural ore bodies. An exact algebraic calculation of the apparent resistivity for these grounds, valid for any dc electrical prospecting devices (Wenner, Schlumberger, dipole, etc.) leads to a set of simultaneous linear equations, with a matrix which is invariant with respect to the position of the quadrupole being used. This greatly simplifies the numerical computation. We also present some examples of cross sections for the real and apparent resistivity obtained by this method.

Approximate rules for the composition of apparent resistivity sections

Abstract: Consideration is given to the form of apparent resistivity sections obtained by varying electrode array position and spacing over two dimensional features. Since basic solutions exist for horizontally layered media and for vertical or dipping single interfaces, simple rules are proposed whereby these solutions can be directly combined to give solutions for more complex sections. Substantial approximations may be involved as the rules do not fully allow for interactions between the constituents. The range of error incurred in application of the rules is explored, with particular reference to the square array system of resistivity measurement. The two extremes- of orientation of the square array with respect to the line of section are separately considered in this survey. Within appropriate limits, the rules appear extendable to a wide variety of simple structures for which rigorous solutions would be formidable. The rules are finally discussed in relation to practical applications.

Detailed electrometric and thermometric observations in offshore areas.

Abstract: The paper deals with the prerequisites of application, specific peculiarities and methods of electrometric and thermometric investigations aimed at the solution of certain engineering-geological problems in offshore areas. Practical examples are supplied.

Direct interpretation of two‐electrode resistivity soundings *

Abstract: This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940).

The interpretation of gradient array chargeability anomalies

Abstract: Empirical equalities derived from time domain induced polarization scale modelling with the gradient array over simple geometries, and from the potential field functions for equivalent simple charge configurations are similar. The function for the dyke like body is analogous to the magnetic case allowing both total and vertical magnetic field interpretation techniques to be applied to gradient array chargeability anomalies.

After‐stack multichannel filters without mixing effects *

Abstract: Several types of multichannel filters have been introduced in the past with the purpose of rejecting, in a seismic section, coherent noise having a slope different from that of the signal. These filters, generally, tend to introduce a certain amount of mixing and therefore the output trace shows increased horizontal coherence. This is due to the model on which these filters are based, since the hypothesis is posed that the reflectors are continuous. This may be dangerous since it could lead to mistaken interpretations, for example when small faults or breaks are made to disappear in the output section. Other problems that could arise in the application of multichannel filters after-stack are space-aliasing and high-pass filtering. The former occurs when coherent noise is rejected with apparent Velocity V and frequency fa=V/X, where X is the distance between traces. In this case, the signal also is distorted since it is rejected in the same frequency range. The high pass filtering effect occurs when the multichannel filter is designed to remove low coherent noise with high apparent velocity. In the paper a family of multichannel filters is presented based on a model of the seismic section such that minimum mixing effects appear. The filters are designed to give good results even in the case of low frequency and high velocity coherent noise. Some practical examples are shown.

Obtaining interval velocities from stacking velocities when dipping horizons are included

Abstract: Common-depth-point stacking velocities may differ from root-mean-square velocities because of large offset and because of dipping reflectors. This paper shows that the two effects may be treated separately, and proceeds to examine the effect of dip. If stacking velocities are assumed equal to rms velocities for the purpose of time to depth conversion, then errors are introduced comparable to the difference between migrated and unmigrated depths. Consequently, if the effect of dip on stacking velocity is ignored, there is no point in migrating the resulting depth data. For a multi-layered model having parallel dip, a formula is developed to compute interval velocities and depths from the stacking velocities, time picks, and time slope of the seismic section. It is shown that cross-dip need not be considered, if all the reflectors have the same dip azimuth. The problem becomes intractable if the dips are not parallel. But the inverse problem is soluble: to obtain, stacking velocities; time picks, and time slopes from a given depth and interval velocity model. Finally, the inverse solution is combined with an approximate forward solution. This provides an iterative method to obtain depths and interval velocities from stacking velocities, time picks and time slopes. It is assumed that the dip azimuth is the same for all reflectors, but not necessarily in the plane of the section, and that the curvature of the reflecting horizons is negligible. The effect of onset delay is examined. It is shown that onset corrections may be unnecessary when converting from time to depth.

Navigation requirements for geophysical exploration

Abstract: Marine geophysical work requires accurate navigation on a continuous basis. A repeatability of 150 m CEP (circular error probable) with sequential positioning of 15 m CEP is usually acceptable. Quoted figures for many presently available navigation systems yield nearly the required accuracy. In actual operations, however, such accuracies may not be achieved, and usually the performance actually realized cannot be determined for want of independent measurements for comparison. If more redundancy in navigation measurements were available on an integrated basis, the limitations of individual systems would no longer be so critical and the accuracy of measurements could be assessed in real time. Failures in navigation continue to occur. Such failures usually result from ignorance of the capabilities of the navigation system and limitations and consequent choice of a system which is not appropriate to the demands of a particular survey. The points to be covered in work standards are listed.

Pulse coding in seismic prospecting sosie and seiscode

Abstract: The conventional seismic technique is subject to a recording time following each transmission of energy, in which it is forbidden to release any new pulse. The recording time depends on the deepest reflection of interest, and is often 10 seconds or more in actual practice. To each transmission corresponds one record, i.e. a fixed amount of data which cannot be increased in a given time. Pulse coding allows us to go beyond this limit, by transmitting several times during the normal recording time. The procedure gives as many records as there are pulses, but they overlap, each event being repeated every time there is a pulse. It is possible to process the composite record back to its usual appearance with all events in their proper place if the time breaks are accurately known and make up a code such that the unavoidable noise generated by the process be kept, on the final section, below the ambient noise. The processing is quite similar to that of records made from vibrating sources, though faster in practice. The additional information can be devoted to a saving of time and money as the same profile may be recorded in a shorter time; or to an improvement of quality of the section due to a higher order of coverage, a multiplication of the ray paths and a closer sampling of the reflectors. It is also possible to record information in several planes at the same time, and to work out a 3-dimensional restitution, without loss of production. The process applies to all kinds of sources provided they can be triggered according to the code with sufficient accuracy. Depending on the source and conditions of implementation, the method benefits from other advantages such as better resolution, increased flexibility, and better coupling. Two different names have been given to the process, Sosie and Seiscode, which apply to slightly different parameters for the sequence of pulses. Sosie is more useful at sea, while the normal scope for Seiscode is onshore. Both names are trademarks for SNPA.

Traitement „a la main” et sur ordinateur des transitoires en polarisation provoquee *

Abstract: Summary Decomposition of IP discharge curve into a sum of exponentials yields more information than present practice does. Such a work was performed, as a beginning, by hand, plotting the ordinates on semi logarithimic paper. It gave, according to the cases, two or three exponentials, each with an amplitude Ai and the time constant τi. Three examples of ground prospection are given, the third of which shows an anomaly, unnoticed with present technique but obvious on a profile curve with A1/A2 in ordinates. A computer processing technique is described which yields directly the time constants τi by seeking a differential equation which the IP voltage satisfies; the order of the equation is set arbitrarily. On a practical prospection record with only two exponentials, the assumption that the differential equation does not depend on charge duration (everything else being equal) has been checked (the shape of the curves would depend on boundary conditions). The assumption roughly holds for charge durations from 5 seconds to 40 seconds. We hope that a larger number of exponentials will yield better results. Sommaire La decomposition de la courbe de decharge en une somme d'exponentielles permet d'en tirer plus d'information que la pratique actuelle. Un tel travail a ete fait, pour commencer, a la main en portant les ordonnees sur papier logarithmique; il a fourni, suivant les cas, deux ou trois exponentielles avec, pour chacune d'elles, le coefficient Ai et la constante de temps τi. On donne trois exemples de prospection sur le terrain, dont le dernier comporte une anomalie, inapercue avec la technique actuelle, mais bien mise en evidence en tracant la courbe de A1/A2 le long du profil. On donne ensuite une technique de calcul sur ordinateur des τi, en recherchant l'equation differentielle a laquelle obeit la tension ΔVPP enregistree, l'ordre de cette equation etant fixe arbitrairement. On a cherchea verifier sur un enregistrement de terrain, avec. deux exponentielles seulement, l'hypothese suivant laquelle l'equation differentielle ne depend pas de la duree de charge (toutes choses egales d'ailleurs). L'hypothese se trouve grossierement verifiee pour les durees de charge allant de 5 secondes a 40 secondes, et nous esperons qu'un plus grand nombre d'exponentielles donnera de meilleurs resultats.

A comparison of transient voltage decay curves obtained with different electrode arrays and configurations over a mineralized zone

Abstract: The Huntec Mark 3 time domain equipment provides information from which the nature of the transient voltage decay curves may be determined. A zone of disseminated mineralization extending above a normal fault zone was selected for a comparative study of decay curves. In a preliminary study in which steel stakes were used as current electrodes it was observed that at some stations the decay curves obtained with reciprocal dipole-dipole configurations were significantly different and that many decay curves initially increased from low values indicating the presence of a negative component. It was assumed that the decay curves were composite and were composed of the superposition of transient voltage components due to electromagnetic and polarization effects which could be described in terms of simple exponential functions. The initial negative component was thought to be an electromagnetic effect, but when the traverses were repeated using porous pots as current electrodes it was found that the initial negative component was usually completely eliminated, indicating that it was due to negative polarization arising from the steel stakes. When the effect of the current electrode polarization was completely eliminated identical decay curves were obtained with the reciprocal array configurations, but the remaining decay curve-which is due to induced ground polarization—cannot be described by a single simple exponential function. It is also demonstrated that the initial negative component due to stake polarization may also be present in decay curves obtained with gradient arrays indicating that separation of the current and potential electrodes does not avoid this effect which may significantly modify the decay curve in certain circumstances up to three seconds after switch-off.

STACKING FILTERS AND THEIR CHARACTERIZATION IN THE (f—k) DOMAIN *

Abstract: The implementation of a stacking filter involves the filtering of each trace with an individual filter and the subsequent summing of all outputs. The actual position of a trace in space as well as certain simultaneous shifts of traces and filter components in time do not influence the process. The resulting output is consequently invariant to various arbitrary coordinate transformations. For a certain useful class of ensembles of non-linear moveout arrival times for signals a particular transformation can be found which transforms a given ensemble into one consisting only of straight lines. It is thus possible to reduce, for instance, the analysis of a stacking filter designed for hyperbola-like moveout curves to the analysis of a velocity filter with linear moveout curves. As the (f—k) transform is a very useful concept to describe a velocity filter, it can consequently be applied to characterize a stacking filter in regard to its performance on input signals with non-linear moveout.

Seismic model studies on diffraction of waves by edges of varying radius of curvature and depth

Abstract: Results of studies carried out with the help of a three-dimensional seismic model on waves diffracted from edges of varying radius of curvature R and depth h with respect to wave length λ are described. The amplitude decay, travel time, and apparent velocity of the wave diffracted from a sub-surface edge of semi-infinite length are found to depend on the parameters R, h, and distance from the edge on the surface provided the ratio of the parameters to λ are less than some limiting values. The nature of the amplitude decay is independent of R when the depth exceeds 2λ, and independent of h when R exceeds 1.5λ. When these are below the limiting values (h= 2λ and R= 1.5λ), the nature of the decay depends appreciably on R and h. The apparent decay in amplitude on the surface due to geometrical spreading by the diffracting edge is less than that of a cylindrical secondary wave source and decreases with increase in depth of the edge. The nature of the travel time curves of the diffracted waves near the edge depend on R/λ when the depth is within about one λ. Apparent velocity of the wave depends largely on R/λ in the zone of diffraction up to a distance of about one λ from the edge on the surface. Beyond this distance the velocity is almost the same irrespective of R/λ and depend only on h/λ. The width of the zone of diffraction caused by an edge of finite length comparable to λ is more and more narrow as the ratio of the distance of the edge on the surface to its depth increases.

A wide-band digital magnetotelluric recording system *

Abstract: A six-channel wide-band digital system for magnetotelluric measurements is described The system is designed to operate in the frequency band 10-.0001 Hz. The recording is made on a 7 track tape in an IBM compatible 12 bit format. The amplitude and phase responses of the system and sample records are presented.