Sausage mode instability of thin current sheets as a cause of magnetospheric substorms

Observations have shown that, prior to substorm explosions, thin current sheets are formed in the plasma sheet of the Earth’s magnetotail. This provokes the question, to what extent current-sheet thinning and substorm onsets are physically, maybe even causally, related. To answer this question, one has to understand the plasma stability of thin current sheets. Kinetic effects must be taken into account since particle scales are reached in the course of tail current-sheet thinning. We present the results of theoretical investigations of the stability of thin current sheets and about the most unstable mode of their decay. Our conclusions are based upon a non-local linear dispersion analysis of a cross-magnetic field instability of Harris-type current sheets. We found that a sausage-mode bulk current instability starts after a sheet has thinned down to the ion inertial length. We also present the results of three-dimensional electromagnetic PIC-code simulations carried out for mass ratios up to M_i/m_e = 64. They verify the linearly predicted properties of the sausage mode decay of thin current sheets in the parameter range of interest.     

Geological characteristics and mineralization setting of the Zhuxi tungsten (copper) polymetallic deposit in the Eastern Jiangnan Orogen

The Zhuxi ore deposit is a super-large scheelite(copper) polymetallic deposit discovered in recent years. It grew above copper/tungsten-rich Neoproterozoic argilloarenaceous basement rocks and was formed in the contact zone between Yanshanian granites and Carboniferous-Permian limestone. Granites related to this mineralization mainly include equigranular, middle- to coarse-grained granites and granitic porphyries. There are two mineralization types: skarn scheelite(copper) and granite scheelite mineralization. The former is large scale and has a high content of scheelite, whereas the latter is small scale and has a low content of scheelite. In the Taqian-Fuchun Basin, its NW boundary is a thrust fault, and the SE boundary is an angular unconformity with Proterozoic basement. In Carboniferous-Permian rock assemblages, the tungsten and copper contents in the limestone are both very high. The contents of major elements in granitoids do not differ largely between the periphery and the inside of the Zhuxi ore deposit. In both areas, the values of the aluminum saturation index are A/CNK1.1, and the rocks are classified as potassium-rich strongly peraluminous granites. In terms of trace elements, compared to granites on the periphery of the Zhuxi ore deposit, the granites inside the Zhuxi ore deposit have smaller d Eu values, exhibit a significantly more negative Eu anomaly, are richer in Rb, U, Ta, Pb and Hf, and are more depleted in Ba, Ce, Sr, La and Ti, which indicates that they are highly differentiated S-type granites with a high degree of evolution. Under the influence of fluids, mineralization of sulfides is evident within massive rock formations inside the Zhuxi ore deposit, and the mean SO_3 content is 0.2%. Compared to peripheral rocks, the d Eu and total rare earth element(REE) content of granites inside the Zhuxi ore deposit are both lower, indicating a certain evolutionary inheritance relationship between the granites on the periphery and the granites inside the Zhuxi ore deposit. For peripheral and ore district plutons, U-Pb zircon dating shows an age range of 152–148 Ma. In situ Lu-Hf isotope analysis of zircon in the granites reveals that the calculated e_(Hf)(t) values are all negative, and the majority range from -6 to -9. The T_(DM2) values are concentrated in the range of 1.50–1.88 Ga(peak at 1.75 Ga), suggesting that the granitic magmas are derived from partial melting of ancient crust. This paper also discusses the metallogenic conditions and ore-controlling conditions of the ore district from the perspectives of mineral contents, hydrothermal alteration, and ore-controlling structures in the strata and the ore-bearing rocks. It is proposed that the Zhuxi ore deposit went through a multistage evolution, including oblique intrusion of granitic magmas, skarn mineralization, cooling and alteration, and precipitation of metal sulfides. The mineralization pattern can be summarized as "copper in the east and tungsten in the west, copper at shallow-middle depths and tungsten at deep depths, tungsten in the early stage and copper in the late stage".     

The probability of occurrence of largest earthquqkes in the European area — Part II

Summary The previous investigation of the probability of occurrence of largest earthquakes in the European area continued by applying the Gumbel theory of largest values to three periods 1901–1930, 1901–1955 and 1901–1967, respectively. The values of magnitudes which will be exceeded with the probabilityP=1%, 2% and 10% were determined from the lines fitting the distributions of magnitudes and corresponding probabilities for all three periods. It was assumed that the relationship between the differences M _P% ^[k](67)=M _k,P%–M ₆₇,P% (k=30, 55, 67) and the observation period follow the hyperbolic law. This tendency was used for the estimation of the probability line corresponding to an infinite observation period.Presented at The Sixth UMC Symposium on Geophysical Theory and Computers in Copenhagen in 1969.     

TIME DOMAIN ELECTROMAGNETIC RESPONSE OF A SHIELDED CONDUCTOR*

Velekin and Bulgakov (1967) in an interesting model experiment while studying the transient electromagnetic response of a conductive sphere placed below a thin conductive sheet found that at the earlier stages of the transience, the composite system response corresponded to the response due to the overlying sheet alone and at the later stages, it corresponded to that of the sphere alone. To examine whether such a separation of responses due to individual components can be analytically studied and applied to other source configurations, we have analyzed an idealized model consisting of two spherical shells. We find that in corroboration with the above results, the general nature of the curve consists of two humps representing the responses dominated by the outer shell and the inner shell respectively. In addition, however, we find that the two humps gradually disappear to yield a smooth decay curve for increasing values of the ratio σd₁b/σ₂d₂a (where σ₁, σ₂ are the conductivities, d₁, d₂ are the thicknesses of the outer and inner shells respectively, and b and a are their respective distances from the centre) and the effect of inner shell on the composite system response is considerably reduced.     

The Polar Cap (PC) indices: Relations to solar wind parameters and global magnetic activity

The polar geomagnetic activity resulting from solar wind–magnetosphere interactions can be characterized the Polar Cap (PC) indices, PCN and PCS. PC index values are derived from polar magnetic variations calibrated on a statistical basis such that the index approximate values in units of mV/m of the interplanetary “geo-effective” (or “merging”) electric field (E_M) conveyed by the solar wind. The timing and amplitude relations of the PC index to solar wind plasma and magnetic field parameters are reported. The solar wind effects are parameterized in terms of the geo-effective electric field (E_M) and the dynamical pressure (P_DYN). The PC index has a delayed and damped response to E_M variations and display saturation-like effects for E_M values exceeding 10 mV/m. Steady or slowly varying levels of solar wind dynamical pressure have little or no impact on the PC index above the effects related to E_M for which the solar wind velocity is also a factor. Sharp increases in the dynamical pressure generate impulsive variations in the PC index comprising a initial negative impulse of 5–10 min duration followed by a positive impulse lasting 10–20 min. Typical amplitudes of both the negative and the positive impulses are 0.2–0.5 units. A sharp decrease in the pressure produces the inverse sequence of pulses in the PC index. Auroral substorm activity represented by the AL index level has a marked influence on the average PC/E_M level at the transition from very quiet (AL0 nT) to disturbed conditions while more or less disturbed conditions (AL<−100 nT) have no systematic effect on the average PC/E_M values. At distinct substorm events the PC/E_M ratio has a minimum (0.8) in the pre-onset phase at around 20 min before substorm onset. The average ratio gradually increases in the expansion phase to reach a maximum value (1.1) at around 40 min after substorm onset (or 20 min after the largest (negative) peak in AL). At substorm recovery during the next 2 h the PC/E_M ratio decreases. Finally, we report on the application of polar magnetic variations to model the disturbance storm time (Dst) index development during magnetic storms by using the PC index as a source function to quantify the energy input to the ring current representing accumulated storm energy and characterized by the Dst index.     

MATHEMATICAL MODELS OF CONDUCTING ORE BODIES FOR DIRECT CURRENT ELECTRICAL PROSPECTING *

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 R_i's are the distances from the point M to n fixed points S_i (i= 1,. n), k is a positive real constant and C_i, C_ii 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.     

Seismic risk of circum-Pacific earthquakes: II. Extreme values using Gumbel's third distribution and the relationship with strain energy release

In a previous paper (Makropoulos andBurton, 1983) the seismic risk of the circum-Pacific belt was examined using a whole process technique reduced to three representative parameters related to the physical release of strain energy, these are:M ₁, the annual modal magnitude determined using the Gutenberg-Richter relationship;M ₂, the magnitude equivalent to the total strain energy release rate per annum, andM ₃, the upper bound magnitude equivalent to the maximum strain energy release in a region.The risk analysis is extended here using the part process statistical model of Gumbel's IIIrd asymptotic distribution of extreme values. The circum-Pacific is chosen being a complete earthquake data set, and the stability postulate on which asymptotic distributions of extremes are deduced to give similar results to those obtained from whole process or exact distributions of extremes is successfully checked. Additionally, when Gumbel III asymptotic distribution curve fitting is compared with Gumbel I using reduced chi-squared it is seen to be preferable in all cases and it also allows extensions to an upper-bounded range of magnitude occurrences. Examining the regional seismicity generates several seismic risk results, for example, the annual mode for all regions is greater thanm(1)=7.0, with the maximum being in the Japan, Kurile, Kamchatka region atm(1)=7.6. Overall, the most hazardous areas are situated in this northwestern region and also diagonally opposite in the southeastern circum-Pacific. Relationships are established between the Gumbel III parameters and quantitiesm ₁(1),X ₂ and , quantities notionally similar toM ₁,M ₂ andM ₃ although is shown to be systematically larger thanM; thereby giving a physical link through strain energy release to seismic risk statistics. Inall regions of the circum-Pacific similar results are obtained forM ₁,M ₂ andM ₃ and the notionally corresponding statistical quantitiesm ₁(1),X ₂ and , demonstrating that the relationships obtained are valid over a wide range of seismotectonic enviroments.     

Evidence for periodic seismicity in the inner Aegean seismic zone

The most complete and reliable data of strong (M _s6.5), shallow (h<70 km) earthquakes which occurred in the inner Aegean seismic zone have been utilized to describe its seismicity time variation during 1800–1986 by two independent statistical models. The first is a sequentially stationary model of seismicity rates which shows that intervals of low seismicity rate, lasting for some 37 years, alternate with high rate intervals of 8–12 years duration. The second model is a statistical model according which seismic energy released within 5-year time windows approximates a harmonic curve within a period of about 50 years. This model is in agreement with the notion that the time series of strong earthquake occurrences in the inner Aegean seismic zone consists of a random (shocks withM _s=6.5–6.8) and a nonrandom component (M _s6.9). Maxima and minima of the harmonic curve coincide with the high and low rate intervals, respectively. A model of regional stationary accumulation of thermal stresses along certain seismic belts and their cyclic relaxation may explain this periodicity.     

An application of the time- and magnitude-predictable model to long-term earthquake prediction in eastern Anatolia

In order to estimate the recurrence intervals for large earthquakes occurring in eastern Anatolia, this region enclosed within the coordinates of 36^∘–42^∘N, 35^∘–45^∘E has been separated into nine seismogenic sources on the basis of certain seismological and geomorphological criteria, and a regional time- and magnitude-predictable model has been applied for these sources. This model implies that the magnitude of the preceding main shock which is the largest earthquake during a seismic excitation in a seismogenic source governs the time of occurrence and the magnitude of the expected main shock in this source. The data belonging to both the instrumental period (M_S≥ 5.5) until 2003 and the historical period (I₀≥ 9.0 corresponding to M_S≥ 7.0) before 1900 have been used in the analysis. The interevent time between successive main shocks with magnitude equal to or larger than a certain minimum magnitude threshold were considered in each of the nine source regions within the study area. These interevent times as well as the magnitudes of the main shocks have been used to determine the following relations:

Case 25 application of the concentration parameter of seismoactive faults to Southern California

In this paper we evaluate the present state of the seismic regime in Southern California using the concentration parameter of seismogenic faults (K _sf ,Sobolev andZavyalov, 1981). The purpose of this work is to identify potential sites for large earthquakes during the next five or ten years. The data for this study derived from the California Institute of Technology's catalog of southern California earthquakes, and spanned the period between 1932 to June 1982. We examined events as small asM _L 1.8 but used a magnitude cutoff atM _L =3.3 for a detailed analysis. The size of the target earthquakes (M _M ) was chosen as 5.3 and 5.8.The algorithm for calculatingK _sf used here was improved over the algorithm described bySobolev andZavyalov (1981) in that it considered the seismic history of each elementary seismoactive volume. The dimensions of the elementary seismoactive volumes were 50 km×50 km and 20 km deep. We found that the mean value ofK _sf within 6 months prior to the target events was 6.1±2.0 for target events withM _L 5.3 and 5.41.8 for targets withM _L 5.8. Seventy-three percent of the targets withM _L 5.8 occurred in areas whereK _sf was less than 6.1. The variance of the time between the appearance of areas with lowK _sf values and the following main shocks was quite large (from a few months to ten years) so this parameter cannot be used here for accurate predictions of occurrence time.Regions where the value ofK _sf was below 6.1 at the end of our data set (June, 1982) are proposed as the sites of target earthquakes during the next five to ten years. The most dangerous area is the area east of San Bernardino whereK _sf values are presently between 2.9 and 3.7 and where there has been no earthquake withM _L 5.3 since 1948.     

Calibration of Local Magnitude M<Subscript>L</Subscript> in the Azores Archipelago Based on Recent Digital Recordings

—The development of the digital seismic network in the Azores Archipelago during recent years made it possible to obtain the amplitudes (waveform) of recorded motion in a large set of stations. With this new data, maximum amplitudes of the Wood Anderson seismograph are computed, for each station/component, which, together with epicentral distances, allows for the estimation of local magnitude M _L . We used data recorded in 8 digital permanent three-component stations, with inter-stations distances up to 300 km, in the period June 1998 – June 2000, corresponding to a set of 1315 events with magnitude (M _L or M _D ) 2<M<5.8 and epicenters located in the Azores region, to estimate the coefficients of the equation to compute M _L , as well as to determine the corrections to be applied to each station. The new set of parameters, formed by attenuation coefficients and station corrections, were introduced in the calculations of the M _L , leading to smaller dispersions in the analyzed dataset. We also conclude that the attenuation in the first 150 km is similar to the California values, although higher for longer distances.     

Scaling of peak ground motions from digital recordings of small earthquakes at Campi Flegrei,southern Italy

The dependence of peak ground acceleration and velocity on seismic moment is studied for a set of small earthquakes (0.7<M _L<3.2) recorded digitally at distances of a few km in the Campi Flegrei volcanic area near Naples, Italy, during the ground uplift episode of 1982–1984. Numerical simulations, using the -square spectral model with constant stress drop and ane ^–kf high frequency decay, fit well both the velocity and acceleration data for an averagek=0.015. The observed ground motions in the 1–24 Hz frequency band appear to consist of radiation from simple sources modified only slightly by attenuation effects. Moreover, the scaling of peak values agrees closely with those determined in nonvolcanic areas, once the difference in stress drop is taken into account.     

Site Specific Ground Motion Modeling and Seismic Response Analysis for Microzonation of Baku,Azerbaijan

We investigated ground response for Baku (Azerbaijan) from two earthquakes of magnitude M6.3 occurred in Caspian Sea (characterized as a near event) and M7.5 in Shamakhi (characterized as a remote extreme event). S-wave velocity with the average shear wave velocity over the topmost 30 m of soil is obtained by experimental method from the V _P values measured for the soils. The downtown part of Baku city is characterized by low V_S30 values (< 250 m/s), related to sand, water-saturated sand, gravel-pebble, and limestone with clay. High surface PGA of 240 gal for the M7.5 event and of about 190 gal for the M6.3 event, and hence a high ground motion amplification, is observed in the shoreline area, through downtown, in the north-west, and in the east parts of Baku city with soft clays, loamy sands, gravel, sediments.     

Seismic source-parameter relations for earthquakes in Greece

A data set of nineteen, mainly shallow, moderate to large earthquakes, which occurred in the Aegean and the surrounding area, has been used to derive empirical relations for kinematic fault parameters. Thus the relations between seismic momentM ₀ and magnitudeM _s andm _b and betweenM ₀ andM _s and fault dimensionsS andL have been determined. From these relations and theoretical ones it was deduced that earthquakes in the Aegean and the surrounding events, chiefly interplate, are characterized by low average stress drop values. Values of ranging from 1 to 30 bar are consistent with the data. It was also found that, in general terms, most of the data obey the geometrical similarity conditionL=2w, whereL is the fault length measured along the strike andw is its width measured along the dip. For strike-slip faults, however, the conditionL=4w seems to hold.     

STATISTICAL ANALYSIS OF AIRBORNE ELECTROMAGNETIC SIGNATURES OF DIFFERENT CONDUCTOR GROUPS IN TROPICAL TERRAIN OF KARNATAKA,INDIA*

AEM (airborne electromagnetic) anomalies caused by massive sulphide conductors and superficial conductors can be recognized with a statistical method, as shown by an analysis of Input AEM data from Karnataka State. The weathering in the survey area is of tropical type. Parameters, such as various amplitude ratios and time parameters (inverse of decay rate) for exponential and power-law decay were analyzed for sulphide bodies, conducting soil, superficial conductors, and cultural conductors. Time parameters τ₁ (exponential decay) is defined as ratio of time differences between the third and fourth channel to the logarithmic value of the relative amplitude of the two channels. Time parameter K₁ (power-law decay) is defined as ratio of the difference of the logarithmic values of the delay times of the third and fourth channels to the logarithmic value of the relative amplitude of the two channels. The two parameters have been useful in recognizing sulphide conductors. Also the first channel Input amplitude and logarithmic plot of the transients appear to be helpful in conductor identification. Channel ratios seem to be the least effective parameters of conductor identification. In the area studied both power-law and the conventional exponential decay were found equally suitable for approximating Input AEM transients.     

Magnitude–intensity and intensity–attenuation relationships for atlas region and Algerian earthquakes

This paper presents the results of an investigation of the magnitude–intensity and intensity–attenuation relationships for earthquakes in the Atlas block and Algeria using macroseismic data. This work is based on a selected sample of isoseismal maps from 32 events which were recently revised. Surface-wave magnitudes, M_s, are recalculated using the Prague formula and range from 4·2 to 7·45. Because the Atlas mountains block is in a collision zone, earthquakes occur in general within a layer 15 km deep. Expressions of general form for the magnitude–intensity and intensity–attenuation correlations are adopted and are, respectively, and where R² = d² + h², d the source distance in km, h the focal depth in km, M_s the revised surface-wave magnitude, M_sc the predicted surface-wave magnitude, I_i the intensity at isoseismal i, I the predicted intensity, σ the standard deviation and P is zero for 50-percentile values and one for 84-percentile, and the coefficients A's and B's are determined by regression analysis. The results of this study show that the intensity–attenuation models are adequate to predict quite well the die-out of intensity with distance in the Atlas zone and coastal Algeria; it is also found that magnitude can be predicted accurately by calibrating isoseismal radii against revised instrumental surface-wave magnitude. Such magnitude–intensity relationships may be used to evaluate the magnitude of historical earthquakes in the region under survey, with no instrumental data, for which isoseismal radii and intensities are available.     

Migrating sand waves

A simple mathematical model is described, which reproduces the major features of sand waves' appearance and growth and in particular predicts their migration speed. The model is based on the linear stability analysis of the flat configuration of the sea bottom subject to tidal currents. Attention is focused on the prediction of the complex growth rate that bottom perturbations undergo because of both oscillatory fluid motions and residual currents. While the real part _r of controls the amplification or decay of the amplitude of the bedforms, the imaginary part _i is related to their migration speed. Previous works on the migration of the sand waves (Németh etal. 2002) consider a forcing tide made up by the M2 constituent (oscillatory period equal to 12 h) plus the residual current Z0 and predict always a downcurrent migration of the bedforms. However, field cases exist of upcurrent-migrating sand waves (downcurrent/upcurrent-migrating sand waves mean bedforms moving in the direction of the steady residual tidal current or in the opposite direction, respectively). The inclusion of a tide constituent characterized by a period of 6 h (M4) is the main novelty of the present work, which allows for the prediction of the migration of sand waves against the residual current Z0. Indeed, the M4 tide constituent, as does also the residual current Z0, breaks the symmetry of the problem forced only by the M2 tide constituent, and induces sand-wave migration. The model proposed by Besio etal. (2003a) forms the basis for the present analysis. Previous works on the subject (Gerkema 2000; Hulscher 1996a,b; Komarova and Hulscher 2000) are thus improved by using a new solution procedure (Besio etal. 2003a) which allows for a more accurate evaluation of the growth rate for arbitrary values of the parameter r, which is the ratio between the horizontal tidal excursion and the perturbation wavelength. Responsible Editor: Jens Kappenberg     

Duration Magnitude Scale and Site Residuals for Northern Morocco

— The first empirical duration magnitude (M_D) formula is developed and tested for the Northern Morocco Seismic Network (NMSNET). This relationship is obtained by relating the IGN (Instituto Geografico National, Madrid) body-waves mbLg^IGN to the duration (), and the epicentral distance (), at 25 analogue stations of the NMSNET for 479 earthquakes with 2.5 mb 5.4, from March 1992 to February 2001. M_D estimates are significantly more precise while introducing a correction term for each of these stations, cSta_j. The magnitude for the i^th event (M_D)_i is the mean value of individual M_Dij=–0.14+1.63log₁₀(_ij)+0.031(_ij)+cSta_j. The cSta_j corrections reduce considerably the local site effects which influence the recorded durations and cause stations to either overestimate, or underestimate M_D up to 0.5 magnitude units. Average station M_D residuals (–cSta_j) are found to be independent of the distance from the epicenter to at least 10 degrees. It seems evident that regional geological features in the immediate behavior of stations have a systematic effect on the corresponding obtained residuals: older well-consolidated Precambrian crystalline rocks produce high negative residuals (shorter durations), younger unconsolidated sediments produce high positive residuals (longer durations), whereas, intermediate M_D site residuals appear to be the result of the effect of various factors, principally age and state of consolidation of the bedrock, combined with the local tectonic.     

Equations for the Estimation of Strong Ground Motions from Shallow Crustal Earthquakes Using Data from Europe and the Middle East: Horizontal Peak Ground Acceleration and Spectral Acceleration

This article presents equations for the estimation of horizontal strong ground motions caused by shallow crustal earthquakes with magnitudes M_w 5 and distance to the surface projection of the fault less than 100km. These equations were derived by weighted regression analysis, used to remove observed magnitude-dependent variance, on a set of 595 strong-motion records recorded in Europe and the Middle East. Coefficients are included to model the effect of local site effects and faulting mechanism on the observed ground motions. The equations include coefficients to model the observed magnitude-dependent decay rate. The main findings of this study are that: short-period ground motions from small and moderate magnitude earthquakes decay faster than the commonly assumed 1/r, the average effect of differing faulting mechanisms is not large and corresponds to factors between 0.8 (normal and odd) and 1.3 (thrust) with respect to strike-slip motions and that the average long-period amplification caused by soft soil deposits is about 2.6 over those on rock sites. Disappointingly the standard deviations associated with the derived equations are not significantly lower than those found in previous studies.     

Analytical study of the energy rate balance equation for the magnetospheric storm-ring current

We present some results of the analytical integration of the energy rate balance equation, assuming that the input energy rate is proportional to the azimuthal interplanetary electric field, E_y, and can be described by simple rectangular or triangular functions, as approximations to the frequently observed shapes of E_y, especially during the passage of magnetic clouds. The input function is also parametrized by a reconnection-transfer efficiency factor (which is assumed to vary between 0.1 and 1). Our aim is to solve the balance equation and derive values for the decay parameter compatible with the observed Dst peak values. To facilitate the analytical integration we assume a constant value for through the main phase of the storm. The model is tested for two isolated and well-monitored intense storms. For these storms the analytical results are compared to those obtained by the numerical integration of the balance equation, based on the interplanetary data collected by the ISEE-3 satellite, with the values parametrized close to those obtained by the analytical study. From the best fit between this numerical integration and the observed Dst the most appropriate values of are then determined. Although we specifically focus on the main phase of the storms, this numerical integration has been also extended to the recovery phase by an independent adjust. The results of the best fit for the recovery phase show that the values of may differ drastically from those corresponding to the main phase. The values of the decay parameter for the main phase of each event, _m, are found to be very sensitive to the adopted efficiency factor, , decreasing as this factor increases. For the recovery phase, which is characterized by very low values of the power input, the response function becomes almost independent of the value of and the resulting values for the decay time parameter, _r, do not vary greatly as varies. As a consequence, the relative values of between the main and the recovery phase, _m/_r, can be greater or smaller than one as varies from 0.1 to 1.