Theoretical amplitudes of body waves from a dislocation source in the earth III. P,S and surface reflections

Expressions are obtained for the ray-theoretical spectral amplitudes of body waves induced by a shear dislocation of arbitrary orientation and depth situated in a radially heterogeneous model of the earth. Account is taken of the azimuthal and colatitudinal radiation patterns of the source, the geometrical spreading, and the reflections and refractions at the free surface and at the mantle-core boundary.In this work spectral amplitudes are calculated for P, SH, SV, PP, PPP, PS, PSS, SP, SPP, SSH, SSSH, SSV, and SSSV. The results are presented in the form of tables for a source of strength U₀dS = 10¹⁵cm³, where U₀ is the amount of the dislocation and dS is the fault area. Given the slip and dip angles of the source, the amplitudes of these surface reflections and direct phases can be obtained from these tables for all azimuths, for most of the epicentral distances at which a particular phase is observable, and for all the fourteen focal depths included in the Jeffreys-Bullen tables. It is found that the depth of the source has a strong effect on the amplitudes of the body wave signals.     

Normal Mode Energetics for Far-field Tsunamis Generated by Dislocations and Landslides

— We apply the normal mode representation of tsunami waves, as introduced by Ward (1980) to the systematic study of the excitation of far-field tsunamis by both dislocation sources (represented by double-couples of moment M ₀), and landslides (represented by single forces). Using asymptotic representations of the continuation of the tsunami eigenfunction into the solid Earth, we derive analytical expressions of the spectral amplitude generated by both systems. We show that the quadrupolar corrections defined by Dahlen (1993) in the case of landslides can result in an increase of 1 to 2 orders of magnitude of the effective force. Even so, the spectrum of tsunami waves generated by landslides is found to be offset significantly to relatively high frequencies (10 mHz), where dispersion becomes important and eventually diminishes time-domain amplitudes. We proceed to calculate the total energy delivered into the tsunami modes by integrating the energy of multiplets for an average source geometry. In the case of dislocation sources, and taking into account the corner frequency of the source, we reproduce the scaling with M ₀ ^4/3 which was derived from purely static arguments by Kajiura (1981). We compare the directivity patterns of far-field tsunami waves by dislocations and landslides, and conclude that the latter cannot give rise to pronounced lobes of directivity for physically acceptable values of the velocity of the slide. Directivity thus constitutes a robust discriminant of the nature of the source which, when applied to the 1946 Aleutian tsunami in the far-field, requires generation by a dislocative source.     

The source of the great Assam earthquake — an interplate wedge motion

The source of the Assam earthquake of Aug. 15, 1950 is revealed from amplitude observations of surface and body waves at Pasadena, Tokyo and Bergen. Seiches' amplitudes in Norway, initial P motions throughout the world, aftershocks and landslides distribution, PP/P ratio at Tokyo, R/L ratio and directivity at Pasadena, are also used. The ensuing fault geometry and kinematics is consistent with the phenomenology of the event and the known geology of the source area. It is found that a progressive strike-slip rupture with velocity 3 km/sec took place on a fault of length 250 km and width 80 km striking 330–337° east of north and dipping 55–60° to ENE. The use of exact surface-wave theory and asymptotic body-wave theory which takes into account finiteness and absorption, rendered an average shear dislocation of 35 m. A three-dimensional theory for the excitation of seiches in lakes by the horizontal acceleration of surface waves was developed. It is confirmed that Love waves near Bergen generated seiches with peak amplitude up to 70 cm depending strongly on the width of the channel.It is believed that the earthquake was caused by a motion of the Asian plate relative to the eastern flank of the Indian plate where the NE Assam block is imparted a tendency of rotation with fracture lines being developed along its periphery.Comparison with other well-studied earthquakes shows that although the magnitude of the Assam event superseded that of all earthquakes since 1950, its potency U₀dS (700,000 m × km²) was inferior to that of Alaska 1964 (1,560,000 m × km²) and Chile 1960 (1,020,000 m × km²).     

Q-structure beneath the Tibetan Plateau from the inversion of Love- and Rayleigh-wave attenuation data

The fundamental mode Love and Rayleigh waves generated by ten earthquakes and recorded across the Tibet Plateau, at QUE, LAH, NDI, NIL, KBL, SHL, CHG, SNG and HKG are analysed. Love- and Rayleigh-wave attenuation coefficients are obtained at time periods of 5–120 s using the spectral amplitudes of these waves for 23 different paths. Love wave attenuation coefficient varies from 0.0021 km^?1, at a period of 10 s, to 0.0002 km^?1 at a period of 90 s, attaining two maxima at time periods of 10 and 115 s, and two minima at time periods of 25 and 90 s. The Rayleigh-wave attenuation coefficient also shows a similar trend. The very low value for the dissipation factor, Q_β, obtained in this study suggests high dissipation across the Tibetan paths. Backus-Gilbert inversion theory is applied to these surface wave attenuation data to obtain average Q_β^?1 models for the crust and uppermost mantle beneath the Tibetan Plateau. Independent inversion of Love- and Rayleigh-wave attenuation data shows very high attenuation at a depth of ～50–120 km ($\text{Q}{}_{\mathrm{\beta }}\text{? 10}$). The simultaneous inversion of the Love and Rayleigh wave data yields a model which includes alternating regions of high and low Q_β^?1 values. This model also shows a zone of high attenuating material at a depth of ～40–120 km. The very high inferred attenuation at a depth of ～40–120 km supports the hypothesis that the Tibetan Plateau was formed by horizontal compression, and that thickening occurred after the collision of the Indian and Eurasian plates.     

Separation of Source, Propagation and Site Effects from S Waves¶of Local Earthquakes in Bursa Region, Northwestern Turkey

—?We have used micro-earthquake recordings (M= 1.8–4.1) of local events in the distance range of 5–60?km in order to quantify the attenuation and site effects in the vicinity of the Bursa city, Marmara region, Turkey. The data set consists of 120 three-component recorded accelograms from 69 earthquakes, recorded at six stations. Each station is deployed on different geologic units, such as massive limestone, slope deposit and Quaternary young sediments, in the framework of the Marmara Poly-Project.¶In this study a nonparametric inversion method was applied to acceleration records from the Bursa region to estimate source, site and path effects using a two-step inversion. At the first step, we determined attenuation functions by analyzing the distance dependence of the spectral amplitudes and retrieved values of Q _s (f) = 46.59f ^0.67. At the second step, the corrected S-waves spectral records for the attenuation function, including the geometrical spreading effect, were inverted to separate source and site response for 21 different frequencies selected between 0.5 and ～25?Hz. The near-surface attenuation, κ value, was also estimated by using the model proposed by Anderson and Hough (1984) at each site. We observed that κ₀ is smaller for stations located on rock site (I?dιr, SIGD, κ₀～0.004) compared to the one that is located on Neogene sediment (Çukurca, SCKR, κ₀～0.018).¶Site amplifications from inversion showed that the station located within the Bursa basin, Çukurca (SCKR), is the most important site with about 4.0 amplification value at 1.8?Hz. Demirta? (SDEM) amplifies the spectral amplitudes about 3.0 times at 2.0?Hz, SHMK about 3.5 times between 2.5 and 3.5?Hz and SHMT nearly reaching 3.5 times between 1.5 and 4.0?Hz. However, stations located on the Uluda? Mountain Massif (SKAY and SIGD), which correspond to a deep limestone geological unit, have the smallest amplification, that values between 0.6 and 1.4.     

Short-period PKP phases and the anelastic mechanism of the inner core

Short-period seismograms are synthesized for PKP phases in anelastic Earth models. The synthetics were constructed using a synthetic technique valid at grazing incidence, a source-time function appropriate for deep-focus earthquakes, and an instrument response for either a short-period WWSSN or SRO seismograph. The agreement between predicted and observed amplitudes and spectral ratios requires neither a low-Q_α zone at 0.2–2 Hz nor a low or negative P-velocity gradient at the bottom of the outer core. Thin low-Q_α zones beneath the inner core boundary fit spectral ratio data that sample the upper 200 km of the inner core but fail to fit data that sample the lower inner core. Only a model having Q_α^?1?[0.003, 0.004] at 0.2–2 Hz, nearly constant with depth in the inner core, satisfies all of the spectral ratio and amplitude data. The assumption of a bulk viscosity of 10-10³ Pa s for the liquid phase of a partially molten inner core combined with the observation of low shear attenuation in the inner core at frequencies less than 0.005 Hz limit the physical parameters associated with two possible attenuation mechanisms: (1) fluid flow and viscous relaxation due to ellipsoidally shaped inclusions of melt, and (2) the solid-liquid phase transformation induced by the stress change during the passage of a seismic wave. Both mechanisms require an order of 0.1% partial melt to reproduce the observed Q_α^?1. In the outer core, the time constant of the mechanism of phase transformation is predicted to be 10⁴–10⁶ s. Confirmation of small shear attenuation in the inner core in the frequency band of seismic body waves would favor the mechanism of phase transformation.     

Empirical model for estimating Fourier amplitude spectra of ground acceleration in Taiwan region

A collection of ground‐motion recordings (1070 acceleration records) of moderate (5.1⩽M_L⩽6.5) earthquakes obtained during the execution of the Taiwan Strong Motion Instrumentation Program (TSMIP) since 1991 was used to study source scaling model and attenuation relations for a wide range of earthquake magnitudes and distances and to verify the models developed recently for the Taiwan region. The results of the analysis reveal that the acceleration spectra of the most significant part of the records, starting from S‐wave arrival, can be modelled accurately using the Brune's ω‐squared source model with magnitude‐dependent stress parameter Δσ, that should be determined using the recently proposed regional relationships between magnitude (M_L) and seismic moment (M₀) and between M₀ and Δσ. The anelastic attenuation Q of spectral amplitudes with distance may be described as Q=225 ƒ^1.1 both for deep (depth more than 35 km) and shallow earthquakes. The source scaling and attenuation models allow a satisfactory prediction of the peak ground acceleration for magnitudes 5.1⩽M⩽6.5 and distances up to about 200 km in the Taiwan region, and may be useful for seismic hazard assessment. Copyright © 2000 John Wiley & Sons, Ltd.     

Source Scaling of Inland Crustal Earthquake Sequences in Japan Using the S-Wave Coda Spectral Ratio Method

We estimate corner frequencies and stress drops for 298 events ranging from M _w 3.2–7.0 in 17 inland crustal earthquake sequences in Japan to investigate the source scaling and variation in stress drops. We obtain the source spectral ratio from observed records by the S-wave coda spectral ratio method. The advantage of using the S-wave coda is in obtaining much more stable source spectral ratios than using direct S-waves. We carefully examine the common shape of the decay of coda envelopes between event pair records. The corner frequency and stress drop are estimated by modeling the observed source spectral ratio with the omega-square source spectral model. We investigate the dependences of stress drops on some tectonic effects such as regionality, focal mechanism, and source depth. The principal findings are as follows: (1) a break in self-similar source scaling is found in our dataset. Events larger than M _w 4.5 show larger stress drops than those of smaller events. (2) Stress drops of aftershocks are mostly smaller than those of mainshocks in each sequence. (3) There are no systematic differences between stress drops of events occurring inside and outside the Niigata-Kobe Tectonic Zone in Japan. (4) Clear dependence of the faulting type on stress drops cannot be seen. (5) Stress drops of aftershocks depend on their source depth. (6) The crack size obtained from the corner frequency corresponds to the total rupture area of heterogeneous slip models for large events.     

Clearance rates of Cerastoderma edule under increasing current velocity

Estimates of clearance rates (CR) of Cerastoderma edule (300 ind. m⁻²) as a function of free-stream current velocity (U) (from 5 to 40 cm s⁻¹) were compared between a small annular (60 l) and a large racetrack (8850 l) flume with different hydrodynamic conditions. Results showed that the flumes differ considerably in their hydrodynamic characteristics. The relationship between CR and U is different in the two flume tanks, however there appears to be a straightforward unimodal trend between CR and shear velocity (U_*). It was found that the cockles themselves influence the benthic boundary layer (BBL) characteristics, by causing steeper velocity gradients and increasing the mixing over the cockle bed compared to bare sediment. This provides new evidence on how endobenthic organisms can affect the BBL. However, the influence of CR on U_* could not be quantified because these parameters have interactive effects that cannot be dissociated.     

Theoretical and Observed Depth Correction for M s

—?Modal summation technique is used to generate 5000, three-component theoretical seismograms of Love and Rayleigh waves, assuming modified PREM (PREM-C) and AK135F global earth models. The focal depth h and the geometrical fault parameters are randomly chosen so as to uniformly cover possible source mechanisms and obtain uniform distribution of log h in the interval 1?h?h?M _s of the form:¶ΔM _s (h)=0 forh< 20km, ΔM _s (h)=0.314log(h)-0.409 for 20≠h< 60km, ΔM _s (h)=1.351log(h)-2.253 for 60≠h< 100km, ΔM _s (h)=0.400log(h)-0.350 for 100≠h< 600km .¶After applying the above correction, the relationship between the surface wave magnitude and the scalar seismic moment for the observational data set significantly improves, and becomes independent of the source depth. In relation to CTBT, no depth correction is needed for M _S when the m _b ???M _S discriminant is computed, because the proposed correction is zero for earthquakes with foci above 20?km.     

T Waves from the 1998 Papua New Guinea Earthquake and its Aftershocks: Timing the Tsunamigenic Slump

— T waves recorded at hydrophone and seismic stations following the Papua New Guinea earthquake of 17 July 1998 and its aftershocks show that a small event at 09:02 GMT featured source properties incompatible with an elastic dislocation of appropriate body-wave magnitude (m _b=4.4). These include an exceptional duration (47 s at the Wake Island hydrophone station WK31), a spectrum rich in high frequencies (7 to 12 Hz), and a generally low spectral amplitude. These characteristics can be explained by the model of an underwater slump, accelerating from a standstill and eventually slowing down. The relocation of the 09:02 event is compatible with its location within an amphitheater inside which shipboard cruises in 1998 and 1999 documented the presence of a 4 – km³ geologically fresh slump. We propose that the slump took place at 09:02 on 17 July 1998, i.e., 13 minutes after the mainshock, and that it generated the locally catastrophic tsunami, whose properties (amplitude and distribution of runup; timing) could not be explained by a dislocation model.     

Regional induction studies: A review of methods and results

The geomagnetic skin-effect is specified by setting three length scales in relation to each other: L₁ for the overhead source. L₂ for the lateral non-uniformity of the subsurface conductor, L₃ for the depth of penetration of a quasi-uniform transient field into this conductor. Relations for the skin-effect of a quasi-uniform source in layered conductors are generalized to include sources of any given geometry by introducing response kernels as functions of frequency and distance. They show that only those non-uniformities of the source which occur within a distance comparable to L₃ from the point of observation are significant. The skin-effect of a quasi-uniform source in a laterally non-uniform earth is expressed by linear transfer functions for the surface impedance and the surface ratio of vertical/horizontal magnetic variations. In the case of elongated structures and E-polarisation of the source, a modified apparent resistivity is defined which as a function of depth and distance gives a first orientation about the internal distribution of conductivity. The skin-effect of a non-uniform source in a non-uniform earth is considered for stationary and “running” sources. Recent observations on the sea floor and on islands indicate a deep-seated change of conductivity at the continent—ocean transition, bringing high conductivity close to the surface, a feature which may not prevail, however, over the full width of the ocean. There is increasingly reliable evidence for high conductivities (0.02 to 0.1 micro ^?1 m^?1) at subcrustal or even at crustal depth beneath certain parts of the continents, in some cases without obvious correlation to geological structure.     

High-frequency vertical current observations in stratified seas

Although large-scale tidal and inertial motions dominate the kinetic energy and vertical current shear in shelf seas and ocean, short-scale internal waves at higher frequencies close to the local buoyancy frequency are of some interest for studying internal wave breaking and associated diapycnal mixing. Such waves near the upper limit of the inertio-gravity wave band are thought to have relatively short O (10²–10³ m) horizontal scales and to show mainly up- and downward motions, which contrasts with generally low aspect ratio large-scale ocean currents. Here, short-term vertical current (w) observations using moored acoustic Doppler current profiler (ADCP) are presented from a shelf sea, above a continental slope and from the open ocean. The observed w, with amplitudes between 0.015 and 0.05 m s⁻¹, all span a considerable part of the water column, which is not a small vertical scale O(water depth) or O (100–500 m, the maximum range of observations), with either 0 or π phase change. This implies that they actually represent internal waves of low vertical modes 1 or 2. Maximum amplitudes are found in layers of largest stratification, some in the main pycnocline bordering the frictional bottom boundary layer, suggesting a tidal source. These ‘pycnocline-w’ compose a regular train of (solitary) internal waves and linearly decrease to small values near surface and bottom.     

Amplitude Corrections for Regional Seismic Discriminants

—?A fundamental problem associated with event identification lies in deriving corrections that remove path and earthquake source effects on regional phase amplitudes used to construct discriminants. Our goal is to derive a set of physically based corrections that are independent of magnitude and distance, and amenable to multivariate discrimination by extending the technique described in Taylor and Hartse (1998). For a given station and source region, a number of well-recorded earthquakes is used to estimate source and path corrections. The source model assumes a simple Brune (1970) earthquake source that has been extended to handle non-constant stress drop. The discrimination power in using corrected amplitudes lies in the assumption that the earthquake model will provide a poor fit to the signals from an explosion. The propagation model consists of a frequency-independent geometrical spreading and frequency-dependent power law Q. A grid search is performed simultaneously at each station for all recorded regional phases over stress-drop, geometrical spreading, and frequency-dependent Q to find a suite of good-fitting models that remove the dependence on m _b and distance. Seismic moments can either be set to pre-determined values or estimated through inversion and are tied to m _b through two additional coefficients. We also solve for frequency-dependent site/phase excitation terms. Once a set of corrections is derived, effects of source scaling and distance as a function of frequency are applied to amplitudes from new events prior to forming discrimination ratios. Thus, all the corrections are tied to just m _b (or M ₀) and distance and can be applied very rapidly in an operational setting. Moreover, phase amplitude residuals as a function of frequency can be spatially interpolated (e.g., using kriging) and used to construct a correction surface for each phase and frequency. The spatial corrections from the correction surfaces can then be applied to the corrected amplitudes based only on the event location. The correction parameters and correction surfaces can be developed offline and entered into an online database for pipeline processing providing multivariate-normal corrected amplitudes for event identification. Examples are shown using events from western China recorded at the station MAKZ.     

Heat flow studies: Constraints on the distribution of uranium,thorium and potassium in the continental crust

To study the amount of heat generated by radioactive decay in the continental crust, the usual practice in the literature is to fit to the heat flow and radioactivity data a relationship of the form: Q = Q_r + D · A where Q and A are the observed heat flow and radiogenic heat production. Q_r is the “reduced” heat flow and D is a depth scale. This procedure implicitly assumes that uranium, thorium and potassium have identical distributions in the crust. We suggest that significant information may be lost as the three radioelements may in fact be affected by processes operating over different depths.Data published for four heat flow provinces throughout the world are used to estimate the distributions of uranium, thorium and potassium in the continental crust. These distributions are characterized by a depth scales defined as follows: D_i =∫0h C_i(z)C_i(0)dz where h is the thickness of the layer containing the bulk of radioactivity and C_i(z) the concentration of element i at depth z. Three depth scales are computed from a least-squares fit to the following relationship: Q = Q_r + D_U · A_U + D_T · A_T + D_K · A_T where Q is the observed heat flow and Q_r some constant (a reduced heat flow). A_i is the heat generation rate due to the radioactive decay of element i, and D_i is the corresponding depth scale.The analysis suggests that the three distributions are different and that they have the same basic features in the four provinces considered. The depth scale for potassium is large in granitic areas, that for thorium is small and that for uranium lies between the other two.We propose a simple model according to which each radioelement essentially provides a record for one process. Potassium gives a depth scale for the primary differentiation of the crust. Thorium gives the depth scale of magmatic or metamorphic fluid circulation. Finally, the uranium distribution reflects the late effects of alteration due to meteoric water. We show that the heat flow and radioactivity data are compatible with this model.Our analysis and numerical results are supported by data from deep boreholes and by geochemical evidence, such as detailed investigations of plutonic series and studies of U-Th-Pb systematics.     

Spectral analysis of body waves for earthquakes and their source parameters in the Himalaya and nearby regions

The source characteristics of 33 earthquakes with magnitude m_b between 4.4 and 6.0, which occurred in the Himalayan and nearby regions, are investigated using the records of the Hyderabad seismograph station. The P- and S-wave spectra of these events are interpreted in terms of Brune's seismic source model for estimating the source parameters, i.e., seismic moment, source dimension, stress drop, average dislocation, apparent stress and the radiated energy. Seismic moments, M₀, vary between 0.3 × 10²⁴ and 9.0 × 10²⁶ dyne cm; source dimensions, r, between 4.3 and 18.6 km; stress-drops, Δσ between 0.3 and 151.6 bar; average dislocations, $\text{u}$ between 0.6 and 381 cm; apparent stresses, $\text{η}\text{σ}$ between 0.1 and 73.2 bar. The radiated energy, E_R is estimated by the spectrum integration method and is found to vary between 0.2 × 10¹⁸ and 9.3 × 10²² erg. In general, the stress drop and apparent stress are found to be high, indicating high stresses in these regions.     

THE INDUCTIVE RESPONSE OF A HORIZONTAL CONDUCTING CYLINDER BURIED IN A UNIFORM EARTH FOR A UNIFORM INDUCING FIELD*

The inductive response of a conducting horizontal cylinder embedded in a uniform earth is studied using numerical results obtained for an analytical solution for the problem of a conducting cylinder buried in a homogeneous earth for the case of a uniform inducing field. A check of the validity of the numerical results is made by a comparison with analogue model measurements for a number of cases. Numerical results for a range of cylinder radii (a = 1–10 km), depths of burial (d= 0–4 km), conductivity contrasts (σ₂= 10^?2-10 Sm^?1), and source frequencies (f= 10^?1-10^?4 Hz) of interest in the interpretation of magnetotelluric field measurements are presented. The results indicate that for a uniform inducing field the conductivity and depth of burial of a horizontal cylindrical inhomogeneity are best determined through a measurement of the amplitudes H_y, H_z and E_x and the phases φ_y and Ψ_x.     

Site effect study in central Mexico using H/V and SSR techniques: Independence of seismic site effects on source characteristics

We study the influence of different source characteristics (depth, distance, type and azimuth) on the site effect in Acapulco and the Valley of Mexico. Site amplification was estimated by means of spectral ratios (both horizontal-to-vertical spectral ratio and standard spectral ratio techniques were applied) from earthquake recordings at soft and hard sites. In Acapulco, 125 Mexican earthquakes covering a hypocentral range of 7–290 km and a depth range (H) of 3–61 km were analyzed in three different groups of hypocentral distances. In the Valley of Mexico, we estimate site effect at five locations using recordings from shallow-coastal interplate (200?Δ?570 km; H?35 km) and normal-faulting, intermediate-depth inslab (132?Δ?738 km; 32?H?178 km) earthquakes, as well as from teleseismic events. Our results seem to point to negligible dependence of site effects on the source location and type.     

Shear wave attenuation estimated from the spectral decay rate in the vicinity of the Petropavlovsk station,Kamchatka

The parameters of S-wave attenuation (the total effect of absorption and scattering) near the Petropavlovsk (PET) station in Kamchatka were estimated by means of the spectral method through an original procedure. The spectral method typically analyzes the changes with distance of the shape of spectra of the acceleration records assuming that the acceleration spectrum at the earthquake source is flat. In reality, this assumption is violated: the source acceleration spectra often have a high-frequency cutoff (the source-controlled f_max) which limits the spectral working bandwidth. Ignoring this phenomenon not only leads to a broad scatter of the individual estimates but also causes systematic errors in the form of overestimation of losses. In the approach applied in the present study, we primarily estimated the frequency of the mentioned high-frequency cutoff and then constructed the loss estimates only within the frequency range where the source spectrum is approximately flat. The shape of the source spectrum was preliminarily assessed by the approximate loss compensation technique. For this purpose, we used the tentative attenuation estimates which are close to the final ones. The difference in the logarithms of the spectral amplitudes at the edges of the working bandwidth is the input for calculating the attenuation. We used the digital accelerograms from the PET station, with 80 samples per second digitization rate, and based on them, we calculated the averaged spectrum of the S-waves as the root mean square along two horizontal components. Our analysis incorporates 384 spectra from the local earthquakes with M = 4–6.5 at the hypocentral distances ranging from 80 to 220 km. By applying the nonlinear least-square method, we found the following parameters of the loss model: the Q-factor Q₀ = 156 ± 33 at frequency f = 1 Hz for the distance interval r = 0–100 km; the exponent in the power-law relationship describing the growth of the Q-factor with frequency, γ = 0.56 ± 0.08; and the loss parameter beneath the station κ₀ = 0.03 ± 0.005 s. The actual accuracy of the estimates can probably be somewhat lower than the cited formal accuracy. It is also established (with a confidence level of 10%) that the losses decrease with distance.