Function Of Focal Depth Research Articles

Analisi critica su le profondità ipocentrali.

The aim of this study is to point out the difficulties in the analytical determination of hypocentral depth h and the consequent uncertainty in its reliability. The former attempt was realized at world-wide level (december 1964), the latter in the Mediterranean Area (19 reigons, accordingly to the division proposed by Flin, Engdal, Hill, 1974). We considered hypocentral data of the earthquakes occurred in that area during the 1964-1974 decade, with a great care to the h values and their standard deviations. First we pointed out the depth features of every region: afterwards we looked into the standard deviations (E) and their respective h values Data analysis suggested us to calculate a series of exponential functions E = P h- showing standard deviations as a function of focal depth; every region is characterized by a and 3 coefficients calculated by a least squares fit. We analysed results and also made an attempt to explain the standard deviations scatter. We also made an attempt by only Italian earthquakes data (ioining the four sections Northern, Central, Southern Italy, and Sicily), and we calculated the t = f(h) function. Both the world-wide analysis and the Mediterranean one pointed out some interesting elements. — Focal depth data, even if joined with their standard deviations, are very unrealiable particularly for crustal earthquakes; in that case standard deviations often are too large and focal depth lose their physical meaning. — In the upper mantle the data are more reliable. Obviously the choise of the travel-times used to calculate focal depth influences data reliability, particularly in the most heterogeneous layers in the crust.

In‐depth analyses by confocal Raman microspectrometry: experimental features and modeling of the refraction effects

AbstractIn‐depth confocal Raman microspectrometry (CRM) studies through a planar interface between materials of mismatched refraction indices are known to be affected by a decrease in both collected Raman intensity and axial resolution as a function of focal depth. A complete treatment of these phenomena would require diffraction and refraction effects to be taken into account. Baldwin and Batchelder have recently modeled the refraction effects by considering the influence of the dimensions of the confocal pinhole aperture on the collection efficiency. Their theoretical predictions are compared here with experimental results obtained for a standard 200 µm thick polyethylene (PE) sample. It is shown that the decrease in Raman intensity as a function of focal depth is weaker than predicted, suggesting that off‐axis refraction effects cannot be neglected. We therefore propose a simple two‐parameter relation which reproduces the observed Raman intensities down to 150–200 µm focal depths. Other in‐depth experiments on various test samples, a silicon wafer buried in Nujol oil, PE films of different thicknesses and a polycarbonate slab, were then performed in order to show how the Raman intensity decrease, the radial resolution and the axial interfacial broadening can be directly estimated as a function of the focal depth position. Also, CRM experiments were carried out on a four‐layer polymer laminate in order to find the best optical conditions. ‘Edge’ analyses remain the most efficient way to investigate polymer interfaces but, when in‐depth analyses are needed, we tried to evaluate to what extent interfacial broadenings impede the investigation of interpenetration effects at buried interfaces. It is demonstrated that the refraction effects sharpen the interfacial broadenings and the apparent axial resolution does not drastically deteriorate with increasing depth. Indeed, when focused 120 µm deep into a non‐absorbing sample, the interface is found to be broadened by a factor of only 7.5 or 3.7 using a 100× or a 50× objective lens; the axial resolution then takes a reasonable value of about 13 µm. Copyright © 2002 John Wiley & Sons, Ltd.

Analysis of worst-case phase quantization sidelobes in focused beamforming

The effect of phase quantization errors on the sidelobe level in a phased-array beamformer is considered. The theory of random and periodic phase errors is reviewed. Periodic phase errors occur for an unfocused array with uniform element distance and give rise to discrete sidelobes. The main result of the paper is an analysis of the periodic phase error in the case that the beamformer is focused. An estimate for the worst-case discrete sidelobe level as a function of focal depth is derived. The theory is illustrated and verified by simulations.

Kinematic Properties of Primary Converted Rays Produced at a Single Boundary

The eight primary P to Sv and Sv to P converted rays generated at a single boundary generally appear at the Earth’s surface as pairs of interfering arrivals consisting of one Sv and one P, of similar kinematic properties. Kinematic equivalence is obtained for the case of a surface source in a laterally homogeneous layered model. The interference, which is a function of focal depth, lateral heterogeneity and the relative amounts of P and Sv energy generated by the source, significantly camplicates the interpretation of the dynamic properties of converted rays. Vertical heterogenity affects converted rays in a multiple fashion as P and Sv segments are both involved. For example, a single low velocity zone will, in general, produce four shadow zones in the primary converted ray branches.

Angles of incidence of S waves

Abstract A table for the angles of incidence of S at the focus and at the Earth's surface, as a function of focal depth and epicentral distance is presented. The calculations are based on Randall's (1971) revised travel-time table for S.

Discrimination Between Earthquakes and Underground Explosions Employing an Improved Ms Scale

Summary The M, Rayleigh wave magnitude formula is revised for purposes of eliminating the heretofore variable effects of near distances and propagation paths on the values computed from standard long-period seismograms. The improved formulation employs a revised distance correction function and a period-dependent path correction that normalizes M, to large teleseismic distance 20-s values. For purposes of earthquake-explosion discrimination, an empirical focal depth correction is derived on the basis of Rayleigh wave frequency content as a function of focal depth, which normalizes M, values to the surface focus equivalent, i.e. aids discrimination when it can be applied by increasing earthquake M, values and moving them away from the equivalent explosion population on M, : m, plots. The revised M, improves on previously achieved discrimination of North American events, and provides reliable discrimination between suites of Eurasian earthquakes and explosions. Having removed the dominant propagation path effects on M,, the residual differences in M, : mb among events are generally attributed to source environment and regional effects on m,,. The 42 Eurasian WWSSN stations employed are shown to have a discrimination threshold at the M,3.2 level. With the improved M, scale now equivalent to first order for North American and Eurasian continental propagation, available Nevada Test Site explosion yields are extrapolated to the Eurasian sites to illustrate that this M,3.2 discrimination threshold is equivalent to an Eurasian explosion of about 20 kt in hard rock. Given improved long-period instrumentation to reduce the Rayleigh wave detection threshold, the principal restriction on further studies of discrimination to lower levels of magnitude and yield will be the availability of earthquake occurrence information at the low magnitudes.

A new analytical method for finding the upper mantle velocity structure from P and S wave travel times of deep earthquakes

abstract A new analytical method for the determination of velocity at the hypocenter of a deep earthquake has been developed making use of P- and S-wave travel times. Unlike Gutenberg's method which is graphical in nature, the present method makes use of the least square technique and as such it yields more quantitative estimates of the velocities at depth. The essential features of this method are the determination from the travel times of a deep-focus earthquake the lower and upper limits Δ1 and Δ2 respectively of the epicentral distance between which p = (dT/dΔ) in the neighborhood of inflection point can be considered stationary so that the travel-time curve there can be approximated to a straight line T = pΔ + a. From p = (1/v*) determined from the straight line least-square fit made on the travel-time observation points between Δ1 and Δ2 for various focal depths, upper-mantle velocity structure can be obtained by making use of the well known relation v = v*(r0 − h)/r0, h being the focal depth of the earthquake, r0 the radius of the Earth, v* the apparent velocity at the point of inflection and v the true velocity at that depth. This method not only gives an accurate estimate of p, at the same time it also yields quite accurate value of a which is a function of focal depth. Calibration curves can be drawn between a and the focal depth h for various regions of the Earth where deep focus earthquakes occur, and these calibration curves can then be used with advantage to determine the focal depths of deep earthquakes in those areas.

Interpreting array records: explosion and earthquake P wavetrains which have traversed the deep mantle

Before 1946 four explosions with yields of a kiloton or more were recorded by seismographs up to ranges of 10°. After the first motion, the seismograms were not obviously different from those of earthquakes at similar distances. In 1946 Bikini Baker was recorded out to distances of 80° with amplitudes equivalent to an earthquake of magnitude m 51/2. Since then numerous explosions have been recorded at teleseismic ranges along nine different transmission paths with signal/noise ratios large enough to enable details of the P wavetrain to be analysed. Between 30 and 90° these explosion seismograms are characterized by a large, relatively simple onset pulse followed by 20 to 30 s of low amplitude oscillations. Variations of waveform across a large array of seismometers are shown to be due to signal-generated noise. The time-shifted and array-sum records of a given explosion are almost identical. Differences between explosion seismograms are a function of focal depth and local geology. A good working hypothesis is that the deep mantle is very homogeneous. Waveforms of the majority of shallow earthquakes recorded under these experimental conditions are dependent upon azimuth and range. Signals related to focal depth may account for only a small proportion of the observed P energy. The conversion of SV waves qualitatively explains the seismograms. The observations are consistent enough to make it worth while taking stock of the capacity of the international network to study earthquake mechanism.

Magnitude determination for deep-focus earthquakes*

Summary The magnitude of deep-focus earthquakes is so defined as to make the energy released in two shocks of the same magnitude equal, regardless of focal depth.—Charts are given which, in connection with the equations for the magnitude of shallow shocks, permit the calculation of the magnitude of a shock at any given depth if the maximum ground amplitude and the corresponding wave period of P, PP, or S at a given epicentral distance are known.—It is found that the energies released in the longitudinal and transverse waves of an earthquake are about equal, regardless of focal depth.—The “shadow zone” for P and S waves at epicentral distances near 10°, indicating a slight minimum in wave velocity at a depth near 100 km., has been confirmed, and quantitative results for amplitudes of P as a function of focal depth are given.—Earthquake magnitudes of 7 ¾ to 8 have been found throughout the range of focal depths, but, during the past forty years, seem to have been relatively less frequent in deep-focus than in shallow shocks. In contrast with shallow shocks, no deep-focus earthquakes of magnitudes 8 ¼ to 8 ½ have been established thus far. This indicates (but does not yet prove) that at depths of about 100 to 700 km. roughly one-tenth as much energy can be stored as at depths of 15 to 40 km. At a depth of about 700 km. earthquake activity seems to stop abruptly.—The amplitudes of surface waves in deep-focus shocks decrease with increasing focal depth approximately as given by the theory.