Arrival-time difference

An example of the location of acoustic emission sources as a function of time is shown in Fig. 8. Each symbol is plotted at the location of its source along the specimen beam at the arrival time at the sensor. Linear location using arrival time differences between two sensors allows location along one axis only, plotted on the abscissa. The co-ordinate system is such that the origin is at the end of the beam. Sensor 1 is at 15 mm and sensor 2 at 225 mm, i.e., the sensors are a distance of 210 mm apart. It is well-known that linear location of AE sources is more accurate within the area enclosed by the sensor array and that the uncertainty is rapidly increasing outside this area. The tip of the insert film is at 164 mm, the first pinning area extends between 125 and 149 mm, and the second between 59 and 84 mm as indicated in Fig. 8. 

The shock velocity at the powder container was measured by the ion gap method, and the shock pressure was calculated using the equations by Cole [3] and Penny and Dasgupta [4] expressing the relationship between the shock pressure and velocity of water. The shock velocity was measimed by arrival time difference of shock wave between pins with different height. The velocity of the shock wave was measured to be about 4600m/s, so that the shock pressure obtained by this assembly was estimated to be 7 GPa in the powder container. 

The multiplet analysis provides information on the micro structures in the seismic cloud. However, it does not give knowledge of absolute locations of individual multiplet clusters with the same order of precision to the relative location of events in a multiplet cluster. Moriya et al. (2002) proposed the multiplet-clustering method" to reduce the location error of multiplet clusters using the technique of clustering analysis. In this method, the waveforms of events in a multiplet group are stacked, and similar phases of the stacked waveforms are compared in time domain. Then, relative arrival time differences (i.e. relative locations between the stacked events) are more precisely determined. 

A monitoring system can analyze such parameters as count, hit, event, rise time, duration, peak amplitude, energy, RMS (root mean square) voltage, frequency spectrum, and arrival-time difference as discussed in Chapter 4. Normally AE signals are processed after the amplitude becomes larger than the threshold level. 

Source location determination is an inverse problem. Due to the arrival time differences of the elastic wave emitted by the fracture and recorded at each sensor, the source location can be calculated. The acoustic emission source location is defined by the origin time (start of the rupture) and the source position in Cartesian coordinates (xo, yo, zo)- The computed location corresponds to the point in space and time where the fracture initiated. Therefore, a point source is assumed. The first arrival time of the elastic... 

In seismology a 2-D source location with no information about the depth of the event is called epicenter. At least 3 sensors are needed for a 2-D localization. Assuming constant velocity and three measured arrival times ti, t2 and t of the compressional wave, at three different sensors, the epicenter can be calculated by the hyperbola method (Bath 1979 Pujol 2004). The epicenter must be located on a curve for which the arrival time difference between two sensors e.g. G - ti is constant (Fig. 6.6). Such a curve is a hyperbola with the corresponding sensor coordinates of sensor 1 and sensor 2 as foci. 

The first term in Eq. 6.29 is the absolute location component the second term has the form of the double difference described by Eq. 6.28, and the last term represents the distance from two planes (oriented vertically and horizontally) that describe the reference line of events. The procedure is iterative and the weighting factors (w , w , w ) control the influence of each term on the system of equations and are recalculated for each iteration. The arrival-time difFerences between all pairs of events are used to obtain hybrid locations by minimizing the weighted sum of squares of all arrival-time difFerences. Minimization is done using the standard Gauss-Newton method (Press et al. 1990). 

In the location procedure, the crack location y is determined from the arrival time differences ti between the observation Xi and Xi+i, solving equations. 

From the arrival time differences, AE somces are located one-dimensionally in Fig. 10.7 (Hearn Shield 1997), two-dimensionally, and three-dimensionally in Fig. 10.8 (Ohtsu 1995). Thus, identification of crack locations and classification of failure mode are readily performed. 

Thus, for typical values of average P velocities, 8-10 times the S - P arrival-time difference gives a reasonable estimate of the epicentral distance from the station. Figure 1 shows that if there are several stations, the intersection of the circles drawn around the stadmis with the corresponding radius of the epicentral distance will define the most likely position of the epicenter. Note that because the velocity model is never perfect and the arrival times suffer from measurement errors, the circles do not intersect in a point The area of the intersection is an indication of epicenter uncertainty. One of the major limitations of the method is that it gives httle constraint on the source depth. Furthermore, measurement error... 

As m increases, At becomes progressively smaller (compare the difference between the square roots of 1 and 2 (= 0.4) with the difference between 100 and 101 (= 0.05). Thus, the difference in arrival times of ions arriving at the detector become increasingly smaller and more difficult to differentiate as mass increases. This inherent problem is a severe restriction even without the second difficulty, which is that not all ions of any one given m/z value reach the same velocity after acceleration nor are they all formed at exactly the same point in the ion source. Therefore, even for any one m/z value, ions at each m/z reach the detector over an interval of time instead of all at one time. Clearly, where separation of flight times is very short, as with TOF instruments, the spread for individual ion m/z values means there will be overlap in arrival times between ions of closely similar m/z values. This effect (Figure 26.2) decreases available (theoretical) resolution, but it can be ameliorated by modifying the instrument to include a reflectron. 

The mass spectrum gives the abundances of ions for different times of arrival at the detector. Since the times are proportional to the square root of the m/z values, it is simple to convert the arrival times into m/z values. 

Although energy resolution is rarely employed in positron camera systems, scatter is not normally a problem. This is because of the very short time window within which two photons must arrive in order to be counted. At low decay rates, the incidence of accidental events is very low, rising only slightly for those that occur as the result of scatter. Some systems employ time-of-flight measurements of the time difference between the arrival of the two photons to obtain additional information about the location of an annihilation along the line. This has been used to improve resolution and statistical accuracy. Resolution is in the range of 3—4 mm and is less dependent on position than is SPECT (16). 

Arrival time gauges alone can lead to equation-of-state data in other ways, as well, but they are most often used in conjunction with other gauges to be described later. Three different arrival time gauges are discussed below. 

The response of the overall structure may be determined by the same techniques described above. The difference between directly loaded elements and supporting elements is the force amplitude and pulse shape of the applied loading. The loading on the overall stmctural system is determined from the reaction force time histories from directly loaded elements. Note that the loads on supporting members, frames, or shear walls, in some cases, may comprise reaction forces from pressures acting on the front and back faces of the structure simultaneously, taking into account the different arrival times of the blast wave. 

D Position Sensitive Detectors. Position sensitivity is accomplished by a so-called delay line. For every pulse11 arriving at the wire the time is measured that it needs to travel to each of the two ends of the wire. Thus the position of the incident photon along the wire can be computed from the time difference, i.e., the delay. Bent high-resolution ID position sensitive detectors (cf. Fig. 4.14) are advantageously used in laboratory equipment for the recording of WAXS curves. 

The output from the TAC is an analog signal that is proportional to the time difference between the start and stop pulses. The next step consists of digitizing the TAC output and storing the event in a multichannel analyzer (MCA). After repeating this process many times, a histogram of the arrival times of photons is accumulated in the memory of the MCA. In fluorescence lifetime spectroscopy the histogram usually contains 512-2048 channels... 

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