Path Length Correction Research Articles

A Pathlength Correction Method for Near-Infrared Spectroscopy

A method for correction of pathlength effects in near-infrared (NIR) spectra is presented. This method, called Pathlength Correction with Chemical Modeling (PLC-MC), requires the use of standards in which the chemistry varies but the pathlength remains constant. Principal Components Analysis (PCA) is used to model the chemical variations in the spectra of the standards. The PCA model can then be used to estimate the pathlength of a future sample from the spectrum of the sample. Theoretical and experimental comparisons of the PLC-MC correction method with the Multiplicative Scatter Correction (MSC) method indicate that the PLC-MC method is more accurate than the MSC method if spectral variability from chemical variations is large.

Presta: The parameter reduced electron-step transport algorithm for electron monte carlo transport

A new electron transport algorithm for use with electron Monte Carlo transport codes is presented. Its components are: a path-length correction (PLC) algorithm which is based on the multiple scattering theory of Molière and which takes into account the differences between the straight path length and the total curved path length for each electron step; a lateral correlation algorithm (LCA) which takes into account lateral transport; and a boundary crossing algorithm (BCA) which ensures that electrons are transported accurately in the vicinity of interfaces. The algorithm has been implemented in the EGS4 code system and a variety of tests validating the algorithms are presented. In its standard configuration, use of this algorithm will allow the inexperienced user to obtain reliable results from the EGS Monte Carlo code without having to do a detailed study of the electron transport parameters. In many situations, substantial savings in computing time may be realized in comparison to the present EGS algorithm. The developments described in this report may be adapted to other electron transport codes where many of the same conclusions may be drawn.

Elimination of near-source ellipticity corrections to body-wave travel times by use of equidistant latitudes

AbstractThe use of equidistant latitudes has been proposed by the author to eliminate discrepancies between angular and kilometric epicentral distances. This is done in combination with a path-length correction which depends on the inclination of the great ellipse containing the epicenter-receiver path. If there were a one-to-one correspondence between source-receiver surface arc length (in kilometers) and, say, P-wave travel time (for constant focal depth) for a standard spheroidal Earth, the ellipticity (time) correction could then be replaced by the distance correction described. However, one would only expect this to be approximately valid for small epicentral distances Δ.In this paper, the travel-time corrections made by using equidistant latitudes (and the great-ellipse correction) are compared with the “true” ellipticity corrections due to Dziewonski and Gilbert. It is seen that the present equidistant-latitude method gives P-wave correction values that, for example, are always within 0.05 sec of the “true” values for Δ ≦ 14° and normal focal depth (h ≦ 40 km). For large Δ(⪞ 45°) and/or great focal depth (h⪞ 475 km), these values may differ by more than 0.2 sec. This equidistant-latitude method of correcting body-wave travel times is thus not recommended for routine use, but it could be used to advantage in special studies involving smaller Δ and h.

On the determination of source-receiver distances using a new equidistant latitude

Summary. In teleseismic and crustal seismic studies, source–receiver distances are commonly expressed in degrees rather than kilometres. The earlier use of geographic latitudes in determining a meridional distance led to variations in the number of kilometres per degree of up to 1.0 per cent (1.1 km deg-1) and discrepancies up to 64.2 km in epicentral distance at Δ= 90°. The present standard practice of using geocentric latitudes reduces this maximum variation by a factor of 3 to 0.34 per cent (0.37 km deg-1) and maximum discrepancies to 21.4 km at Δ= 90°. A third, arbitrarily defined latitude is here proposed which reduces this maximum variation by a further factor of 800 to 0.00042 per cent (0.00047 km deg-1) and reduces the maximum discrepancy by a further factor of 1600 to 0.0135 km (or 13.5 m) at Δ= 45° (zero at Δ= 90°). This equidistant latitude will be useful in certain geophysical applications where a consistent proportionality between angular distances, Δ, and arc lengths, u, is of prime importance. This could be the case at a high-latitude station observing many events, or for a single high-latitude event observed at many stations; in whichever case all source–receiver paths are close to meridional. An additional correction is presented which removes distance discrepancies between meridional and nonmeridional (in the worst case, equatorial) paths; this latter correction being equivalent to the conventional path-length correction for Earth-encircling urface waves (namely in the single-station method). Some areas of application, where the improved accuracy attainable by using equidistant latitudes might be significant, are suggested. In the determination of surface-wave velocities by the two-station method, the use of geocentric latitudes introduces relative errors of ∼ 10-3, Such errors could be significant with high-accuracy data; and for very long-period surface waves (τ? 200s) errors of this same order of magnitude are removed by the period dependent apparent-path-length correction. Combining this correction with equidistant latitudes would reduce relative errors to ∼ 10-5 or 10-6. In determining epicentral distances for local earthquakes (say Δ < 5°) the use of geocentric latitudes leads to a maximum discrepancy of 0.16 km within a single locality around 45° latitude, although the discrepancies among all geocentric 5° paths on the Earth can reach 1.9 km. By Richter's rectangular coordinate method, maximum discrepancies are of the same order as the geocentric ones within a single locality; moreover they remain at this level for any two such paths (Δ < 5°) on the Earth. With equidistant latitude, however, the maximum discrepancies are 4 × 10-4 km for a single locality around 22½° or 67½° latitude and 2 × 10-3km for the whole Earth.

Third sound on Hopg surface

Abstract We have made third sound velocity measurements via the time-of-flight technique for 4 He films adsorbed on the surface of a single leaf of highly oriented pyrolytic graphite between 1.0 and 1.3 K. Our results are in qualitative agreement with an earlier experiment involving third sound on Grafoil foam. As a function of film thickness, the third sound velocity shows oscillatory variation with a period roughly equal to one atomic layer. This novel effect is not seen with other substrates. The third sound velocity determined in this experiment suffers relatively little path-length correction. This is a condition not met in the foam experiment.

Third sound on HOPG preface

We have made third sound velocity measurements via the time-of-flight technique for 4 He films adsorbed on the surface of a single leaf of highly oriented pyrolytic graphite between 1.0 and 1.3 K. Our results are in qualitative agreement with an earlier experiment involving third sound on Grafoil foam. As a function of film thickness, the third sound velocity shows oscillatory variation with a period roughly equal to one atomic layer. This novel effect is not seen with other substrates. The third sound velocity determined in this experiment suffers relatively little path-length correction. This is a condition not met in the foam experiment.

Optimum frequencies of a passive microwave radiometer for tropospheric path-length correction

Radio-astronomical observations require accurate calibration of tropospheric path length. Such calibration can be achieved by microwave radiometers operating near the 22-GHz water vapor line. However, the performances of current passive microwave radiometers are meteorology-profile dependent. This is shown due mainly to incorrect frequency combinations and to saturation of brightness temperatures. By properly selecting an optimum frequency pair and removing the saturation effect, the dependency is alleviated and can be further adjusted by surface measurements alone. Hence, a universal calibration equation is applicable to all environmental conditions. Optimum frequency pairs are systematically searched. Simulation analysis indicates that calibration for the tropospheric water-vapor path-length error is better than 0.3 cm at zenith and better than 2 cm for an elevation angle as low as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10\deg</tex> .