Multiple Source Model Research Articles

Multiple-source models for electron beams of a medical linear accelerator using BEAMDP computer code

AimThe aim of this work was to develop multiple-source models for electron beams of the NEPTUN 10PC medical linear accelerator using the BEAMDP computer code. BackgroundOne of the most accurate techniques of radiotherapy dose calculation is the Monte Carlo (MC) simulation of radiation transport, which requires detailed information of the beam in the form of a phase-space file. The computing time required to simulate the beam data and obtain phase-space files from a clinical accelerator is significant. Calculation of dose distributions using multiple-source models is an alternative method to phase-space data as direct input to the dose calculation system. Materials and methodsMonte Carlo simulation of accelerator head was done in which a record was kept of the particle phase-space regarding the details of the particle history. Multiple-source models were built from the phase-space files of Monte Carlo simulations. These simplified beam models were used to generate Monte Carlo dose calculations and to compare those calculations with phase-space data for electron beams. ResultsComparison of the measured and calculated dose distributions using the phase-space files and multiple-source models for three electron beam energies showed that the measured and calculated values match well each other throughout the curves. ConclusionIt was found that dose distributions calculated using both the multiple-source models and the phase-space data agree within 1.3%, demonstrating that the models can be used for dosimetry research purposes and dose calculations in radiotherapy.

Simulation study of a magnetocardiogram based on a virtual heart model: effect of a cardiac equivalent source and a volume conductor**Project supported by the State Key Development Program for Basic Research of China (Grant Nos. 2007CB512100 and 2006CB601007), the National Natural Science Foundation of China (Grant No. 10674006), the National High Technology Research and Development Program of China (Grant No.

In this paper, we present a magnetocardiogram (MCG) simulation study using the boundary element method (BEM) and based on the virtual heart model and the realistic human volume conductor model. The different contributions of cardiac equivalent source models and volume conductor models to the MCG are deeply and comprehensively investigated. The single dipole source model, the multiple dipoles source model and the equivalent double layer (EDL) source model are analysed and compared with the cardiac equivalent source models. Meanwhile, the effect of the volume conductor model on the MCG combined with these cardiac equivalent sources is investigated. The simulation results demonstrate that the cardiac electrophysiological information will be partly missed when only the single dipole source is taken, while the EDL source is a good option for MCG simulation and the effect of the volume conductor is smallest for the EDL source. Therefore, the EDL source is suitable for the study of MCG forward and inverse problems, and more attention should be paid to it in future MCG studies.

Simulation of a 6 MV Elekta Precise Linac photon beam using GATE/GEANT4

The GEANT4-based GATE Monte Carlo (MC) platform was initially focused on PET and SPECT simulations. The new release v6.0 (February 2010) proposes new tools dedicated for radiation therapy simulations. In this work, we investigated some part of this extension and proposed a general methodology for Linac simulations. Details of the modeling of a 6 MV photon beam delivered by an Elekta Precise Linac, with radiation fields ranging from 5 × 5 to 30 × 30 cm2 at the isocenter are presented. Comparisons were performed with measurements in water. The simulations were performed in two stages: first, the patient-independent part was simulated and a phase space (PhS) was built above the secondary collimator. Then, a multiple source model (MSM) derived from the PhS was proposed to simulate the photon fluence interacting with the patient-dependent part. The selective bremsstrahlung splitting (SBS) variance reduction technique proposed in GATE was used in order to speed up the accelerator head simulation. Further investigations showed that the SBS can be safely used without biasing the simulations. Additional comparisons with full simulations performed on the EGEE grid, in a single stage from the electron source to the water phantom, allowed the evaluation of the MSM. The proposed MSM allowed for calculating depth dose and transverse profiles in 48 hours on a single 2.8 GHz CPU, with a statistical uncertainty of 0.8% for a 10 × 10 cm2 radiation field, using voxels of 5 × 5 × 5 mm3. Good agreement between simulations and measurements in water was observed, with dose differences of about 1% and 2% for depth doses and dose profiles, respectively. Additional gamma index comparisons were performed; more than 90% of the points for all simulations passed the 3%/3 mm gamma criterion. To our knowledge, this feasibility study is the first one illustrating the potential of GATE for external radiotherapy applications.

A survey of computational methods and error rate estimation procedures for peptide and protein identification in shotgun proteomics

This manuscript provides a comprehensive review of the peptide and protein identification process using tandem mass spectrometry (MS/MS) data generated in shotgun proteomic experiments. The commonly used methods for assigning peptide sequences to MS/MS spectra are critically discussed and compared, from basic strategies to advanced multi-stage approaches. A particular attention is paid to the problem of false-positive identifications. Existing statistical approaches for assessing the significance of peptide to spectrum matches are surveyed, ranging from single-spectrum approaches such as expectation values to global error rate estimation procedures such as false discovery rates and posterior probabilities. The importance of using auxiliary discriminant information (mass accuracy, peptide separation coordinates, digestion properties, and etc.) is discussed, and advanced computational approaches for joint modeling of multiple sources of information are presented. This review also includes a detailed analysis of the issues affecting the interpretation of data at the protein level, including the amplification of error rates when going from peptide to protein level, and the ambiguities in inferring the identifies of sample proteins in the presence of shared peptides. Commonly used methods for computing protein-level confidence scores are discussed in detail. The review concludes with a discussion of several outstanding computational issues.

Central magnetic anomalies of Nectarian-aged lunar impact basins: Probable evidence for an early core dynamo

A re-examination of all available low-altitude LP magnetometer data confirms that magnetic anomalies are present in at least four Nectarian-aged lunar basins: Moscoviense, Mendel–Rydberg, Humboldtianum, and Crisium. In three of the four cases, a single main anomaly is present near the basin center while, in the case of Crisium, anomalies are distributed in a semi-circular arc about the basin center. These distributions, together with a lack of other anomalies near the basins, indicate that the sources of the anomalies are genetically associated with the respective basin-forming events. These central basin anomalies are difficult to attribute to shock remanent magnetization of a shocked central uplift and most probably imply thermoremanent magnetization of impact melt rocks in a steady magnetizing field. Iterative forward modeling of the single strongest and most isolated anomaly, the northern Crisium anomaly, yields a paleomagnetic pole position at 81° ± 19°N, 143° ± 31°E, not far from the present rotational pole. Assuming no significant true polar wander since the Crisium impact, this position is consistent with that expected for a core dynamo magnetizing field. Further iterative forward modeling demonstrates that the remaining Crisium anomalies can be approximately simulated assuming a multiple source model with a single magnetization direction equal to that inferred for the northernmost anomaly. This result is most consistent with a steady, large-scale magnetizing field. The inferred mean magnetization intensity within the strongest basin sources is ∼1 A/m assuming a 1-km thickness for the source layer. Future low-altitude orbital and surface magnetometer measurements will more strongly constrain the depth and/or thicknesses of the sources.

Regional provenance study of Eocene clastic sedimentary rocks within the South America–Caribbean plate boundary zone using detrital zircon geochronology

Previous on- and offshore studies have postulated that the Caribbean plate has translated hundreds of kilometers eastward during the Cenozoic along strike-slip and oblique thrust faults bounding the northern margin of the continental South America plate. Two previously proposed tectonic-sedimentary models to explain the complex linkages between plate motions and sedimentation within the broad plate boundary zone include: 1) eastward bulldozing by the Caribbean plate of a single, large point source, thick Eocene proto-Maracaibo deltaic system of northwestern South America, over 1000 km to the east and incorporation of these continentally derived sediments into the ∼ 12-km-thick Barbados accretionary prism along the leading edge of the Caribbean plate; and 2) eastward bulldozing by less than 300 km of smaller point and line sources of Eocene and younger clastic sediments derived from erosion of the Guyana shield located in north-central and northeastern South America. We test both models by sampling eight Eocene localities that span a 1200-km-length of the plate boundary zone from the proto-Maracaibo delta in western Venezuela to Barbados Island in the subaerial part of the large accretionary prism bounding the eastern margin of the Caribbean plate. Ages of 972 single grains from samples at these eight localities support the multiple-source model, in which the Barbados prism was partly constructed from the bulldozing and incorporation of smaller point and line sources derived from older-than 1500 Ma crustal provinces of the Precambrian Guyana shield in central and northeastern South America. Eocene clastic sediments of the proto-Maracaibo delta derived from Paleozoic and Precambrian crustal provinces in northwestern South America are distinct in their ranges of detrital zircon ages from the ranges of the Guyana shield sources to the east.

A Convenient Multiple Source Model for VARIAN 2300C 6 MV-X Beam Based on Monte Carlo Simulated Linac

Photon external radiotherapy of cancer takes advantage of the physical interaction of the photon and the secondary electron with biological tissue to kill cancer cells. The current linac is important equipment for producing an X-ray. The Monte Carlo method has been demonstrated to be the most accurate method for radiotherapy issues such as dose calculation and plan verification. However, its application in the clinic requires detailed information on the beam characteristics. A large quantity of the consumptive time for multiple simulation phases, such as linac treatment head simulation, beam trimmer module simulation, and patient/phantom simulation, and storage for the phase-space file (PSF), which records the information of the transported particle, are two knotty issues also. Therefore, a set of simple and convenient multiple source models (MSMs) including five subsources for regular fields from 3 × 3 cm to 30 × 30 cm was built, which is based on a VARIAN 2300C 6 MV-X beam simulated by the Monte Carlo code BEAMnrc and produced by BEAMnrc’s beam characteristics analysis utility BEAMDP (BEAM Data Processor). This MSM reduced the three simulation phases to one to effectively decrease the consumptive time. The storage issue about the PSF was also solved for MSM’s small volume. The dose distribution of the five-source model in a homogeneous phantom was compared with that of the full linac simulation and measurement data to verify reliability. The characteristics of the subsources were analyzed to present their feature. This work provided the base for implementing the Monte Carlo algorithm into the Accurate Radiotherapy System.

Using stable isotopes and a multiple-source mixing model to evaluate fish dietary niches in a mesotrophic lake

Christensen, D.R. and B.C. Moore. 2009. Using stable isotopes and a multiple-source mixing model to evaluate fish dietary niches in a mesotrophic lake. Lake Reserv. Manage. 25:167–175. We used stable isotope analysis (SIA) of δ13C and δ15N and a multiple-source mixing model to evaluate dietary niches within the Twin Lakes, Washington, fish community to identify potential for exploitative competition, resource partitioning, and predation. The SIA revealed distinct spatial feeding niches; pelagic species were δ13C depleted, while littoral organisms were δ13C enriched. Trophic feeding niches were identified from δ15N enrichment with each successive trophic level. We found δ15N progression with increasing largemouth bass size, suggesting ontogenetic diet variability. Model results suggested that the smaller bass (i.e., ⩽299 mm length) fed principally on golden shiner, crayfish, and macroinvertebrates while larger bass (⩾300 mm) primarily consumed brook trout and golden shiner. Isotopic signatures for golden shiner were intermediary, indicating both pelagic and littoral feeding sources, including phantom midges (nocturnal and pelagic) and damselflies (littoral) as principal diet sources, suggesting possible horizontal diel migration in golden shiner. Pelagic zooplankton was indicated as the most important food source for rainbow trout. Food resources appeared to be partitioned among the Twin Lakes fish community, possibly limiting competitive interactions. Piscivory in largemouth bass was focused on golden shiner and brook trout, suggesting possible top-down regulation of lower trophic levels. Stable isotope analysis and multiple-source mixing models are useful tools that can improve lake and fishery management decisions by providing data on food web dynamics such as competition, resource partitioning, and predation in lakes.

A planar circular detector based on multiple point chemi- or bio-luminescent source within a coaxial cylindrical reactor

An analytical method was proposed for calculating radiative fluxes incident on a planar circular detector from a volume multiple point chemi- or bio-luminescent source inside a coaxial cylindrical reactor. The method was designed for a cylindrical reactor when the surface reflections were neglected and when chemi- or bio-luminescence reaches a detector embedded in the same homogeneous optical medium as the point emitters of the volume multiple point source model. The radiative fluxes from arbitrarily distributed point emitters were expressed by one generalized quadruple-integral formula. Then some double- and single-integral formulas were obtained for calculating radiative fluxes from identically radiating point emitters uniformly distributed within the reactor. Selected results were computed and illustrated graphically. The obtained formulas are suitable for optimizing and/or calibrating the considered source-detectors systems (optical radiometers or luminometers) and determining radiative fluxes generated by chemical, biological, and physical processes leading to chemi-, bio-, radio-, and sono-luminescence for example.

A Study of Complex Substructures in a Foothill Belt of Northwestern Taiwan Using Two-Dimensional Gravity Multiple-Source Model Inversion

The goal of this paper is to improve the capability of gravity inversion assessment of complex structures using a multiple-source model as indicated by a study of a foothill belt of northwestern Taiwan. In this study, a gravity inversion computer program is applied based on research developed by Tsai, which contains a Marquardt inversion algorithm for mathematical calculations and incorporates constraints on geological parameters. The computed and modified geological parameters are transformed into coordinates. The response of a proper geological model is calculated using the Talwani technique. The method is applied to a field example in a foothills belt of Taiwan that possesses complex subsurface structures. The density profile from 2D gravity data, obtained using our inversion computer program, reveals a good correlation with the geological model obtained from seismic, borehole, and geologic data. Furthermore, potential hydrocarbon traps associated with some of the interpreted geological structures (where no seismic data are available) in the eastern and western seismic sections are being evaluated and assessed for possible future development. This profile highlights features that are important to a good understanding of an area with complex subsurface structures. It also helps to define subsurface geology and assess potential hydrocarbon traps. This

Fault Diagnosis Method Based on Acoustic Holography

Fault diagnosis method based on vibration signals has limits in certain situations. However, machine noise contains abundant condition information about machines. It possesses the advantage of non-contacting test. It can be used for fault diagnosis as a substitution of vibration signals. Traditional fault diagnosis methods based on noise signals are mainly on the basis of spectrum analysis. They cannot provide the location and the strength of sound sources. So they can only be used in some simple conditions. A fault diagnosis method based on acoustic holography is presented. A microphone array composed of a few microphones is used to acquire sound field. And the wave superposition method is adopted for sound field reconstruction. The sound field around a machine can be easily visualized by using such a method. Once the exterior sound field around the machine is reconstructed, the information extracted from the holography can be used for fault diagnosis. A number of templates of normal condition and fault condition can be made from the holography. A certain condition of the machine can be confirmed by comparison of it with these templates. Then the faults of the machine can be found. Numerical simulations are performed on the basis of a multiple pulse-ball sound source model, and experiments are also done with two sound boxes in an anechoic chamber. Both the simulations and the experiments have accurately identified the changes of the sound field radiated from the radiator, and have found out the faults. It shows that the method is validated and feasible, which lays a foundation for its on-site applications.

A 3D pencil-beam-based superposition algorithm for photon dose calculation in heterogeneous media

In this work, a novel three-dimensional superposition algorithm for photon dose calculation is presented. The dose calculation is performed as a superposition of pencil beams, which are modified based on tissue electron densities. The pencil beams have been derived from Monte Carlo simulations, and are separated into lateral and depth-directed components. The lateral component is modeled using exponential functions, which allows accurate modeling of lateral scatter in heterogeneous tissues. The depth-directed component represents the total energy deposited on each plane, which is spread out using the lateral scatter functions. Finally, convolution in the depth direction is applied to account for tissue interface effects. The method can be used with the previously introduced multiple-source model for clinical settings. The method was compared against Monte Carlo simulations in several phantoms including lung- and bone-type heterogeneities. Comparisons were made for several field sizes for 6 and 18 MV energies. The deviations were generally within (2%, 2 mm) of the field central axis dmax. Significantly larger deviations (up to 8%) were found only for the smallest field in the lung slab phantom for 18 MV. The presented method was found to be accurate in a wide range of conditions making it suitable for clinical planning purposes.

Temporal Dynamics of Adaptation to Natural Sounds in the Human Auditory Cortex

We aimed at testing the cortical representation of complex natural sounds within auditory cortex by conducting 2 human magnetoencephalography experiments. To this end, we employed an adaptation paradigm and presented subjects with pairs of complex stimuli, namely, animal vocalizations and spectrally matched noise. In Experiment 1, we presented stimulus pairs of same or different animal vocalizations and same or different noise. Our results suggest a 2-step process of adaptation effects: first, we observed a general item-unspecific reduction of the N1m peak amplitude at 100 ms, followed by an item-specific amplitude reduction of the P2m component at 200 ms after stimulus onset for both animal vocalizations and noise. Multiple dipole source modeling revealed the right lateral Heschl's gyrus and the bilateral superior temporal gyrus as sites of adaptation. In Experiment 2, we tested for cross-adaptation between animal vocalizations and spectrally matched noise sounds, by presenting pairs of an animal vocalization and its corresponding or a different noise sound. We observed cross-adaptation effects for the P2m component within bilateral superior temporal gyrus. Thus, our results suggest selectivity of the evoked magnetic field at 200 ms after stimulus onset in nonprimary auditory cortex for the spectral fine structure of complex sounds rather than their temporal dynamics.

SU‐FF‐T‐439: Using Electron Beam Modifiers in the DPM Monte Carlo Code for Electron Beam Treatment Planning

Purpose: To investigate the feasibility of modeling patient‐specific beam modifiers for electron beams using the DPM MC code. Methods and material: We investigate the applicability of modeling a beam modifier ‘applicator’(vs. a multiple source model or beam fitting approach) inside the DPM code for electron beam dose calculation. DPM is only used for in‐phantom calculations; however, we have included beam modifiers such as Jaws, MLCs and now applicators within the code to improve its clinical applicability. Varian 21EX (Type III) was modeled for beam energies (6, 9 and 12 MeV) using the BEAMnrc MC code. The patient‐independent components were simulated once and the phase space (PS) is stored just below the ion chamber. As a first approximation, a preliminary model of the applicator blocks all the particles through the applicators but allows those in the open beam region. Verification of the beam modifier model with diode measurements and full PS simulations was performed using percent depth doses (PDDs) and profiles for various energies for the standard 15×15 cm2 cutout, and for square and rectangular cutouts from 4×4 to 25×25 cm2 in a homogeneous geometry. Results: PDD calculations with DPM beam modifiers showed agreement within 2% with measurements and full PS simulation for the 6MeV beam. The 9 and 12 MeV PDD calculations showed discrepancies up to 4% in the surface buildup region, and a slightly larger difference in the tail. A full 3‐d simulation currently takes roughly 10mins on 8 processors to achieve a relative uncertainty of less than 1% in voxels > dmax/2 using a 2×2×2 mm3 voxel size. Conclusions: Preliminary investigation of dose calculations with beam modifiers in DPM MC code shows good agreement with measurement. Future work will focus on modeling 16 and 20 MeV beams and their verification in a homogeneous and heterogeneous medium.

SU-FF-T-227: Extra-Focal Analytical Source Model for the Radiation Output From a Linear Accelerator

Purpose: To describe in detail the recently improved extra-focal photon source component of an accurate analytical source model for the radiation output from a linear accelerator. Method and Materials: In the Anisotropic Analytical Algorithm used in the Eclipse™ Integrated Treatment Planning System (Varian Medical Systems Inc.) the radiation output from a linear accelerator is modeled using a multiple-source model with separate sub-sources for primary photon radiation, extra-focal photon radiation and electron contamination. Closely related to this, analytical models for accessories such as hard wedges and dynamic wedges are included. We describe in detail the extra-focal photon source component. A recent improvement to the extra-focal source leading to enhanced accuracy in cases of small MLC apertures that are common during IMRT treatments is discussed. Another related improvement significantly improves the modeling of the Varian Enhanced Dynamic Wedge (EDW). Results: The new extra-focal source model significantly improves the modeling of small MLC apertures that occur during dynamic IMRT treatments. In our test case to water phantom the maximum error (disregarding the buildup region) in depth dose curves has been reduced to 1% of dose maximum. Modeling of the Varian Enhanced Dynamic Wedge has been significantly improved also: in our example dataset the worst case deviation of local value at CAX has been reduced by more than 50%. Conclusion: The analytical source and accessory models used in the Anisotropic Analytical Algorithm in combination with a scheme to optimize the free parameters of the model has been already shown to be clinically acceptable. In this work we discuss two improvements related to the extra-focal source model which further improve its accuracy. Conflict of Interest: The authors are employed by Varian Medical Systems Finland Oy.

Determination of parameters for a multiple-source model of megavoltage photon beams using optimization methods

Accurate modelling of the radiation output of a medical linear accelerator is important for radiotherapy treatment planning. The major challenge is the adjustment of the model to a specific treatment unit. One approach is to use a multiple-source model containing a set of physical parameters. In this work, the parameters were derived from standard beam data measurements using optimization methods. The source model used includes sub-sources for bremsstrahlung radiation from the target, extra-focal photon radiation and electron contamination. The cost function includes a gamma error measure between measurements and current dose calculations. The procedure was applied to six beam data sets (6 MV to 23 MV) measured with accelerators from three vendors, but the results focus primarily on Varian accelerators. The obtained average gamma error (1%, 1 mm) between dose calculations and measurements used in optimization was smaller than 0.7 for each studied treatment beam and field size, and a minimum of 83% of measurement points passed the γ < 1 criterion. For experiments made at different SSDs and for asymmetric fields, the average gamma errors were smaller than 1.1. For irregularly shaped MLC apertures, the differences in point doses were smaller than 1.0%. This work demonstrates that the source model parameters can be automatically derived from simple measurements using optimization methods. The developed procedure is applicable to a wide range of accelerators, and has an acceptable accuracy and processing time.

Testing of the analytical anisotropic algorithm for photon dose calculation

The analytical anisotropic algorithm (AAA) was implemented in the Eclipse (Varian Medical Systems) treatment planning system to replace the single pencil beam (SPB) algorithm for the calculation of dose distributions for photon beams. AAA was developed to improve the dose calculation accuracy, especially in heterogeneous media. The total dose deposition is calculated as the superposition of the dose deposited by two photon sources (primary and secondary) and by an electron contamination source. The photon dose is calculated as a three-dimensional convolution of Monte-Carlo precalculated scatter kernels, scaled according to the electron density matrix. For the configuration of AAA, an optimization algorithm determines the parameters characterizing the multiple source model by optimizing the agreement between the calculated and measured depth dose curves and profiles for the basic beam data. We have combined the acceptance tests obtained in three different departments for 6, 15, and 18 MV photon beams. The accuracy of AAA was tested for different field sizes (symmetric and asymmetric) for open fields, wedged fields, and static and dynamic multileaf collimation fields. Depth dose behavior at different source-to-phantom distances was investigated. Measurements were performed on homogeneous, water equivalent phantoms, on simple phantoms containing cork inhomogeneities, and on the thorax of an anthropomorphic phantom. Comparisons were made among measurements, AAA, and SPB calculations. The optimization procedure for the configuration of the algorithm was successful in reproducing the basic beam data with an overall accuracy of 3%, 1 mm in the build-up region, and 1%, 1 mm elsewhere. Testing of the algorithm in more clinical setups showed comparable results for depth dose curves, profiles, and monitor units of symmetric open and wedged beams below dmax. The electron contamination model was found to be suboptimal to model the dose around dmax, especially for physical wedges at smaller source to phantom distances. For the asymmetric field verification, absolute dose difference of up to 4% were observed for the most extreme asymmetries. Compared to the SPB, the penumbra modeling is considerably improved (1%, 1 mm). At the interface between solid water and cork, profiles show a better agreement with AAA. Depth dose curves in the cork are substantially better with AAA than with SPB. Improvements are more pronounced for 18 MV than for 6 MV. Point dose measurements in the thoracic phantom are mostly within 5%. In general, we can conclude that, compared to SPB, AAA improves the accuracy of dose calculations. Particular progress was made with respect to the penumbra and low dose regions. In heterogeneous materials, improvements are substantial and more pronounced for high (18 MV) than for low (6 MV) energies.

A mixture‐model based algorithm for real‐time terrain estimation

AbstractA real‐time terrain mapping and estimation algorithm using Gaussian sum elevation densities to model terrain variations in a planar gridded elevation model is presented. A formal probabilistic analysis of each individual sensor measurement allows the modeling of multiple sources of error in a rigorous manner. Measurements are associated to multiple locations in the elevation model using a Gaussian sum conditional density to account for uncertainty in measured elevation as well as uncertainty in the in‐plane location of the measurement. The approach is constructed such that terrain estimates and estimation error statistics can be constructed in real‐time without maintaining a history of sensor measurements. The algorithm is validated experimentally on the 2005 Cornell University DARPA Grand Challenge ground vehicle, demonstrating accurate and computationally feasible elevation estimates on dense terrain models, as well as estimates of the errors in the terrain model. © 2006 Wiley Periodicals, Inc.

Spatial correlation of aftershock locations and on‐fault main shock properties

We quantify the correlation between spatial patterns of aftershock hypocenter locations and the distribution of coseismic slip and stress drop on a main shock fault plane using two nonstandard statistical tests. Test T1evaluates if aftershock hypocenters are located in low‐slip regions (hypothesis H1), test T2evaluates if aftershock hypocenters occur in regions of increased shear stress (hypothesis H2). In the tests, we seek to reject the null hypotheses H0: Aftershock hypocenters are not correlated with (1) low‐slip regions or (2) regions of increased shear stress, respectively. We tested the hypotheses on four strike‐slip events for which multiple earthquake catalogs and multiple finite fault source models of varying accuracy exist. Because we want to retain earthquake clustering as the fundamental feature of aftershock seismicity, we generate slip distributions using a random spatial field model and derive the stress drop distributions instead of generating seismicity catalogs. We account for uncertainties in the aftershock locations by simulating them within their location error bounds. Our findings imply that aftershocks are preferentially located in regions of low‐slip (u≤umax) and of increased shear stress (Δσ &lt; 0). In particular, the correlation is more significant for relocated than for general network aftershock catalogs. However, the results show that stress drop patterns provide less information content on aftershock locations. This implies that static shear stress change of the main shock may not be the governing process for aftershock genesis.

The lodide/lodate Actinometer in UV Disinfection: Determination of the Fluence Rate Distribution in UV Reactors

Thirty-seven Suprasil quartz spheres, each approximately 1 cm in diameter and containing an iodide-iodate actinometric solution, were attached to a metal rack and inserted into a bench-scale UV reactor filled with water. The spheres were located at various distances and heights around a 12.4 W low-pressure Hg lamp housed inside a 3.2 cm-radius quartz sleeve in the middle of an annular batch reactor. UV light exposure at 254 nm was performed with the percent transmittance of the water present in the reactor at either 73% or 100% defined over a 1 cm path length. The spheres were simultaneously exposed to the UV light for a given period of time, after which the solutions were removed from the spheres and the yield of triiodide determined from the increase in absorbance at 352 nm. The resulting fluence rate at each site was then calculated on basis of the yield of triiodide. These results were compared with the predictions of a mathematical model based on the multiple point source summation approximation, including reflection and refraction at the air-quartz-water interface. Initially, the agreement was not satisfactory, especially in regions at an oblique angle to the lamp. The model was modified from a multiple point source model to a multiple cylindrical segment model by incorporating a cosine factor. The agreement between the new model and the experimental data was excellent and these experiments provide a strong validation of the model, even under conditions in which the fluence rate varied by >1000-fold between extreme sites in the reactor.