Analysis Of Refraction Data Research Articles

Multivariate analysis of refractive state in eyes with keratoconus

ObjectiveTo demonstrate a multivariate method of analysis of the short-term variation of refractive state in keratoconus (KC) patients.Methods and analysisIn this observational study, 19 eyes with KC and 19 healthy...

Interexaminer reproducibility for subjective refractions for an ametropic participant

ObjectiveTo investigate interexaminer reproducibility of non-cycloplegic subjective refractions. Subjective refractions are frequently determined, and it is important to know whether differences in refractive state over time constitute meaningful, non-random change.Methods...

Seismic refraction data analysis using machine learning and numerical modeling for characterization of dam construction sites

Seismic refraction is a cost-effective tool to reveal subsurface compressional wave (P-wave) velocity. Inversion of traveltimes for estimating a realistic velocity model is a significant step in the processing of seismic refraction data. The results of the seismic data inversion are stochastic; thus, using prior information or complementary geophysical data can have a significant role in estimating the structural properties based on the observed data. Nevertheless, sufficient prior information or auxiliary data are not available in many geophysical sites. In such situations, developing advanced computational modeling is a vital step in providing primary information and improving the results. To this aim, a new inversion framework through hybrid committee artificial neural networks (CANNs) and the flower pollination (FP) optimization algorithm is introduced for inversion of refracted seismic traveltimes. Synthetic models generated by a forward-modeling approach are used to train the machine-learning model. Then, model parameters, such as the number of layers, thicknesses, and P-wave velocities, are predicted using a committee machine constructed based on several neural networks, which is achieved by averaging and stack generalization methods in which the latter method provides a better result. Then, the CANN results are used in the FP inversion algorithm to estimate the final model because it provides essential prior information on the number of layers and model parameters, which can be used in the FP searching algorithm. Our inversion procedure is tested on different synthetic data sets and applied at a dam site to determine the number of layers and their thicknesses. Our findings indicate a successful performance on synthetic and real data for automatic inversion of seismic refraction data.

Refrapy: A Python program for seismic refraction data analysis

The development and use of open-source software in geophysics over the last decade have grown considerably. However, there are few open-software alternatives for seismic methods and even fewer regarding seismic refraction data processing and inversion. We present Refrapy, an open-source package for seismic refraction data analysis written in Python, using some of the main libraries for scientific computing and geosciences. Divided into two main programs (Refrapick and Refrainv), it is possible to perform basic waveform processing, picking of first breaks, and inversion through time-terms analysis or traveltimes tomography, all with GUIs interaction. To evaluate and validate the products obtained using Refrapy, we analyzed sets of synthetic data and real field data. The calculated models recovered the geometry and velocities values of the actual synthetic models satisfactorily. The joint interpretation of the results obtained with both available inversion techniques permitted a more detailed interpretation. As for the analysis of real data, the results presented a compatible response compared to the model obtained by a well-established commercial software, satisfactorily representing the geological context interpreted initially. The software presented in this work is expected to contribute to the activities of researchers, practitioners, and students regarding the analysis of seismic refraction data as a free, open, and user-friendly alternative.

Detection of Cover Collapse Doline and Other Epikarst Features by Multiple Geophysical Techniques, Case Study of Tarimba Cave, Brazil

Reliable characterization of the karst system is essential for risk assessment where many associated hazards (e.g., cover-collapse dolines and groundwater pollution) can affect natural and built environments, threatening public safety. The use of multiple geophysical approaches may offer an improved way to investigate such cover-collapse sinkholes and aid in geohazard risk assessments. In this paper, covered karst, which has two types of shallow caves (vadose and fluvial) located in Tarimba (Goias, Brazil), was investigated using various geophysical methods to evaluate their efficiency in the delineation of the geometry of sediments filled sinkhole. The methods used for the investigation were Electrical Resistivity Tomography (ERT), Seismic Refraction Survey (SRS), Seismic Refraction Tomography (SRT) and the Very Low Frequency Electromagnetic (VLF-EM) method. The study developed several (2D) sections of the measured physical properties, including P-wave velocity and electrical resistivity, as well as the induced current (because of local bodies). For the analysis and processing of the data obtained from these methods, the following approaches were adopted: ERT inversion using a least-square scheme, Karous-Hjelt filter for VLF-EM data and time-distance curves and Vp cross-sections for the SRS. The refraction data analysis showed three-layered stratigraphy topsoil, claystone and carbonate bedrock, respectively. The findings obtained from ERT (three-layered stratigraphy and sediment-filled doline), as well as VLF-EM (fractured or filled caves as a positive anomaly), were found to be consistent with the actual field conditions. However, the SRS and SRT methods did not show the collapsed material and reached the limited the depth because of shorter profile lengths. The study provides a reasonable basis for the development of an integrated geophysical approach for site characterization of karst systems, particularly the perched tank and collapse doline.

High‐resolution reflection seismic imaging for the planning of a double‐train‐track tunnel in the city of Varberg, southwest Sweden

ABSTRACTA newly developed broadband digital‐based seismic landstreamer system was employed for the planning of a double‐train‐track tunnel in the city of Varberg, southwest Sweden. Twenty‐five seismic profiles, totalling more than 7.5 km of data, were acquired using a 2‐ to 4‐m receiver and source spacing. At places where it was not possible to move the streamer such as road crossings, wireless recorders connected to 28‐Hz geophones were used. In addition to the earlier refraction data analysis and first‐break traveltime tomographic modelling, reflection processing of the data was considered in this study, given the realisation of reflections in raw shot gathers and their good quality. Bedrock is strongly reflective in most cases but is not evident in the sections when it gets near the surface. Bedrock undulation is noticeable in most reflection sections, and at one occasion, strong diffraction is observed in the bedrock or near to it. The diffraction is originated, not known during the survey, from a 400‐m3 cylindrical (of about 3‐m‐height and 13‐m‐diameter) concrete‐made fire‐protection water tank situated in the bedrock and used in emergency situations. Reflection seismic data greatly complement the tomographic models and support deep bedrock where the excavation of the tunnel is planned in downtown Varberg. This interpretation implies different reinforcements and tunnel construction methods (e.g., roofed concrete) at this section of the tunnel. In addition, weakness zones associated with fracture systems are inferred from the reflection characteristics and in conjunction with the velocity models requiring verification by additional boreholes.

PQC: A novel approach for robust automatic near-surface analysis in low-relief geology

A novel approach, named pQC, was developed to automatically derive near-surface velocities and statics by applying surface-consistent analysis to refraction data, where the data consist of first-break (FB) traveltimes and early-arrival waveforms. This approach is facilitated by the introduction of a new sorting domain in which FB traveltimes and traces are organized in a multidimensional space consisting of a common-midpoint (CMP) location, offset, and azimuth, called the XYOA domain. The FB traveltime data sorted in this domain can be analyzed efficiently with statistical methods to obtain localized average depth domain velocity trends for calculation of long-wavelength statics. Short-wavelength (residual) refraction statics are then calculated based on the cross correlation of early-arrival waveforms in the XYOA gathers over multiple offset classes and inverted for surface-consistent source and receiver corrections. The application of the combined statics solution to the traces enhances the continuity and power of the stacked reflected events without the need to perform tomography. Surface-consistent analysis of refraction data in the XYOA domain is fully automatic, provides robust solutions for noisy data, and enhances subsequent reflection residual statics calculations. This method can also be exploited for quality-control analysis of FB picks and for automating, in an iterative procedure, the picking of large 3D seismic data sets. The method is demonstrated on a 3D land survey over complex geology where the novel refraction surface-consistent solution enhances the imaging results and employs a fraction of the time needed by a typical tomographic workflow.

Objective evaluation of refractive data and astigmatism: quantification and analysis

The aim of this study was to present methods to improve the analysis of refractive data. A comparison of methods is used to analyse refractive powers using individual powers and aggregate data. Equations are also developed for the representation of the average power of a lens or refractive data as a univariate measure, which includes spherical, coma, and/or other aberrations. The equations provide a precise representation of refractive power, which is useful for comparing individual and aggregate data. Average lens power in the principal meridian can be adequately computed as can the average lens power through orthogonal and oblique meridians, providing a good univariate representation of astigmatism and refractive power. Although these formulae are perhaps not as easy to use as, for example, the spherical equivalent, they are more precise and superior in principle involving fewer approximations and are not subject to systematic bias. These effects are of significance when dealing with high-powered lenses such as intraocular lenses or the cornea. They need to be taken into account particularly for calculations of intraocular lens power, toric intraocular lenses, and cornea refractive surgery, especially if outcomes are to be improved. Such issues are of particular importance when dealing with aggregate data and determining statistical significance of treatment effects.

An analysis of the first-arrival times picked on the DSS and wide-angle seismic section recorded in Italy since 1968

We performed an analysis of refraction data recorded in Italy since 1968 in the frame of the numerous deep seismic sounding and wide-angle reflection/refraction projects. The aims of this study are to construct a parametric database including the recording geometric information relative to each profile, the phase pickings and the results of some kinematic analyses performed on the data, and to define a reference 1D velocity model for the Italian territory from all the available refraction data. As concerns the first goal, for each seismic section we picked the P-wave first-arrival-times, evaluated the uncertainties of the arrival-times pickings and determined from each travel time-offset curve the 1D velocity model. The study was performed on 419 seismic sections. Picking was carried out manually by an algorithm which includes the computation of three picking functions and the picking- error estimation. For each of the travel time-offset curves a 1D velocity model has been calculated. Actually, the 1D velocity-depth functions were estimated in three different ways which assume: a constant velocitygradient model, a varying velocity-gradient model and a layered model. As regards the second objective of this work, a mean 1D velocity model for the Italian crust was defined and compared with those used for earthquake hypocentre locations and seismic tomographic studies by different institutions operating in the Italian area, to assess the significance of the model obtained. This model can be used in future works as input for a next joint tomographic inversion of active and passive seismic data.

Assessment and Statistics of Surgically Induced Astigmatism

The aim of the thesis was to develop methods for assessment of surgically induced astigmatism (SIA) in individual eyes, and in groups of eyes. The thesis is based on 12 peer-reviewed publications, published over a period of 16 years. In these publications older and contemporary literature was reviewed(1). A new method (the polar system) for analysis of SIA was developed. Multivariate statistical analysis of refractive data was described(2-4). Clinical validation studies were performed. The description of a cylinder surface with polar values and differential geometry was compared. The main results were: refractive data in the form of sphere, cylinder and axis may define an individual patient or data set, but are unsuited for mathematical and statistical analyses(1). The polar value system converts net astigmatisms to orthonormal components in dioptric space. A polar value is the difference in meridional power between two orthogonal meridians(5,6). Any pair of polar values, separated by an arch of 45 degrees, characterizes a net astigmatism completely(7). The two polar values represent the net curvital and net torsional power over the chosen meridian(8). The spherical component is described by the spherical equivalent power. Several clinical studies demonstrated the efficiency of multivariate statistical analysis of refractive data(4,9-11). Polar values and formal differential geometry describe astigmatic surfaces with similar concepts and mathematical functions(8). Other contemporary methods, such as Long's power matrix, Holladay's and Alpins' methods, Zernike(12) and Fourier analyses(8), are correlated to the polar value system. In conclusion, analysis of SIA should be performed with polar values or other contemporary component systems. The study was supported by Statens Sundhedsvidenskabeligt Forskningsråd, Cykelhandler P. Th. Rasmussen og Hustrus Mindelegat, Hotelejer Carl Larsen og Hustru Nicoline Larsens Mindelegat, Landsforeningen til Vaern om Synet, Forskningsinitiativet for Arhus Amt, Alcon Denmark, and Desirée and Niels Ydes Fond.

Reproducibility of sphero‐cylindrical prescriptions*

To investigate the reproducibility of the sphero-cylindrical prescriptions provided by 40 optometrists. Forty registered optometrists were randomly selected from the cities of Oxford and Westminster in the UK to perform a sphero-cylindrical refraction on an asymptomatic 29-year-old male subject. The 95% limits of reproducibility for each component of refraction were assessed and are presented together with scatterplots, distribution ellipsoids and polar profiles of dioptric power. The mean stigmatic (spherical equivalent) refraction for the right eye was -0.83 D (S.D. = 0.28 D) with 95% limits of agreement -1.38 and -0.28 D. The 95% reproducibility limits for stigmatic data [1.96(square root of 2) (S.D.)] was 0.78 D. The average inter-ocular difference in the stigmatic components of refraction was -0.044 D (S.D. = 0.20 D) but estimates ranged from -0.50 to +0.50 D. Mean ortho- and oblique antistigmatic refractions were -0.23 D (S.D. = 0.084 D) and -0.14 D (S.D. = 0.086 D) respectively. The findings of this paper suggest that refractions performed by multiple optometrists on a single eye will differ in their stigmatic component by over 0.78 D on average not more than once in 20 refractions. The reproducibility of refractions reported here, approximately twice as variable as those reported under repeatability conditions, has profound implications for the analysis of refractive data collected by multiple optometrists over the course of replication, longitudinal and epidemiological studies.

Analyzing refractive data

Purpose To provide a general approach to the analysis of refractive data that overcomes the shortcomings of traditional treatments and can be easily adapted to most spreadsheets. Setting Corneal Service, Royal Liverpool Hospital, Liverpool United Kingdom, and Optometric Science Group, Rand Afrikaans University, Auckland Park, South Africa. Method The basis of the analyses is the dioptric power matrix. Using a hypothetical sample of data on pre-event and post-event refractions, the calculation of the mean pre-event and post-event refractions and the effect of an event on the refractive outcome, for example the refractive surgical effect, are illustrated. The most important statistics, the mean and the variance–covariance of refractions, and the formal testing of hypotheses on the mean are provided. Results The method of analysis demonstrated how an event such as cataract surgery, occlusion treatment of amblyopia, or anisometropia can be evaluated in terms of refractive outcome. Hypothesis testing showed how the significance of this effect may be demonstrated. Conclusions This standardized method of analyzing and reporting refractive data enables a quantitative analysis and statistical hypothesis testing of the complete refractive data. This approach has generalized applicability in a range of commonly encountered contexts such as the refractive change after cataract and refractive surgery, corneal transplantation, and treatment for amblyopia or the significance of anisometropia. The method is relatively straightforward and can be adapted to most conventional spreadsheets.

Multivariate analysis of refractive data: Mathematics and statistics of spherocylinders

Purpose To develop methods for multivariate statistical analysis of spherocylinders and to use these methods to compare autorefraction and manifest subjective refraction in 50 healthy eyes. Setting Department of Ophthalmology, Århus University Hospital, Århus, Denmark. Methods A method was developed to transform a spherocylinder to a suitable format as a spherical equivalent power (SEP) and 2 polar values, separated by an arch of 45 degrees, a so-called power-vector format. The accuracy of autorefraction was defined as the difference between autorefraction and manifest refraction, using the described power vector. These entities were subjected to multivariate analysis using the Hotelling T 2 test. A method of graphic analysis was developed, using matrix algebra and computation of eigenvectors and eigenvalues. Results For individual data, the variation was considerably larger for the SEP than for the astigmatism. For aggregate data, univariate, bivariate, and trivariate statistical analysis did not demonstrate significant average differences between the 2 refraction methods. No refractive components and no combinations of refractive components displayed significant mean differences. Conclusions The study confirmed our clinical experience that the astigmatism derived from autorefraction is nearly identical to manifest refraction, while the sphere needs some adjustment. In groups of healthy eyes, autorefraction can be used as a substitute for manifest refraction. Statistical analysis of spherocylinders, including evaluation of refractive procedures, can be performed in an exact manner with multivariate statistics.

Variations in the crustal structure of the Lützow–Holm Bay region, East Antarctica using shear wave velocity

Crustal structure in the Lützow–Holm Bay region (LHB), East Antarctica, is studied by analyzing seismic waveforms derived from records in the vicinity of Syowa Station (SYO; 69.0°S, 39.6°E). One-dimensional crustal models for shear waves, in particular, are obtained in order to investigate crustal heterogeneity. Radial receiver functions developed from teleseismic P-waveforms of broadband seismographs at SYO in 1990–1993 are used in the time domain inversion. As the starting model in the receiver function inversion, a crustal attenuation model ( Q s) for shear waves from local earthquakes of telemetry networks in 1987–1989 is derived by shifting the lapse time of the coda part of S-waves. Lateral heterogeneity is investigated by analyzing several backazimuth groups; namely the 50°–100°, 120°–160°, 210°–250° and 300°–360° sectors are investigated. Velocity changes are recognized as a sharp Moho at 36–38 km depth in the continental areas in the 50°–100° and the 120°–160° sectors; in contrast smooth variation of crustal velocities is revealed together with transitional Moho in the bay backazimuths in the 210°–250° and the 300°–360° sectors. In the continental backazimuths, a difference in crustal velocities is recognized between metamorphic terrain of granulite facies and the granulite–amphibolite transitional zone. Shear velocity models are compared with crustal reflectivity derived from the analysis of refraction data on the Mizuho Plateau. The reflective layers are found at depths of 24–45 km and appear to be related to the Bouguer gravity anomalies. By correlating the seismic models of crustal structure with other geophysical and geological evidence, the crustal evolution in LHB can be explained in relation to the regional metamorphism at 500 Ma and the last break-up of Gondwana at 150 Ma.

Delineation of faults, using deep seismic sounding refraction data, West Bengal basin

A systematic analysis of refraction data obtained in West BengaI basin, has been carried out to bring into focus the utility of the seismic refraction data in delineating fault zones. The study clearly points out the different conspicuous signatures present in the refraction travel time data, associated with the shallower fault zones affecting the top sedirnentry column and the crystalline basement.

Oceanographer transform fault structure compared to that of surrounding oceanic crust: Results from seismic refraction data analysis

A high quality seismic refraction data set was collected near the intersection of the tranform portion of the Oceanographer Fracture Zone (OFZ) with the adjacent northern limb of the Mid-Atlantic Ridge spreading center (MAR). One seismic line was shot down the axis of the transform valley. Another was shot parallel to the spreading center, crossing from normal oceanic crust into the transform valley, and out again. This latter line was recorded by four Ocean Bottom Seismometers (OBSs) spaced along its length, providing complete reversed coverage over the crucial transform valley zone. Findings indicate that whereas the crust of the transform valley is only slightly thinner (4.5 km) compared to normal oceanic crust (5–8 km), the structure is different. Velocities in the range of 6.9 to 7.7. km/sec, which are characteristics of seismic layer 3B, are absent, although a substantial thickness (approximately 3 km) of 6.1–6.8 km/sec material does appear to be present. The upper crust, some 2 km in thickness, is characterized by a high velocity gradient (1.5 sec −1) in which veloxity increases from 2.7 km/sec at the seafloor to 5.8 km/sec at the base of the section. A centrally-located deep of the transform valley has thinner crust (1–2 km), whereas the crust gradually thickens past the transform valley-spreading center intersection. Analysis of the seismic line crossing sub-perpendicular to the transform valley demonstrates abrupt thinning of the upper crustal section, and thickening of the lower crust outside of the trasform valley. In addition, high-velocity material seems to occur under the valley flanks, particularly the southern flanking ridge. This ridge, which is on the side of the transform opposite to the intersection of spreading ridge and transform, may be an expression of uplifted, partially serpentinized upper mantle rocks.

A LONGITUDINAL STUDY OF THE AGE‐DEPENDENCE OF HUMAN OCULAR REFRACTION‐I. AGE‐DEPENDENT CHANGES IN THE EQUIVALENT SPHERE

Following on from a cross-sectional analysis of refraction data (Saunders, 1981), the present paper attempts the evaluation of serial recordings of a new sample of refractive corrections using longitudinal methods. This study compares the results of the cross-sectional and longitudinal methods, investigates whether or not the latter supports the conclusions of the former, examines to what accuracy this is achieved and, where the results differ, seeks a reason for this. It is demonstrated that in spite of such differences the two methods coincide in their conclusions.

Crustal structure along Mehmadabad-Billimora profile in the Cambay basin, India, from deep seismic soundings

Deep Seismic Sounding (DSS) investigations were carried out along a 220-km long N-S profile from Mehmadabad (22°50'N 72°46'E) to Billimora (20°46'N 72°58'E) in the Cambay basin, India, for studying the detailed crustal structure in the region. Seismic refraction as well as narrow and wide-angle reflection travel-time data were obtained for various crustal boundaries, starting from the sedimentary section down to the Moho, by continuous profiling. Analysis of reversed reflection and refraction travel-time data has yielded crustal velocity—depth functions for the Mehmadabad—Broach and Broach-Navsari sections along the profile, which are significantly different from each other. The average velocities at depths in the Magmadabad—Broach section have been found to be considerably lower than those in the Broach—Navsari section, by about 25% at 5 km, 17% at 10 km, 7% at 20 km, and 2% at the Moho depth and even deeper down in the upper mantle. The presence of a relatively thicker sedimentary section, especially in the Jambusar—Broach area, as revealed by the reversed refraction data analysis, is responsible for this gross difference in the average velocity functions for the two parts of the profile and the same have therefore been used for obtaining the detailed crustal depth along the profile. The Cambay basin, which is well known to be bounded by step faults on the eastern and western margins, is also dissected into seven major crustal blocks in the N-S direction from Mehmadabad to Billimora. The various crustal blocks identified are, from the north: 1. (I) Mehmadabad block 2. (II) Tarapur block 3. (III) Petlad—Katana block 4. (IV) Jambusar—Broach block 5. (V) Kosamba block 6. (VI) Surat block, and 7. VII) Navsari—Billimora block. These blocks are displaced, up or down, relative to the adjacent blocks due to movements along the faults bounding them. Most of the faults have been found to extend quite deep and to affect the Moho boundary considerably, as is quite evident from the relief of the Moho found along the profile. Further, the seismic activity observed in the region, during historical as well as modern times, suggests that these deep faults may even be currently active. The Jambusar—Broach block, which is well known as a broad regional syncline with the maximum thickness of Cenozoic sediments, has been found to be a major graben revealing a maximum crustal thickness of 38–40 km. The granitic basement in this graben is also the deepest, at 6.0–6.5 km depth. Towards the north and south of this major graben, the Moho as well as the granitic basement are found to be at relatively shallower depths in various crustal blocks. The boundary velocity at the Moho has been found to be 8.1–8.2 km/sec, whereas at the granitic basement level there seems to be a lateral velocity variation from 5.7 to 6.3 km/sec. The crustal depth section obtained in the present study reveals a close relationship between the deep and shallow structural features in this region. The Deccan Traps, which form the basement of the overlying Tertiary sediments over most part of the profile, vary in thickness from 1.0 to 1.8 km. However, the Trap surface rises to very shallow depths on the southern part of the profile. The boundary velocity in the Deccan Traps has been found to vary between 4.8 and 5.2 km/sec. In the Anklesvar-Kosamba area, there is also evidence for the presence of a 1.2 km thick layer of Mesozoic sediments (with a velocity of about 4.0 km/sec) underlying the 1.1 km thick Deccan Traps layer.

A microprocessor interactive graphics engineering seismic and computing system

A general purpose microprocessor graphics computing system has been interfaced to a single channel signal enhancement seismograph to provide a seismic system useful for waveform analysis and geophysical engineering studies. A description is given of the system components, computer processing system organization and use of the system for seismic refraction data analysis. The system represents one application of the new microprocessor technology to the field of geophysics and geotechnical engineering.

An investigation into the time term method in refraction seismology

abstract The time term method of seismic refraction data analysis allows an areal arrangement of shot points and stations and yields directly a three-dimensional representation of underlying structure. This method was investigated analytically and through numerical experiments to determine implicit sources of error and to provide guidelines for its proper use. Error terms for computed refractor depths were derived for two site arrays over two structures, a simply dipping refractor surface and a symmetric anticlinal refractor surface. These error terms proved to be qualitatively reliable guides to the performance of the time term method using models of multi site arrays over planar and biplanar refractor structures. Neither continuity of time terms nor use of a known refractor velocity in the computations offered a guarantee of a more accurate refractor reconstruction. In the two models tested a refractor velocity greater than the true velocity yielded the best reconstruction. Sensitivity to angle of dip indicated preferred orientation of shot-station lines along gentle apparent dips when the underlying structure is known and their orientation along several azimuths when the structure is unknown so as to mute the effect of high dip angles. If the structure has refractor surfaces dipping more than a few degrees, the time term method will give inaccurate results unless previous knowledge of the refractor configuration permits model studies to determine error terms and arrangement of shots and stations. Unfortunately such knowledge is usually the goal of a seismic experiment.