Absolute Delay Time Research Articles

Equivalence of RABBITT and Streaking Delays in Attosecond-Time-Resolved Photoemission Spectroscopy at Solid Surfaces

The dynamics of the photoelectric effect in solid-state systems can be investigated via attosecond-time-resolved photoelectron spectroscopy. This article provides a comparison of delay information accessible by the two most important techniques, attosecond streaking spectroscopy and reconstruction of attosecond beating by interference of two-photon transitions (RABBITT) at solid surfaces, respectively. The analysis is based on simulated time-resolved photoemission spectra obtained by solving the time-dependent Schrödinger equation in a single-active-electron approximation. We show a continuous transition from the few-cycle RABBITT regime to the streaking regime as two special cases of laser-assisted photoemission. The absolute delay times obtained by both methods agree with each other, within the uncertainty limits for kinetic energies >10 eV. Moreover, for kinetic energies >10 eV, both streaking delay time and RABBITT delay time coincide with the classical time of flight for an electron propagating from the emitter atom to the bulk-vacuum interface, with only small deviations of less than 4 as due to quantum mechanical interference effects.

A Flexible Millimeter-Wave Channel Sounder With Absolute Timing

This paper presents a novel ultrawideband wireless spread spectrum millimeter-wave (mmWave) channel sounder that supports both a wideband sliding correlator mode and a realtime spread spectrum mode, also known as wideband correlation or direct correlation. Both channel sounder modes are capable of absolute propagation delay (time of flight) measurements with up to 1 GHz of radio frequency null-to-null bandwidth, and can measure multipath with a 2-ns time resolution. The sliding correlator configuration facilitates long-distance measurements with angular spread and delay spread for up to 185 dB of maximum measurable path loss. The real-time spread spectrum mode is shown to support short-range, small-scale temporal, and Doppler measurements (minimum snapshot sampling interval of 32.753 μs) with a substantial dynamic fading range of 40 dB for human blockage and dynamic urban scenarios. The channel sounder uses field programmable gate arrays, analog-to-digital converters, digital-to-analog converters, and low-phase-noise rubidium standard references for frequency/time synchronization and absolute time delay measurements. Using propagation theory, several methods are presented here to calibrate and verify the accuracy of the channel sounder, and an improved diffraction model for human blockage, based on the METIS model but now including directional antenna gains, is developed from measurements using the channel sounder. The mmWave channel sounder described here may be used for accurate spatial and temporal raytracing calibration, to identify individual multipath components, to measure antenna patterns, for constructing spatial profiles of mmWave channels, and for developing statistical channel impulse response models in time and space.

Complement of Special Relativity and Limitation of General Relativity

<p class="1Body">For a set of forces being in equilibrium, the equilibrium state will not vary from one observer to another. This generally acknowledged fact has been called as the Force Equilibrium Invariance Axiom. On the basis of this axiom, the force transformation formula can be derived when an object is in motion, so that the force, length, time and mass can be calculated as per the basic transformation formula for the special relativity. According to the results of experimental analysis obtained by J.C. Hafele and R.E. Keating, the concepts of absolute time delay and relative time delay have been put forward herein, so as to solve any problems on the traveling velocity and records of any object being in motion at the real-time. For the properties of the force, the force applied on an object being accelerated will be deemed as the energy transfer force, while the universal gravitation will be deemed as the applied force of field. Both forces have the different basic properties. It is unscientific to consider both forces being the same properties. Based on the Force Equilibrium Invariance Axiom, it is deduced that the gravitational mass can only be the constant irrelevant to the motion of an object. Therefore, the principle of equivalence will not be tenable in theory. Only if the motion velocity of an object is very small relative to the velocity of light, can the principle of equivalence be deemed being approximately tenable. Under this condition, the general relativity can be only consistent with the practical deducing principle. However, if the motion velocity of an object is relatively large, there will be a significant difference between the constant gravitational mass and the inertial mass; as a result, there may be a deviation between the inference on the general relativity and the practical deducing principle. Take the Black Hole as an example. Even if the Black Hole is made almost completely of neutrons, its actual volume is one million times greater than its theoretical volume. Therefore, it is concluded that the Black Hole cannot be deemed as the substance composed of real atoms. It also shows accordingly that, according to the general relativity of theoretical source of Black Hole, the analysis results obtained when an object is in motion at high-velocity can not conform to the reality.</p>

Defining the optimal systolic phase targets using absolute delay time for reconstructions in dual-source coronary CT angiography.

To define the optimal systolic phase for dual-source computed tomography angiography using an absolute reconstruction delay time after the R-R interval based on the coronary artery motion, we analyzed images reconstructed between 200 and 420 miliseconds (ms) after the R wave at 20 ms increments in 21 patients. Based on the American Heart Association coronary segmentation guidelines, the origin of six coronary artery landmarks (RCA, AM1, PDA, LM, OM1, and D2) were selected to calculate the coronary artery motion velocity. The velocity of the given landmark was defined as the quotient of the route and the length of the time interval. The x, y and z-coordinates of the selected landmark were recorded, and were used for the calculation of the 3D route of coronary artery motion by using a specific equation. Differences in velocities were assessed by analysis of variance for repeated measures; Bonferroni post hoc tests were used for multiple pair wise comparisons. 1488 landmarks were measured (6 locations at 12 systolic time points) in 21 patients and were analyzed. The mean values of the minimum velocities were calculated separately for each heart rate group (i.e. <65; 65-80; and >80 bpm). The mean lowest coronary artery velocities in each segment occurred in the middle period of each time interval of the acquired systolic phase i.e. 280-340 ms. No differences were found in the minimal coronary artery velocities between the three HR groups, with the exception of the AM1 branch (p = 0.00495) between <65 and >80 bpm (p = 0.03), and at HRs of 65-80 versus >80 bpm (p = 0.006). During an absolute delay of 200-420 ms after the R-wave, the ideal reconstruction interval varies significantly among coronary artery segments. Decreased velocities occur between 280 to 340 ms. Therefore a narrow range of systolic intervals, rather than a single phase, should be acquired.

Observed and predicted North American teleseismic delay times

Using a newly developed cross-correlation-based computer tool we measured absolute delay times of teleseismic P and S waves recorded by about 2000 broadband seismic stations from EarthScope's USArray, previous PASSCAL arrays, and additional permanent networks in North America. We estimate contributions to the delays from crustal structure, using various prior crustal models, and from event-side heterogeneity, using the delay time distribution itself. We then subtract these contributions from our measurements and map the average delay at each station location. We analyze these average delay times to investigate the structure of the North American mantle and formation of the North American continent. Mantle S delay times from stations west of the Rocky Mountains are 4.2 s larger than delay times from stations within the US portion of stable North America. Locally, S delays at Yellowstone are another 4 s larger than those west of Rocky Mountains. Decreasingly sharp delay time contrasts occur across the Rocky Mountains, the Appalachian Mountains, and on the southern edge of the North American Craton, respectively. These delay time gradients of various steepness broadly coincide with surface geological boundaries, but are offset to either side of these boundaries. Predictions of teleseismic S delays from twelve three-dimensional tomographic mantle S velocity models agree generally with observed delay time patterns, but underestimate the delays and advances to varying degrees. Tomographic models derived from different data than teleseismic arrival times predict similarly valid delays as models derived from teleseismic arrivals, while overestimating the smoothness of delay time patterns to varying degrees. We further utilize these tomographic models to predict and study the size and distribution of delay contributions from modeled heterogeneity in different depth ranges. This study shows that the 80–240 km depth range is the dominant contributor to delay time contrasts and variance. This depth range generally corresponds to asthenosphere in the western US and lithosphere in the central and eastern US. The average depth to which the observed delays require the central US lithosphere to extend is likely shallower than 240 km and consistent with the seismic bottom of lithosphere imaged in seismic-velocity models not derived from teleseismic delay times.

AIMBAT: A Python/Matplotlib Tool for Measuring Teleseismic Arrival Times

Seismic travel‐time tomography, a common method for studying the Earth’s three‐dimensional seismic velocity variations, relies on robust measurement of seismic phase arrival times. Absolute arrival times are estimated by visually picking the emergence of the seismic phase of interest on seismograms. Subtracting theoretical arrival times (calculated using a known source location and origin time) from these picked absolute times yields absolute delay times. A widely used method whereby careful picking of absolute arrival times is not required is multi‐channel cross‐correlation (MCCC), developed by VanDecar and Crosson (1990). In MCCC, phase arrival times relative to an unknown average time are obtained by finding the maximum of the cross‐correlation function between each possible pair of seismograms. The preprocessing time of marking the phase to be cross‐correlated in MCCC has increased with the tremendous growth in seismic data volume over the past decade. In this paper, we introduce an efficient and robust computer tool, Automated and Interactive Measurement of Body‐wave Arrival Times (AIMBAT), to measure teleseismic body‐wave arrival times for phases for which arrival time predictions exist. The tool is based on MCCC, but an iterative cross‐correlation and stack (ICCS) algorithm replaces the initial phase marking part of the MCCC procedure, which significantly reduces the need for early user labor. The tool is written in Python (http://www.python.org) and utilizes its open‐source packages Numpy (http://numpy.scipy.org) and Scipy (http://scipy.org) for numerical array computation and Matplotlib (Hunter, 2007) for two‐dimensional plotting and graphical user interface (GUI) applications. We also transcribed the Fortran version of MCCC from VanDecar and Crosson (1990) into Python, which was validated by running both versions on the same data. Python is an efficient, high‐level, object‐oriented, and platform‐independent (Linux, Mac, and Windows) …

Extracting decay curves of the correlated fluorescence photons measured in fluorescence correlation spectroscopy

We have developed a new method to extract the decay curves of the correlated fluorescence photons from the data of fluorescence correlation spectroscopy using time-correlated single photon counting. In this method, a two-dimensional correlation map of photon pairs is generated at an absolute delay time with reference to the excitation-emission delay of each photon. Using a dye-labeled DNA as an example, we have demonstrated that the decay curve of the correlated fluorescence photons is separated from the uncorrelated background signals simply by subtracting a two-dimensional correlation map at sufficiently long delay time without additional prior information.

SU‐FF‐I‐10: Evaluation of a Generalized Contrast Enhancement Protocol for 4D‐CT Imaging of Liver Tumors

Purpose: Intravenous contrast is needed to enhance tumor visibility in the liver. Unfortunately, conventional diagnostic CT protocols cannot be used due to the extended acquisition time required. We present results of a generalized contrast enhancement protocol for 4D‐CT imaging of liver tumors. Method and Materials: 92 patients (metastases: 39, cholangiocarcinomas: 44 hepatocellular carcinomas: 9) were enrolled in the study. All 4D‐CT images were acquired on a GE Discovery ST PET/CT scanner in cine mode. 150 mL of intravenous contrast was delivered at a rate 5 mL/s. Liver metastases and cholangiocarcinomas were imaged in the portal venous phase with a delay of 45 seconds while hepatocellular carcinomas were imaged in the delayed phase at 270 seconds. A region of interest inside and outside of the tumor was created, and the average CT numbers were analyzed. Results: The protocol produced enhancement of greater than 35 CT numbers in 72% of patients with liver metastases and cholangiocarcinomas and 44% in patients with hepatocellular carcinomas. The image quality of the metastases and cholangiocarcinomas patients was improved considerably (vessels and the tumor borders could be more easily distinguished) but modest improvement was detected in hepatocellular carcinomas. Tumor contrast enhancement was not directly correlated with body surface area, but rather with the inherent contrast of the tumor. Average absolute delay time of tumor imaging was 70 seconds for cholangiocarcinomas (σ=15 s) and 66 seconds for metastases (σ=13 s). In this range the degree of enhancement in metastases was more sensitive to the absolute delay time compared to the cholangiocarcinomas and for longer delays less contrast enhancement was observed. Conclusion: The protocol works well for the majority of patients with cholangiocarcinomas and liver metastases. For tumors located well below the dome of the liver, a reduction in delay time may enhance tumor visibility.

Upper mantle seismic structure beneath the Ethiopian hot spot: Rifting at the edge of the African low‐velocity anomaly

The Miocene‐Recent East African Rift in Ethiopia subaerially exposes the transitional stage of rifting within a young continental flood basalt province. As such, it is an ideal study locale for continental breakup processes and hot spot tectonism. We combine teleseismic traveltime data from 108 seismic stations deployed during two spatially and temporally overlapping broadband networks to present detailed tomographic images of upper mantle P and S wave seismic velocity structure beneath Ethiopia. Tomographic images reveal a ∼500 km wide low P and S wave velocity zone at 75 to ≥400 km depth in the upper mantle that extends from close to the eastern edge of the Main Ethiopian Rift (MER) westward beneath the uplifted and flood basalt‐capped NW Plateau. We interpret this broad low‐velocity region (LVR) as the upper mantle continuation of the African Superplume. Within the broad LVR, zones of particularly low velocity are observed with absolute delay times (δtP ∼ 4 s) that indicate the mantle beneath this region is amongst the slowest worldwide. We interpret these low velocities as evidence for partial melt beneath the MER and adjacent NW Plateau. Surprisingly, the lowest‐velocity region is not beneath Afar but beneath the central part of the study area at ∼9°N, 39°E. Whether this intense low‐velocity zone is the result of focused mantle upwelling and/or enhanced decompressional melting at this latitude is unclear. The MER is located toward the eastern edge of the broad low‐velocity structure, not above its center. This observation, along with strong correlations between low‐velocity zones and lithospheric structures, suggests that preexisting structural trends and Miocene‐to‐Recent rift tectonics play an important role in melt migration at the base of the lithosphere in this magmatic rift zone.

Rapid estimation of relative and absolute delay times across a network by adaptive stacking

SUMMARY Adaptive stacking provides a powerful and rapid procedure for estimating the residual patterns across a network of seismic stations. The approach exploits predictions from some propagation model to achieve an approximate alignment of traces, which are then stacked to form a reference trace. Iterative improvement of the alignment, by comparison of the reference trace with each station trace, leads to a direct estimate of the residuals from the propagation model. Our implementation is fast and robust in the presence of significant noise and waveforms of different character. The major difference from earlier forms is the use of a direct minimization scheme for determining the best match between the reference stacked trace and each recorded trace based on an L 3 measure of misfit. This approach has the benefit of generating automatic error estimates. For teleseismic applications, the ak135 model has proved to be very effective for selection of the window around the desired phase and in achieving initial alignment. The approach can be applied to both first motion (P) and later phases (e.g. PcP), with extraction of absolute time via the improved signal-to-noise properties of the stacked trace, after full alignment. The new method is illustrated with three teleseismic events from a similar source region that were recorded by the 72 station TIGGER array in northern Tasmania. Despite significant levels of noise and contrasting waveforms produced by the three events, the residual patterns are very similar. Even when large time-shifts are introduced into the records, trace alignment is achieved with rapid convergence of the iterative procedure and excellent recovery of the imposed shifts. These results confirm adaptive stacking as a valuable alternative to data based cross-correlation techniques, particularly when heterogeneous instrumentation is employed.

Optimal measurement of relative and absolute delay times by simulated annealing

Summary Conventional approaches to determine relative arrival times of body waves recorded by a local or a regional array rely on cross-correlations between pairs of traces. This problem is better posed as a non-linear inverse problem, which involves the minimization of a cost function that measures the difference between a reference unknown waveform that can be time delayed, and the observed data. The unknown parameters that are solved for, are the amplitude values at each time sample of the optimal waveform and its time delay defined for each trace. The problem, which has a large number of unknown parameters, is solved with simulated annealing. The algorithm is very efficient and can be used for a routine analysis of seismic data. The application of this method to several earthquakes recorded during different PASSCAL experiments demonstrates that it provides accurate and robust differential traveltime measurements even with very noisy data.

The diastolic decay constant in spontaneously hypertensive rats versus WKY rats as an indicator for vasomotor control

This research uses the diastolic decay constant ( τ) to investigate the short term mechanism responsible for vasomotor control, mainly the α-sympathetic control system. Previous studies have shown that vasomotor control is altered in spontaneously hypertensive rats (SHR) preceding the phase of overt hypertension. The diastolic decay, according to the two element Windkessel model, displays an exponential shape with a decay constant, τ, depending on both the vascular resistance and the compliance. In our experiments, we used τ to characterize vasomotor activity and its control in the normotensive rats as well as in the spontaneously hypertensive rats (SHR) prone to hypertension. The beat to beat value of τ was evaluated from a continuous arterial blood pressure (ABP) signal, measured in the tail artery of the conscious, unrestrained rat. Four months old prehypertensive SHR were compared to their age matched normotensive controls (WKY). To study vasomotor regulation, we computed gains and delay times by investigating the compensatory response in τ to changes in mean ABP (MBP). These parameters are expected in the short term to be neurally controlled by the sympathetic system, mainly α-sympathetic. Our set of experiments consisted of changing MBP by performing successive injections in bolus of increasing doses of the vasoconstrictor angiotensin II. This procedure was repeated under double cardiac autonomic blockade of the vagal and β 1-sympathetic limbs. Our results show that, under baseline conditions, the absolute gain and delay times of τ are reduced in SHR compared to WKY. Double cardiac blockade decreases the absolute gain in both strains, while abolishing the baseline strain differences. These results reinforce our assumption that, in SHR, the α-sympathetic system is in a basic state of excitation even prior to the onset of overt hypertension and therefore reacting with reduced sensitivity (lower gain) to changes in MBP.

Coordinate Transformation VLSI Processor for Redundant Manipulator Control

A computationally efficient algorithm called 'Subsequent-division algorithm' is presented to develop a special-purpose VLSI processor for differential inverse kinematics computation of redundant manipulators. Because the computation is performed in a feedback loop, not only throughput but also absolute delay time must be considered as performance factor An architecture of a reconfigurable parallel VLSI processor is proposed to improve the utilized ratio of the multipliers contained in processor elements (PEs). In each PE, switching hardware is used to change the connections between the multipliers and the adders, so that we can reconfigure the multiply-adders having desired numbers of multipliers. The chip evaluation based on Iμm CMOS design rule shows that the total delay time for a 12 degrees-of-freedom (DOF) redundant manipulator becomes about 13μsec which is about ninety times faster than that of a parallel processor approach using general-purpose microprocessors.

Measured time delay and re-synchronization time in digital microwave radio systems

The transition from analog to digital transmission systems has been slower for electric power utilities than other industrial sectors because of concern that digital transmission system delay times could adversely impact the response time of transfer trip protective relaying equipment. Alcatel Network Systems has completed a comprehensive testing program to measure the absolute time delay and various re-synchronization times through analog and digital transmission systems. The general conclusion is that the worst case absolute time delay of 577 microseconds, VF to VF, through the digital microwave system is approximately one half the delay for a typical analog system. Absolute time delays of 500-600 microseconds should cause no problems to transfer trip protective relaying systems.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Comodulation masking release as a function of bandwidth and time delay between on-frequency and flanking-band maskers

The threshold for a signal masked by a narrow band of noise centered at the signal frequency (the on-frequency band) may be reduced by adding to the masker a second band of noise (the flanking band) whose envelope is correlated with that of the first band, an effect called comodulation masking release (CMR). This paper examines CMR as a function of masker bandwidth and time delay between the envelopes of the on-frequency and flanking bands. The 1.0-kHz sinusoidal signal had a duration of 400 ms. The on-frequency band was presented alone (reference condition) or with the flanking band. The flanking-band envelope was either correlated or uncorrelated with that of the on-frequency band. Flanking-band center frequencies ranged from 0.25-2.0 kHz. The flanking band was presented either in the same ear as the on-frequency band (monaural condition) or in the opposite ear (dichotic condition). The noise bands had bandwidths of 6.25, 25, or 100 Hz. In the correlated conditions, the flanking-band envelope was delayed with respect to that of the on-frequency band by 0, 5, 10, or 20 ms. For the 100-Hz bandwidth, CMRs were small (typically less than 1 dB) in both monaural and dichotic conditions at all delay times. For the 25-Hz bandwidth, CMRs were about 3.5 dB for the 0-ms delay, and decreased to about 1.5 dB for the 20-ms delay. For the 6.25-Hz bandwidth, CMRs averaged about 5 dB and were almost independent of delay time. The results suggest that the absolute delay time is not the critical variable determining CMR. The magnitude of CMR appears to depend on the correlation between the envelopes of the on-frequency and flanking bands. However, the results do not support a model of CMR that assumes that signal threshold corresponds to a constant change in across-band envelope correlation when the correlation is transformed to Fisher's z.

Time-resolved phonon-assisted stimulated emission in quantum-well heterostructures

Summary form only given. The authors report the observation of time-resolved photo-pumped operation of phonon-assisted stimulated emission in a series of AlGaAs-GaAs single quantum wells with different well thicknesses (20, 34, and 54 AA). The temporal characteristics of the phonon-assisted stimulated emission are distinct from the laser operation of the confined particle states in that the phonon-assisted process is always delayed in time (30-80 ps) and has a larger temporal full width at half-maximum. Also, lasing on the confined particle states is quenched as the lasing on the phonon sidebands begins. Data are presented on the emission intensity versus wavelength versus time and the dependence of the relative (and absolute) delay times as a function of excitation power and sample geometry. The delay time is uncorrelated with the sample geometry (and thus photon lifetime in the cavity) but is correlated with the excitation power (capacity to generate phonons). The delay is interpreted to be the time necessary to build up a sufficiently large phonon density (possibly by stimulated phonon emission) to initiate the phonon-assisted stimulated emission, which then dominates the spectral output. >

Synchronous Composite Packet Switching-A Switching Architecture for Broadband ISDN

A new switching architecture for broadband ISDN, "Synchronous Composite Packet Switching (SCPS)," is proposed and evaluated. It efficiently integrates circuit and packet switching functions on a single switching system and accommodates very high speed-up to several tens of Mbit/s-communication services, such as very high speed bursts of data, still picture, and motion video, as well as 64 kbit/s or less voice and data services. The SCPS system comprises plural switch modules and plural Very high speed synchronous loops. In the SCPS system, messages on plural circuit switched channels are assembled into quasi-packets, called "composite packets," and switched synchronously between switch modules, maintaining complete time transparency and short absolute delay time. A system parameter design to obtain high system efficiency and appropriate system modularity is explained, and an example for a very large capacity transit switch of 4 Gbit/s throughput is presented. System implementation problems to realize the SCPS principle, such as efficient implementation of the composite packet assembling and loop transmission functions, are investigated and an experimental system constructed for circuit switching part is presented. The most remarkable characteristic of the SCPS is that it efficiently integrates <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">64 \times n</tex> kbit/s circuit switching with packet switching. Moreover, the SCPS system retains compatibility with existing networks and the possibiliy of evolution toward a future broadband ISDN. On the basis of the above investigations and experimental system construction, the authors conclude that the SCPS is one of the most practical switching architectures for the coming broadband ISDN era.

IF Variable Equalizers for FM Microwave Radio Links

The circuit configuration, operational principles, and some test data on three new types of equalizers applicable for use in FM microwave radio links are described. The equalizers are namely of the reflection type, frequency converter type, and AM-PM conversion type. The reflection type delay equalizer permits variation of relative delay time while keeping the absolute delay time constant at the center frequency or permits variation of absolute delay time while keeping the relative delay time constant. The frequency converter type equalizer adopts a principle whereby variation in local frequency (supplied to the frequency converter) facilitates continuous variation of the relative delay time, absolute delay time, and amplitude frequency response. The AM-PM conversion type differential gain equalizer enables equalization of differential gain through the combined use of the AM-PM converter circuit and the delay circuit.

IF variable equalizers for FM microwave radio links

The circuit configuration, operational principles, and some test data on three new types of equalizers applicable for use in FM microwave radio links are described. The equalizers are namely of the reflection type, frequency converter type, and AM-PM conversion type. The reflection type delay equalizer permits variation of relative delay time while keeping the absolute delay time constant at the center frequency or permits variation of absolute delay time while keeping the relative delay time constant. The frequency converter type equalizer adopts a principle whereby variation in local frequency (supplied to the frequency converter) facilitates continuous variation of the relative delay time, absolute delay time, and amplitude frequency response. The AM-PM conversion type differential gain equalizer enables equalization of differential gain through the combined use of the AM-PM converter circuit and the delay circuit.

AN AREAL PLAN OF MAPPING SUBSURFACE STRUCTURE BY REFRACTION SHOOTING

Under suitable geologic conditions, arrival events of refraction wave trajectories following a relatively high speed “marker horizon” may be observed and identified and the associated travel times may be measured on refraction setups having detectors located at suitable distances from shot point locations. On each refraction setup, the sum of the two “delay times” at positions offset from the shot point and detector position may be determined. Depth of the marker horizon and the location of the “offset position” at which this depth applies are dependent on and determinable from “delay time” if the seismic wave speeds in the geologic section overlying the marker horizon are known. By arranging two or more refraction setups angularly disposed so that they have a common location for one offset position of each setup, differential delay times and corresponding differential depths at the free offset positions may be determined. By a geometrical arrangement of three setups in a triangular manner such that each offset position of each line is coincident with one offset position of another line, absolute delay times and depths at the common offset positions may be determined. By coordinating these two types of geometrical arrangements in shooting over an area, the depths and undulations of the marker horizon may be determined.