Wave Delay Time Research Articles

Separation of fast and slow shear waves and prediction of fracture parameters based on non-orthogonal assumptions

SUMMARY Natural fractures play a significant role in oil and gas reservoirs. Accurate predictions of fracture parameters are vital in reservoir prediction and oil and gas development. The birefringent phenomenon of shear waves in fractured media makes shear wave splitting (SWS) analysis an important tool in formulating fracture predictions. The traditional SWS analysis method is based on an orthogonal assumption of fast and slow shear waves. However, in an orthotropic medium composed of a background vertical transversely isotropic medium and a set of vertical fractures, fast and slow shear waves are not necessarily orthogonal. This causes the traditional SWS analysis method to fail. To solve this problem, we proposed an SWS analysis algorithm with a non-orthogonal assumption of fast and slow shear waves in this study. First, we introduced a parameter (difference angle) to characterize the angle between slow shear waves and the normal polarization directions of the fast shear waves. Subsequently, based on the traditional two-parameter scanning algorithm, a parameter was added to facilitate three-parameter scanning. In addition, we derived an expression for the two-parameter scanning objective function using the non-orthogonal assumption. Two-parameter scanning can accurately extract fast and slow wave time delay data, but it cannot determine an accurate fast shear wave polarization direction. Therefore, we optimized the three-parameter scanning algorithm as follows: first, we used two-parameter scanning to obtain the fast and slow wave time delays and then performed further scanning to determine the polarization direction of the fast shear wave and difference angle. The optimization algorithm significantly improved the computational efficiency. Subsequently, we tested the accuracy of this method using synthetic single-trace and three-component vertical seismic profile data. We demonstrated the implementation process of the three-parameter scanning method using actual data, separated fast and slow shear waves, and predicted fracture parameters. The final fracture parameters were verified.

Extraction of Reflected Wave Delay Time for the Location of Buried PE Pipeline

Extraction of Reflected Wave Delay Time for the Location of Buried PE Pipeline

Possible layered lithospheric anisotropy around Longmenshan Faults by teleseismic S wave splitting and receiver functions

This study conducts an in-depth analysis of seismic anisotropy around the Longmenshan Faults. Utilizing a dataset of about 7710 earthquake catalogs from July 2007 to March 2023, we applied S wave splitting and receiver function methods to examine Pms and XKS waveforms collected from 12 fixed broadband stations across Gansu and Sichuan provinces. Our analysis revealed significant variations in seismic anisotropy between the crust and lithosphere, marked by distinct fast wave directions and delay times. These characteristics point to the possibility for layered anisotropy within the region. A two-layer anisotropy inversion analysis at key stations further delineated the differential anisotropic behaviors between the crust and the upper mantle, underscoring the impact of local geological structures and mantle dynamics. Crucially, our study posits the existence of layered anisotropy around the Longmenshan Fault Zone, a finding that significantly advances our comprehension of the region’s seismic anisotropy and adds a vital dimension to our understanding of its subsurface structural intricacies and tectonic evolution.

ВИЗНАЧЕННЯ ТА ВРАХУВАННЯ СИСТЕМАТИЧНИХ ПОХИБОК ПРИ ВИМІРЮВАННІ НАВІГАЦІЙНИХ ГЛИБИН

The scientific study considers the issue of studying the features and determining the inherent values of systematic errors that occur when measuring navigation depths with multibeam echosounders, the elimination of these errors from the measurement results, which requires a special organization and methodology for performing multibeam echosounders tests. Systematic errors of navigation data can affect as on the magnitude of the depth itself, as well as on its planned position, and their influence should be evaluated after studying the angular measurements by echo sounder beams and calibration. The calibration of multi-beam systems, as well as the horizontal and vertical movements of the vessel, is much more significant and complicated compared to the calibration of single-beam systems. It is necessary to perform system accuracy control tests to confirm the reliability of multibeam echosounder data. These tests should preferably be carried out on board before taking depth measurements. For this, it is necessary to capture data, process and edit them in real time. Periodic performance of accurate calibration and testing is necessary to confirm that the multibeam survey meets the accuracy requirements. Multibeam echosounders calibration tests are performed with the aim of minimizing errors, taking into account the delay time of data acquisition, sea waves and changes in the ship's course. Keywords: multibeam echosounder, systematic errors, sensor calibration, hydrographic surveys, relief of the seabed, marine navigation chart, measured tacks, survey software.

Crustal anisotropy of the South China block and tectonic implications

Exploiting the teleseismic waveform data from permanent seismic stations distributed in the South China block, we obtained the crustal anisotropy parameters at 51 stations by fitting the azimuthal variations of arrival times of the PMs converted wave of radial receiver functions. The results show the dominant direction of fast wave polarity in the South China block is NW–SE, which is basically consistent with the absolute plate motion direction. Combining the shear wave splitting and GPS results, we speculated that the tectonic extension of the Paleo-Pacific plate subduction dominates the crust–mantle anisotropy, which reflects the large-scale tectonic stress setting of the South China block. The fast wave directions of NE–SW and E–W calculated by a few stations might represent a local complex tectonic environment, and the crustal anisotropy of NE–SW is well related to the tectonic deformation in Paleozoic. The delay time of slow waves caused by crustal anisotropy ranges from 0.14 s to 0.71 s, with an average of 0.33 s. The delay time of Jiangnan orogenic belt, which located in the southeast of Yangtze block, is particularly large, which reflects the complex and intense intra-continental tectonic movements since Neoproterozoic. The crustal anisotropy along the southeast coast can be contributed to the local lithosphere underplating caused by the upwelling of asthenosphere in Cretaceous.

Finite-Frequency Delay Times of Phase Segments for Body Waves

ABSTRACT We propose a new way of measuring the delay times of body waves, based on the time differences between short segments of a phase. Using this proposed methodology, which we call the delay time of phase segments (DTPSs) method, we believe it is possible to (1) optimize the reduction mode that reduces finite-frequency kernels to ray-theoretical kernels, (2) reduce computation and memory storage costs by reducing the volume of finite-frequency sensitivity kernels, and (3) achieve greater linearity between delay times and velocity variations for larger velocity perturbations up to ±30%. The DTPS kernel can also be used in adjoint methods. Theory and our calculations indicate that the width of the DTPS kernel decreases as the length of the phase segment decreases from the length of the entire phase. The scattering caused by inhomogeneity is more likely to complicate the latter parts of a phase more than its beginning. For this reason, the DTPS method using a phase segment in the first quarter of a phase is robust for velocity perturbations up to ±30% from the initial model, whereas traditional methods using the entire phase are only robust for velocity perturbations up to ±10%. The DTPS method may reduce computation times by up to 70% because the size of the DTPS kernels is smaller than that of other methods by up to 70%. Synthetic tests indicate that the DTPS method produces inverse models nearly as accurate as generalized seismological data functionals.

Numerical simulation of laser ultrasonic detection of the surface microdefects on laser powder bed fusion additive manufactured 316L stainless steel

A numerical model is presented in this article to investigate the interactions between laser generated ultrasonic and the microdefects (0.01 to 0.1 mm), which are on the surface of the laser powder bed fusion additive manufactured 316L stainless steel. Firstly, the influence of the transient sound field and detection positions on Rayleigh wave signals are investigated. The interactions between the varied microdefects and the laser ultrasonic are studied. It is shown that arrival time of reflected Rayleigh (RR) waves wave is only related to the location of defects. The depth can be checked from the feature point Q, the displacement amplitude and time delay of converted transverse (RS) wave, while the width information can be evaluated from the RS wave time delay. With the aid of fitting curves, it is found to be linearly related. This simulation study provides a theoretical basis for quantitative detection of surface microdefects of additive manufactured 316L stainless steel components.

Measurement of elastic modulus of laser cladding coatings by laser ultrasonic method

The elastic modulus is an important parameter that can be used to evaluate the properties of laser cladding coatings. However, methods of measuring the elastic modulus are destructive, time consuming, and inefficient. A nondestructive testing method based on a laser ultrasonic is presented. It can be used to measure the elastic modulus, but also to characterise the uniformity of the laser cladding coating. First, the surface microstructure of a laser cladding coating was observed using an optical microscope, and the elastic modulus of the coating was evaluated by a micro-indentation tester. The results showed that large dendrites with a small elastic modulus were mostly distributed in the joints, while the smaller equiaxed grains with a large elastic modulus were mainly distributed in the beads. However, there was no obvious difference between the joint and the bead in the energy spectrum measured by energy dispersive spectroscopy. Second, the surface wave signals were collected on the coating by laser ultrasonic, and the maximum amplitude and the delay time of surface waves of the scanning area were obtained. Through the relationship between the velocity of the surface wave and the elastic modulus, the distribution of the elastic modulus could be measured by a laser ultrasonic C-scan method. Comparison with the micro-indentation results shows that the laser ultrasonic is feasible for measuring the elastic modulus and characterising the uniformity of laser cladding coatings.

Analysis of shear wave splitting parameters in los Humeros geothermal field, Puebla, Mexico

A study of anisotropic characteristics based on shear wave splitting (SWS) parameters (fast shear wave polarization and delay time) was carried out on 121 microearthquakes recorded by seismic arrays installed in Los Humeros Geothermal Field, Puebla, Mexico from 2011 to 2016. This analysis determined how both parameters seem to have been influenced by the geothermal field operation and by the spatial variations of the seismic sources with respect to the seismic array. There is a clear evidence of anisotropy since most of the SWS results show a main NW-SE polarization direction, which is not consistent with the maximum horizontal stress orientation in the region. The fast polarizations remained mostly constant for the analyzed period, keeping a preferential direction of NW-SE at the central-southern section of the study region, which in some cases follows the orientation of some proximal local faults. In the northern region, the fast polarizations appear uniform without following the orientations of the local faults. This preferential direction may be due to the shallow structures are being affected by the tectonism inhered from the basement, controlled in part by the Mexican fold and thrust belt whose main orientation is NW-SE and, to a lesser extent, by the pre-existing caldera ring faults.Observations of mean delay times mostly range between 0.025 s and 0.07 s for all seismic stations analyzed, with some individual values reaching up to 0.15 s, but with a total average of 0.041 s for the period analyzed. The maximum anisotropy percentage found was 13.54%, and the variations allowed us to characterize the geothermal field in two main areas with high fracturing. Results show Los Humeros, Antigua, Los Conejos and Las Viboras faults, and other minor faults around them as the main conduits of permeable sources. However, the inferred Antigua and Malpaís faults may also be considered important areas.Delay times δt and their respective error bars, showed an apparent decrease from 2014 to 2016, which may indicate a possible inverse correlation with an increase in fluid injection. However, the lack of data during 2013 and 2014 makes it difficult to robustly prove this hypothesis due to the change in station configuration.

Quantifying hydraulically induced fracture height and density from rapid time-lapse distributed acoustic sensing vertical seismic profile data

Several recent studies have advanced the use of time-lapse distributed acoustic sensing vertical seismic profile data in horizontal wells for determining hydraulically stimulated fracture properties. Hydraulic fracturing in a horizontal well typically generates vertical fractures in the rock medium around each stage. We have modeled the hydraulically stimulated formation with vertical fracture sets about the lateral wellbore as a horizontally transverse isotropic medium. Rock-physics modeling is used to relate the anisotropy parameters to the fracture properties. This modeling is used to develop an inversion for compressional wave time delay to the fracture height and density of each stage. Field data from two horizontal wells are analyzed, and the fracture height evaluated using this technique is consistent with the microseismic analysis.

Experimental Realization of Optimal Energy Storage in Resonators Embedded in Scattering Media

AbstractThe ability to enhance light–matter interactions by increasing the energy stored in optical resonators is inherently dependent on the resonators' coupling to the incident wavefront. In practice, weak coupling may result from resonators' irregular shapes and/or the scrambling of waves in the surrounding scattering environment. Here, a blind and non‐invasive wavefront shaping technique providing optimal coupling to resonators is presented. The coherent control of the incident wavefront relies on the lengthening of delay times of waves efficiently exciting the resonator. Using a modal approach, the optimality of the proposed technique is proven and its limitations are quantified. The proposed concept is demonstrated in microwave experiments by injecting in situ optimal wavefronts that maximize the energy stored in high‐permittivity dielectric scatterers and extended leaky cavities embedded in a complex environment. The introduced framework is expected to find important applications in the enhancement of light–matter interactions in photonic materials as well as to enhance energy harvesting.

Upper mantle anisotropy in the northwest Himalaya and Ladakh-Karakoram zone based on SKS splitting analysis

Seismic anisotropy of the upper mantle beneath the northwest Himalaya and eastern part of the Ladakh-Karakoram zone has been investigated using shear-wave splitting of core-mantle refracted SKS waveforms from 94 teleseismic earthquakes recorded at 28 broadband seismic stations. The SKS splitting parameters (Φ and δt) show a significant strength of anisotropy with a wide range of delay time of split waves (∼0.75−2.94 s). The distinct variations in Fast Polarization Directions (FPDs) along the study section suggest a complex source of anisotropy that cannot be explained by a simple model. In the frontal part of the Himalaya, the FPDs are mostly parallel or sub-parallel to the strike of the Himalayan orogeny suggesting deformation in the shallow lithospheric mantle under compression owing to the India-Asia collision. On the other hand, FPDs observed in the Lesser, Higher, and Tethyan Himalaya largely follow NE-oriented absolute plate motion (APM) of the Indian plate which can be attributed to basal shear as the Indian plate moves over the asthenospheric mantle with a minor contribution from shallow lithospheric deformation. A complex anisotropy pattern is observed in the Indus Suture Zone. The FPDs near the Karakoram Fault Zone (KFZ) are parallel or sub-parallel to the strike of the KF. The strike-slip or transpressional deformation in the lithospheric mantle in the KFZ is considered as the major source of anisotropy beneath the KFZ. The study envisaged that the KF is a lithospheric scale fault that largely accommodates the India-Asia collision and extrusion in the Tibetan Plateau.

Delay time of waves performing L\xe9vy walks in 1D random media

The time that waves spend inside 1D random media with the possibility of performing Lévy walks is experimentally and theoretically studied. The dynamics of quantum and classical wave diffusion has been investigated in canonical disordered systems via the delay time. We show that a wide class of disorder—Lévy disorder—leads to strong random fluctuations of the delay time; nevertheless, some statistical properties such as the tail of the distribution and the average of the delay time are insensitive to Lévy walks. Our results reveal a universal character of wave propagation that goes beyond standard Brownian wave-diffusion.

Transient quantum beats, Rabi oscillations, and delay time of modulated matter waves

Transient phenomena of phase modulated cut-off wavepackets are explored by deriving an exact general solution to Schr\"odinger's equation for finite range potentials involving arbitrary initial quantum states. We show that the dynamical features of the probability density are governed by a virtual \textit{self-induced two-level system} with energies $E_{+}$, and $E_{-}$, due to the phase modulation of the initial state. The asymptotic probability density exhibits Rabi-oscillations characterized by a frequency $\Omega=(E_{+}-E_{-})/\hbar$, which are independent of the potential profile. It is also found that for a system with a bound state, the interplay between the virtual levels with the latter causes a \textit{quantum beat} effect with a beating frequency, $\Omega$. We also find a regime characterized by a \textit{time-diffraction} phenomenon that allows to measure unambiguously the delay-time, which can be described by an exact analytical formula. It is found that the delay-time agrees with the phase-time only for the case of strictly monochromatic waves.

РАСПРОСТРАНЕНИЕ ПУЛЬСОВОЙ ВОЛНЫ ПО МАЛЫМ СОСУДАМ: РЕЗУЛЬТАТЫ ИЗМЕРЕНИЙ И ПОДХОДЫ К МОДЕЛИРОВАНИЮ

The objective of the research work was to develop devices and algorithm for synchronous recording of pulse waves and ECG for measuring the delay time of pulse waves in the branches of various arteries relative to the R wave on an ECG, and to carry out computer simulation of the pulse wave propagation process to determine the dependence of the pulse wave propagation velocity on branching and other hemodynamic and morphological parameters of blood vessels. Material and methods. The study was conducted in 74 healthy subjects aged 18-23 years. The propagation time of the pulse wave by the arterial branches of the vessels of the common carotid, internal, external carotid and radial arteries was measured. The time was calculated by the delay of the beginning of the pulse wave relative to the tip of the R wave on the ECG. Vascular pulsations were recorded using mechanical sensitive and photosensitive sensors, which signals were amplified, digitized, recorded and analyzed using original computer soft wares. Computer simulation of the propagation of pulse waves along the wall of an “equivalent” vessel corresponding to the branching of several arterial vessels was carried out. Results. The velocity of propagation of a pulse wave along the branches of small arterial vessels was lower than its value for larger main arteries. The simulation results confirmed that the propagation velocity of a pulse wave can significantly slow down its movement along branched arterial vessels, which differ in the mechanical properties of the main arteries. Conclusion. The data obtained indicate that the developed devices and measurement algorithms make it possible to register pulse waves of various small arteries and obtain reproducible indices of the delay time of the pulse wave relative to the R wave on the ECG. The time and velocity of the pulse wave propagation depends on the length of the studied vessels, the mechanical properties of the walls of the vessels, which follows from the comparison of the obtained data with the morphological features of the structure of vascular networks. Simulation results for an “equivalent” vessel show that one of the possible causes of a lower pulse wave propagation velocity in small vessels is lower mechanical properties of the branches of small vessels compared with those of larger arteries. However, the identification of the nature of these dependencies and their connection with stiffness of the walls of small vessels requires further study.

Location and Length Measurement of Invisible Fatigue Crack in Metal Components Using Wave Mixing Methods

Abstract For the invisible fatigue crack embedded in metal components, wave mixing methods are applied for the fatigue crack location and length measurement. When two incident waves meet within a component, a nonlinear interaction occurs and a third wave is generated, which is related to the damage degree of the meeting position of the two incident waves. When the delay time of incident waves changed in collinear wave mixing experiments, different meeting positions along the length direction of components were detected. The relationship between the sideband amplitude at difference or sum frequencies and delay time is obtained, and the delay time corresponding to the maximum amplitude is applied to locate the fatigue crack along the length direction. Then, adjusting the placing locations of transducers in the noncollinear wave mixing experiment, the meeting position of incident waves is controlled at the fatigue crack decided by the collinear wave mixing experiment. Next, changing the separation distance of two transmitters, the detection positions would be along the vertical direction of the components. The mixing nonlinear parameters of different detection positions are calculated, and the length of the fatigue crack can be measured in a vertical direction based on the distribution of the mixing nonlinear parameter.

Upper‐Crustal Anisotropy of the Conjugate Strike‐Slip Fault Zone in Central Tibet Analyzed Using Local Earthquakes and Shear‐Wave Splitting

Abstract Remarkable V‐shaped conjugate strike‐slip faults extend along the Bangong–Nujiang suture in central Tibet. Motions of these faults are considered to accommodate ongoing east–west extension and north–south contraction. Fabrics within the fault zone that are anisotropic to seismic waves can provide clues as to the unusual scale and style of lithospheric deformation. With the goal of determining the upper‐crustal anisotropy pattern in central Tibet, we measured shear‐wave splitting parameters (fast wave polarization direction and delay time) using waveforms generated by 194 local earthquakes recorded by 49 stations of the SANDWICH network. Stations located in eastern and western zones of the study area show anisotropy directions that agree well with the maximum horizontal compressive stress direction. The fast polarization directions at stations near active strike‐slip faults generally run parallel to the strikes of these faults. Pervasive inactive thrust faults caused by Cretaceous–Tertiary shortening in central Tibet also clearly correlate with the anisotropy detected at nearby stations. These results demonstrate that both local structures and stress contribute to upper‐crustal anisotropy in the region. Combining the new results with previous SKS‐wave splitting results and other seismic evidence, we propose that deformation in the upper crust is mechanically decoupled from that in the upper mantle, due to eastward middle‐lower crustal flow. This crustal flow causes basal shearing required for the formation of conjugate strike‐slip faults in central Tibet.

Seismic interferometry for earthquake-induced damage identification in historic masonry towers

The inherent vulnerability of masonry structures to seismic events makes Structural Health Monitoring of pivotal importance for the conservation of architectural heritage. In this regard, methods based on Operational Modal Analysis are becoming popular for damage identification. Nonetheless, these techniques may fail at detecting local damages with limited effects on the modal properties of the system. Recent studies report seismic interferometry to be a promising alternative for seismic damage identification of structures. This technique assesses the travelling times of propagating seismic waves between pairs of sensors, which are directly related to the local stiffness of the structure. Therefore, damage-induced degradation can be tracked through wave time delays. While some encouraging results have been reported on the application of acceleration-based seismic interferometry to reinforced-concrete structures, the number of works on masonry structures is far scarce. In this light, this paper is aimed at investigating the suitability of acceleration- and strain-based seismic interferometry for damage identification in historic masonry towers. To do so, an analytical layered Timoshenko beam model is devised for the wave propagation analysis of masonry towers under base motion. Parameter sensitivity analyses are first reported, with a special focus on the effects of dispersion upon system identification results. Secondly, a validation case study of a 41.6 m high masonry tower is presented. A realistic three-dimensional non-linear finite element model is built and subjected to seismic inputs causing increasing damage severities. The numerical results, used as pseudo-experimental data, demonstrate that it is possible to identify (detect, localize and quantify) earthquake-induced damages by wave propagation analysis of strain/acceleration records and inverse calibration of the proposed Timoshenko beam model. A particularly notable result is the possibility of detecting, localizing and, to some extent, quantifying earthquake-induced damage in a fully data-driven way by simply measuring wave travel times between pairs of sensors.

The Gravitational waves merger time distribution of binary neutron star systems

Binary neutron stars (BNSs) mergers are prime sites for r-process nucleosynthesis. Their rate determines the chemical evolution of heavy elements in the Milky Way. The merger rate of BNS is a convolution of their birth rate and the gravitational radiation spiral-in delay time. Using the observed population of Galactic BNS we show here that the lifetimes of pulsars in observed BNSs are sufficiently short that the ages of BNSs have little to no effect on the observed merger time distribution. We find that at late times (t ≳ 1 Gyr) the gravitational wave delay time distribution (DTD) follows the expected t−1. However, a significant excess of rapidly merging systems (between |$40\,\,\mathrm{ and}\,\,60{{\ \rm per\ cent}}$| of the entire population) is apparent at shorter times. Although the exact shape of the DTD cannot be determined with the existing data, in all models that adequately describe the data we find at least |$40{{\ \rm per\ cent}}$| of BNSs with merger times less than 1 Gyr. This population of garapid mergers implies a declining deposition rate of r-process materials that is consistent with several independent observations of heavy element abundances in the Milky Way. At the same time this population that requires initial binary separations of roughly one solar radius clearly indicates that these binaries had common envelope progenitors. Our results suggest that a significant fraction of future LIGO/Virgo BNS mergers would reside in star-forming galaxies.

P Wave Teleseismic Traveltime Tomography of the North American Midcontinent

AbstractThe remains of the 1.1‐Ga Midcontinent Rift (MCR) lie in the middle of the tectonically stable portion of North America. Previous and ongoing studies have imaged strong heterogeneity associated with the MCR in the crust but have not imaged such within the mantle. It is unclear whether this is due to the absence of rift‐related mantle structures or these studies had insufficient resolution to image them. To address this issue, we measured 46,374 teleseismic P wave delay times from seismograms recorded by the USArray Transportable Array, Superior Province Rifting EarthScope Experiment, and surrounding permanent stations. We included these and 54,866 delay times from prior studies in our tomographic inversion. We find that high‐velocity anomalies are widespread in our study area, but there are also prominent low‐velocity anomalies. Two of these are coincident with high‐Bouguer gravity anomalies associated with the MCR in Iowa and the Minnesota/Wisconsin border at 50‐ to 150‐km depth. Extensive resolution testing shows that these anomalies could be the result of downward vertical smearing of relatively low velocities from rift‐related material that “underplated" the crust, although we cannot exclude that the subcrustal mantle lithosphere beneath the MCR is anomalously enriched, hydrated, or warm. Other anomalies occur at syntaxes of the Penokean Orogen. One with the Superior Province and Marshfield Terrane in southern Minnesota and another with the Yavapai and Mazatzal Terranes, both at 100‐ to 250‐km depth. In the midmantle, we image two linear high‐velocity anomalies, interpreted as subducted fragments of the Farallon and Kula plates.