This review discusses several computational methods used on different length and time scales for the simulation of material behavior. First, the importance of physical modeling and its relation to computer simulation on multiscales is discussed. Then, computational methods used on different scales are shortly reviewed, before we focus on the molecular dynamics (MD) method. Here we survey in a tutorial-like fashion some key issues including several MD optimization techniques. Thereafter, computational examples for the capabilities of numerical simulations in materials research are discussed. We focus on recent results of shock wave simulations of a solid which are based on two different modeling approaches and we discuss their respective assets and drawbacks with a view to their application on multiscales. Then, the prospects of computer simulations on the molecular length scale using coarse-grained MD methods are covered by means of examples pertaining to complex topological polymer structures including star-polymers, biomacromolecules such as polyelectrolytes and polymers with intrinsic stiffness. This review ends by highlighting new emerging interdisciplinary applications of computational methods in the field of medical engineering where the application of concepts of polymer physics and of shock waves to biological systems holds a lot of promise for improving medical applications such as extracorporeal shock wave lithotripsy or tumor treatment.

The governing Partial Differential Equation (PDE) for wave propagation or the wave equation involves multi-scale and multi-dimensional oscillatory phenomena. Wave PDE challenges traditional computational methods due to high computational costs with rigid assumptions. The advent of scientific machine learning (SciML) presents a novel paradigm by embedding physical laws within neural network architectures, enabling efficient and accurate solutions. This study explores the evolution of SciML approaches, focusing on PINNs, and evaluates their application in modeling acoustic, elastic, and guided wave propagation. PINN is a gray-box predictive model that offers the strong predictive capabilities of data-driven models but also adheres to the physical laws. Through theoretical analysis and problem-driven examples, the findings demonstrate that PINNs address key limitations of traditional methods, including discretization errors and computational inefficiencies, while offering robust predictive capabilities. Despite current challenges, such as optimization difficulties and scalability constraints, PINNs hold transformative potential for advancing wave propagation modeling. This comprehensive study underscores the transformative potential of PINN, followed by recommendations on why and how it could advance elastic, acoustic, and guided wave propagation modeling and sets the stage for future research in the field of Structural Health Monitoring (SHM)/Nondestructive Evaluation (NDE).

Observations of seismic body waves that traverse the Earth's inner core (IC) as shear (J) waves are critical for understanding the IC shear properties, advancing our knowledge of the Earth's internal structure and evolution. Here, we present several seismological observations of J phases detected in the earthquake late-coda correlation wavefield at periods of 15-50 s, notably via the correlation feature I-J, found to be independent of the Earth reference velocity model. Because I-J is unaffected by compressional wave speeds of the Earth's inner core, outer core, and mantle, it represents an autonomous class of seismological measurements to benchmark the inner core properties. We estimate the absolute shear-wave speed in the IC to be 3.39 ± 0.02 km/s near the top and 3.54 ± 0.02 km/s in the center, lower than recently reported values. This is a 3.4 ± 0.5% reduction from the Preliminary Reference Earth Model (PREM), suggesting a less rigid IC than previously estimated from the normal mode data. Such a low shear-wave speed requires re-evaluating IC composition, including the abundance of light elements, the atomic properties and stable crystallographic phase of iron, and the IC solidification process.

Perturbation method is then applied to derive the dispersion equation for the propagation of Love waves. This dispersion equation is graphically analysed using MATLAB to observe how the dimensionless phase velocity changes with dimensionless wave number for different values of the inhomogeneity parameter and various values of the ratio of irregularity depth to layer height. The obtained results show that both rectangular-shaped interface irregularity and inhomogeneity significantly affect phase velocity, particularly at the lower wave numbers. This study enhances the understanding of surface wave behaviour in complex elastic structures and provides practical implications for subsurface imaging, seismic hazard assessment, and material characterization in civil engineering and geotechnical applications. Published in Journal of Nigerian Society of Physical Sciences

Seismic Rayleigh waves on an exponentially graded, orthotropic half-space Efforts at modelling the propagation of seismic waves in half-spaces with continuously varying properties have been mostly focused on shear-horizontal waves. Here a sagittaly polarized (Rayleigh type) wave travels along a symmetry axis (and is attenuated along another) of an orthotropic material with stiffnesses and mass density varying in the same exponential manner with depth. Contrary to what could be expected at first sight, the analysis is very similar to that of the homogeneous half-space, with the main and capital difference that the Rayleigh wave is now dispersive. The results are illustrated numerically for (i) an orthotropic half-space typical of horizontally layered and vertically fractured shales and (ii) for an isotropic half-space made of silica. In both examples, the wave travels at a slower speed and penetrates deeper than in the homogeneous case; in the second example, the inhomogeneity can force the wave amplitude to oscillate as well as decay with depth, in marked contrast with the homogeneous isotropic general case.

systems—results in intelligence that detects, tracks, identifies or describes the signatures (distinctive characteristics) of fixed or dynamic target sources. MASINT Geophysical MASINT is a branch of Measurement and Signature Intelligence (MASINT) that involves phenomena transmitted through the earth (ground, water, atmosphere) and manmade structures including emitted or reflected sounds, pressure waves, vibrations, and magnetic field or ionosphere disturbances. According to the United States Department of Defense, MASINT has technically derived intelligence ( Geophysical MASINT is a branch of Measurement and Signature Intelligence (MASINT) that involves phenomena transmitted through the earth (ground, water, atmosphere) and manmade structures including emitted or reflected sounds, pressure waves, vibrations, and magnetic field or ionosphere disturbances. According to the United States Department of Defense, MASINT has technically derived intelligence (excluding traditional imagery IMINT and signals intelligence SIGINT) that—when collected, processed, and analyzed by dedicated MASINT systems—results in intelligence that detects, tracks, identifies or describes the signatures (distinctive characteristics) of fixed or dynamic target sources. MASINT was recognized as a formal intelligence discipline in 1986. Another way to describe MASINT is a "non-literal" discipline. It feeds on a target's unintended emissive by-products, the "trails"—the spectral, chemical or RF that an object leaves behind. These trails form distinct signatures, which can be exploited as reliable discriminators to characterize specific events or disclose hidden targets." As with many branches of MASINT, specific techniques may overlap with the six major conceptual disciplines of MASINT defined by the Center for MASINT Studies and Research, which divides…

Analyse Isogéométrique Non-Structurée avec Applications à la Propagation des Ondes Sismiques Dans ce travail, on explore l’utilisation des espaces de fonctions splines non-structurées dans la résolution des problèmes hyperboliques discrétisés par des schémas en temps explicites, et en particulier le problème de la propagation des ondes acoustiques avec conditions aux limites absorbantes, et son problème inverse associé, l’inversion sismique.Notre analyse repose sur la définition, connue, de spline simplexe à travers les projections de polyèdres et les moyennes de Dirichlet, et on se concentre en particulier sur la construction d’espaces de splines simplexes capables de reproduire les polynômes. On introduit des espaces de splines associées aux pavages fins de zonotopes, ce qui constitue une extension combinatoire de certains résultats connus sur les configurations de Delaunay, et permet de construire des espaces de fonctions splines sur des configurations incluant des points répétés et affinement dépendants. La réduction de la régularité de l’espace de fonctions qui en découle permet de définir des conditions aux limites, ainsi que de subdiviser l’espace de splines en sous-domaines. De plus, les propriétés combinatoires des pavages de zonotopes nous permettent de dériver un certain nombre d’algorithmes utiles pour la construction de l’espace de splines dans n’importe quel nombre de dimensions, généralisant un algorithme connu en dimension deux d'espace, ainsi que pour l’évaluation de toutes les fonctions splines de l'espace en un point donné. On se sert des espaces précédemment construits afin de définir une version non-structurée des schémas multi-patch Galerkine discontinu (DG) – analyse isogéométrique (IGA) connus, puis on montre que le schéma usuel DG Bernstein-Bézier ainsi que la version complètement non-structurée du schéma IGA sont des cas particuliers de cette méthode. On montre aussi que le comportement de ces espaces de fonctions splines à proximité des bords externes et internes est très proche de celui des fonctions standards utilisées dans les schémas DG, ce qui nous permet de dériver des inégalités inverses simples et de réutiliser certains résultats connus concernant la coercivité et l’analyse d’erreur a priori qui avait été développés à l'origine pour la méthode de Galerkine discontinue avec pénalisation symétrique (IPDG). On illustre les propriétés numériques de notre schéma de discrétisation à travers un certain nombre d’expériences numériques.Pour terminer, on explore certaines applications possibles des fonctions splines non-structurées pour le problème d’inversion sismique, en utilisant la technique de l’inversion des formes d’ondes complètes (FWI). Plus précisément, on interprète la position des nœuds définissants les fonctions splines comme des degrés de liberté d’inversion, en utilisant certaines propriétés connues sur les dérivées de ces fonctions afin d’optimiser le processus. Comme la fonction de coût utilisée en FWI n’est pas en général différentiable par rapport aux degrés de liberté géométriques, on introduit cette technique en utilisant la notion de sous-différentiel, et on montre que la technique de l’état adjoint, utilisée pour le calcul du gradient de la fonction coût, peut être dérivée simplement d’un théorème connu de dualité convexe, qui est aussi valable pour les fonctions convexes non-différentiables.

With the widespread application of acoustic emission (AE) technology in geotechnical engineering, effectively separating and identifying dense AE signals generated during rock fracturing remains a critical challenge. This study proposes an AE event identification technique based on waveform energy envelopes and multi-indicator characteristic parameters. First, the waveform energy envelope is used to adaptively segment dense and partially overlapping AE waveforms without relying on fixed timing parameters. Then, a template sliding-window scan integrating waveform correlation, ring count, rise time, and signal energy is performed to identify candidate AE events. In addition, a time-difference correction and window-stacking strategy is adopted to improve multi-channel arrival picking. Experimental validation on representative single-peak single-event and double-peak multi-waveform cases extracted from laboratory rock-failure tests demonstrates that the proposed method can effectively separate and identify AE waveforms under the tested conditions. Compared with conventional timing-parameter-based segmentation and correlation-dominated matching, the proposed workflow is more robust to waveform attenuation and distortion. The method provides a methodological basis for AE waveform identification and arrival-time extraction in rock-failure monitoring and has potential to support early warning after further validation.

Seismic Phases | Springer Nature Link # Seismic Phases - Reference work entry - pp 903–908 - Cite this reference work entry Save reference work entry Encyclopedia of Geomagnetism and Paleomagnetism The body wave portion of a seismogram is marked by the arrival of distinct bursts of energy which we associate with different classes of propagation path through the Earth, as illustrated in Figure S18, where the arrivals are marked with their phase code. The individual seismic arrivals sample different parts of the Earth in their passage between the source and the receiver and their properties are dictated by the structure they encounter. Thus the time of arrival of PcP which is reflected from the core‐mantle boundary is a strong function of the radius of the core. Information from many different phases, with sensitivity to structure in different parts of the Earth, is used in the construction of models of seismic wavespeed. Figure S18 Three‐component seismogram from an intermediate depth earthquake in Vanuatu recorded in Kazakhstan at approximately 100° from the source, showing a rich set of seismic phase arrivals. ## Access this chapter Log in via an institution ## Bibliogr

of reflected wave physically persists among all the reflected waves. This type of reflected wave is identical to the incident wave. iii. The energy shares associated with distinct energy types are functions of incident direction, water saturation, porosity, inclusion radius, WIFF, and wave frequency. iv. For the incidence of the wave, an increase in porosity and inclusion radius strengthens (weakens) the reflected wave but weakens (strengthens) the refracted SV wave. Other reflected waves may weaken slightly with the increase in porosity and inclusion radius in both cases. v. For the incidence of the wave, an increase in water saturation weakens (strengthens) the reflected wave but strengthens (weakens) the refracted SV wave. Other reflected waves may strengthen slightly with the increase in water saturation in both cases. vi. The increase in wave frequency weakens the reflected wave for both incident waves. In contrast, all other refracted waves may strengthen with the increase in frequency. vii. The energy partition remains unchanged near grazing incidence for longitudinal waves despite variations in porosity, inclusion radius, water saturation, and frequency for the incidence of the wave. In contrast, the SV wave is unaffected at both normal and grazing incidences. viii. It has been demonstrated that the conservation law for incident energy is upheld at all angles of incidence during the reflection process. To accurately account for the distribution of energy among the various reflected waves, it is essential to consider the energy dissipated during the interference process that occurs between different pairs of waves in the dissipative medium. This further substantiates the correctness of the numerical calculations from an analytical perspective. ix. For the incidence of the wave, the reflected wave is amplified across the entire range of incident directions in the presence of WIFF. A similar behavior is observed for the and waves in the presence of WIFF for bo

Multi-phase seismic source imprint of tropical cyclones | Nature Communications ### Subjects - Seismology - Solid Earth sciences ## Abstract The coupling between the ocean activity driven by winds and the solid Earth generates seismic signals recorded by seismometers worldwide. The 2–10 s period band, known as secondary microseism, represents the largest background seismic wavefield. While moving over the ocean, tropical cyclones generate particularly strong and localized sources of secondary microseisms that are detected remotely by seismic arrays. We assess and compare the seismic sources of P, SV, and SH waves associated with typhoon Ioke (2006) during its extra-tropical transition. To understand their generation mechanisms, we compare the observed multi-phase sources with theoretical sources computed with a numerical ocean wave model, and we assess the influence of the ocean resonance (or ocean site effect) and coastal reflection of ocean waves. We show how the location and lateral extent of the associated seismic source is period- and phase-dependent. This information is crucial for the use of body waves for ambient noise imaging and gives insights about the sea state, com

Path Corrections for Source Discriminants: A Case Study at Two International Seismic Monitoring Stations | Pure and Applied Geophysics | Springer Nature Link # Path Corrections for Source Discriminants: A Case Study at Two International Seismic Monitoring Stations - Published: February 2002 - Cite this article - Volume 159, pages 651–678, (2002) Save article View saved research pure and applied geophysics Aims and scope Submit manuscript ## Abstract — Improving the performance of short-period regional seismic discriminants by applying propagation corrections is explored using observations from two seismic monitoring stations in Asia. Frequency-dependent regional phase amplitude ratio measurements at stations NIL and ZAL for earthquakes and underground nuclear explosions were obtained from the prototype-International Data Center (pIDC) that has been established for developing monitoring capabilities of the Comprehensive Nuclear-Test-Ban Treaty (CTBT). The pIDC discriminant measurements have large scatter, much of which is attributed to wave propagation effects in the heterogeneous crustal waveguide. Linear regressions indicate that the phase ratios are correlated with topogr

Analytical representation of phase characteristics for source time function modeled by stochastic impulse train - ScienceDirect [Skip to main content](#screen-reader-main-content)[Skip to article](#screen-reader-main-title) [ScienceDirect](https://www.sciencedirect.com/) [My account](https://www.sciencedirect.com/user/login?targetURL=/science/article/pii/S0267726102001045&from=globalheader) [Sign in](https://www.sciencedirect.com/user/institution/login?targetURL=/science/article/pii/S0267726102001045) * [Access through**your institution**](https://www.sciencedirect.com/user/institution/login?targetUrl=/science/article/pii/S0267726102001045) * [Purchase PDF](https://www.sciencedirect.com/getaccess/pii/S0267726102001045/purchase) Search ScienceDirect ## Article preview * [Abstract](#preview-section-abstract) * [Introduction](#preview-section-introduction) * [Section snippets](#preview-section-snippets) * [References (5)](#preview-section-references) * [Cited by (1)](#preview-section-cited-by) [![Elsevier](https://sdfestaticassets-us-east-1.sciencedirecta