Seismic Spectrum Research Articles

Impact of several seismic scenarios on the dynamic responses of self-steady structures of different heights

Seismic load resistance is a crucial aspect of safety for self-stabilizing reinforced concrete (RC) structures, which are particularly vulnerable to damage caused by destructive earthquakes. These structures, often used in high seismic risk areas, require special attention to ensure their stability and durability under significant dynamic demands. This study focuses on the dynamic responses of low- and medium-rise RC buildings subjected to various seismic response spectra, including those from historic earthquakes such as El-Centro, Kobe, and Boumerdès (recorded at the Dar El-Beida station in Algeria), as well as the spectrum provided by the Algerian seismic code RPA 99/version 2003. The analysis examines three structures with 1, 3, and 6 stories to evaluate the influence of these spectra on key parameters: shear forces, maximum displacements, the ratio between dynamic and static base shear, and overturning moments. These investigations contribute to a deeper understanding of structural behavior under diverse seismic scenarios. The findings emphasize the need to complement the RPA99/v2003 code with studies based on real earthquakes to better address various structural periods and ensure optimal seismic design practices.

Exploring seismic warning thresholds for vehicle-track systems through combined shaking table tests and dynamic numerical simulations

This study conducted vehicle-track shaking table model tests at the Seismic Laboratory of the China Academy of Building Research, employing both unidirectional (horizontal) and bidirectional (horizontal and vertical) seismic waves. Discussions were made on the dynamic response of the vehicle-track system and the mechanism of derailment, providing data support for the research on seismic early warning thresholds for vehicles. Additionally, three-dimensional finite element numerical simulations were performed on the vehicle-track dynamic model, successfully incorporating track irregularities into the model. In this paper, the main conclusions are as follows: The limits of the wheel load reduction rate and that of the derailment coefficient specified in China’s national standard “Code for Dynamic Performance Evaluation and Test Identification of Railway Vehicles” are conservative. The primary cause of vehicle derailment was identified as horizontal vibration of the track structure induced by seismic activity. Different seismic waves have varying effects on the dynamic response of the vehicle-track model, necessitating further research on the impact of seismic wave spectrum characteristics on vehicle safety during operation. When horizontal and vertical seismic waves are simultaneously applied, horizontal seismic waves have a greater impact on dynamic response. The numerical simulation results align well with experimental results, confirming the accuracy of the vehicle-track dynamic numerical model. It is recommended to adopt a more conservative seismic early warning threshold of 0.04 g to ensure the safety of train operation.

Dynamic model and performance assessment of inter-story isolation system with supplement inerter (IISI)

The hybrid control combining the conventional seismic isolation and tuned mass damper inerter is recently gaining popularity for the seismic protective strategy. This paper presents a simplified dynamic model of the inter-story isolation system with a supplement inerter (IISI) for seismic performance assessment. The dynamic characteristics, such as modal frequencies, mode shapes, damping ratios, and participation factors, as well as the seismic response spectrum, were studied considering the importance of the equivalent linear model for seismic design. The vibration characteristic formula of the IISI was derived using a simplified 2-degree-of-freedom (2DOF) model. The influence of the calculated parameters of the model on the vibration characteristics was analyzed. To understand the isolation control mechanism, the response transfer function in the frequency domain was derived, and the effects of model parameters on the deformation amplitude amplification factor of the superstructure and substructure were analyzed. Based on equivalent linear properties, a seismic response prediction formula based on the response spectrum method is provided and verified by time history analysis (THA). The effect of soil-structure interaction (SSI) on the simplified 4-DOF model was also studied. The seismic responses and effectiveness of the IISI were evaluated using a Multi-degree-of-freedom (MDOF) model example. The research results demonstrate that the addition of an inerter changes the vibration characteristics of the traditional isolation system. The supplement inerter is effective in controlling the seismic response of the IISI, and the established analysis method can be used to analyze the seismic response of the IISI by incorporating additional inerter mounted in the isolation layer. The hybrid control strategy shows better effectiveness in reducing displacement in the isolation layer.

Dynamic response analysis of pipelines in gas distribution stations under seismic loads

Seismic loads in earthquake-prone regions significantly affect the structural integrity of pipelines at urban natural gas distribution stations, compromising safety. This study analyzes the dynamic response of pipelines in gas distribution stations under seismic loading and proposes effective measures to mitigate stress concentration. A numerical model of the pipeline in the gas distribution station, based on actual cases, was established. The material’s constitutive relationship was derived from tensile tests. The seismic response spectrum, obtained from ground motion data, was introduced to analyze the pipeline’s mechanical behavior. The dynamic response analysis identified critical stress concentration locations in the pipeline under operational conditions. Based on displacement analysis, the study recommended seismic measures. Results indicated that under seismic loading, higher stress values occurred primarily in pipeline sections with intricate flow pattern variations. The manifold connection was the most vulnerable point, with its average stress being 3.37 times that of the system’s average stress. The proposed seismic measures effectively reduced stress concentration at these critical points, mitigating the earthquake’s impact on the gas distribution station. This study establishes a theoretical framework for improving the seismic design and maintenance of natural gas distribution stations, enhancing their seismic resilience and operational safety.

Experimental study and numerical analysis of a novel serrated-and-plate truss structure

High-speed rail station has extensive span and height, making daylighting a challenge. This paper proposes the serrated-and-plate truss structure (SPTS) to improve station daylighting. SPTS combines a serrated truss structure (STS) for daylighting and a plate truss structure (PTS) for lateral stability and deformation resistance. A downscaled SPTS with support-loading system is designed and built to test mechanical properties. It has 264 stress and 19 displacement measuring points, tested under four vertical and two horizontal load cases. Maximal stress and displacement are 150.7 MPa and 5.07 mm, with peak chord axial force and column base bending moment of 13.5 kN and 663.7 kN mm. Simulated and measured results match well, confirming the numerical method's accuracy. Thermal effects of SPTS are studied via conventical and extreme thermal analyses, with stress and displacement well below limits. Seismic spectrum and time-history analyses indicate SPTS stress and deformation at 63.9 % and 68.3 % of limits. Comparative analysis across 64 load cases reveal that STS is significantly less stable and resistant to deformation than SPTS, validating PTS's boundary constraint effects. Experimental and numerical studies confirm SPTS's engineering applicability and provide valuable references for similar truss structure research.

A Pn-wave spectral inversion technique based on trust region reflective algorithm

This paper suggests utilizing the trust region reflective (TRR) algorithm to address the inverse problem related to seismic spectrum analysis of Pn waves. By applying this approach, it becomes feasible to simultaneously deduce the seismic moment, corner frequency, tomographic model of Pn-wave attenuation, and site responses while incorporating appropriate constraints based on prior knowledge to ensure solution accuracy. The efficacy of this method has been validated using synthetic data. Specifically, the recorded Pn waves from four underground explosions in North Korea were employed to evaluate the performance of the proposed technique. The derived seismic moment and corner frequency for these events were found to align with the characteristics of the seismic data, earthquake magnitude calculations, and empirical data. The resulting tomographic model of Pn-wave attenuation revealed a spatial distribution of high and low attenuation, indicating significant lithospheric heterogeneity in northeastern China. Areas with low Q0 and low η, such as the Xialiaohe Basin and southwestern Changbai Mountain, suggest a high-temperature environment in the upper mantle cap layer or the presence of molten substances. Conversely, regions with high Q0 and high η, like the northern Changbai Mountain and the vicinity of the eastern Tanlu Fault Zone, characterized by high Pn-wave velocity and thick crust, indicate minimal modification or destruction in the lithosphere. Furthermore, site responses were determined for 75 seismic stations in northeastern China, with their characteristics preliminarily analyzed and interpreted in conjunction with geological context. The iterative process based on the TRR algorithm for Pn-wave spectral inversion proposed in this study demonstrates robust convergence and enhances the fitting accuracy of the observed spectrum. The inversion outcomes from this spectral technique yielded synthetic Pn-wave spectra that closely matched the observed spectra of the four underground explosions in North Korea across various frequency bands for over 90 % of the stations.

Forecasting ocean wave-induced seismic noise

Ocean waves induce the power peak in the seismic ground motion seen everywhere in the world between 0.03 and ~ 1 Hz, defining the seismic noise baseline. The precise generation mechanisms are well understood, and the dependence of seismic noise on sea weather has been precisely quantified using long-term time series. However, this knowledge has never been exploited to forecast the seismic noise background. Here we report the prediction of the seismic noise spectrum around 1 Hz at the Low-Noise Underground Laboratory (LSBB) in Rustrel, for up to 16 days in advance, limited by the time span of sea weather forecasts. We first characterize the dependence of the seismic noise at the LSBB on the Mediterranean Sea and Atlantic Ocean weather, using buoy data for 2020–2021. We exploit significant correlation in the 0.15Hz<f<2.5Hz\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0.15~\ extrm{Hz}< f < 2.5~\ extrm{Hz}$$\\end{document} frequency band to make predictions, converting sea weather forecasts into seismic noise forecasts. The expected seismic background noise can be used to optimize the performance and running costs of scientific and industrial activities, by scheduling them during quiet intervals or adopting adaptive data analysis techniques to identify target signals in the predicted noise.

Probabilistic Programming for Transportable Source Characterization and Uncertainty Quantification of the North Korean Nuclear Tests 2006–2017

Abstract We introduce a transportable technique to determine the yield and depth of burial (DOB) from seismic source spectra of underground nuclear explosions. We demonstrate this technique on the six declared North Korean nuclear tests. This approach derives source spectra in absolute units from regional phase (Pg) amplitudes by correcting the observations for geometric spreading, attenuation, and site amplification. We couple the source spectra and explosion source models with a probabilistic programming framework that integrates deep learning techniques and Bayesian modeling. This approach permits the exchange of information across various data categories to quantify both the data and model uncertainty. This technique stands out as an innovative use of broad-area propagation models, making it transportable across various geologic settings. This method proves to be effective in scenarios with diverse and/or limited observational data, even when the source depth is unknown. We present new independent estimates of absolute yield and DOB that are consistent with the prior assessments, underscoring the potential of this method in enhancing transportable nuclear explosion monitoring capabilities.

Novel small-size seismic metamaterial with ultra-low frequency bandgap for Lamb waves

Seismic metamaterials (SMs) possess bandgap characteristics, enabling effective attenuation of seismic waves within a specific frequency range. However, small-sized SMs typically struggle to achieve a wide low-frequency bandgap. This paper proposes four types of SMs. The dispersion curves of these models were analyzed, and their vibration modes were studied to elucidate the bandgap mechanism. To investigate the influence of structural parameters on the bandgap, geometric variables are analyzed. Subsequently, the spectrum and acceleration time history curves of Lamb waves in a finite SM system are analyzed to verify the bandgap's authenticity. The designed structure exhibits a bandgap ranging from 1.24 Hz to 16.86 Hz, with a relative bandwidth as high as 172.6% and over 96% maximum vibration displacement attenuation of the El Centro seismic wave. The designed SMs effectively cover the 2 Hz seismic peak spectrum that leads to structural damage. They possess ideal relative bandwidth and excellent isolation performance, further advancing the engineering application of SMs.

The Stagger Code for Accurate and Efficient, Radiation-coupled Magnetohydrodynamic Simulations

We describe the Stagger code for simulations of magnetohydrodynamic (MHD) systems. This is a modular code with a variety of physics modules that will let the user run simulations of deep stellar atmospheres, sunspot formation, stellar chromospheres and coronae, proto-stellar disks, star formation from giant molecular clouds, and even galaxy formation. The Stagger code is efficiently and highly parallelizable, enabling such simulations with large ranges of both spatial and temporal scales. We describe the methodology of the code and present the most important of the physics modules, as well as its input and output variables. We show results of a number of standard MHD tests to enable comparison with other, similar codes. In addition, we provide an overview of tests that have been carried out against solar observations, ranging from spectral line shapes, spectral flux distribution, limb darkening, intensity and velocity distributions of granulation, to seismic power spectra and the excitation of p-modes. The Stagger code has proven to be a high-fidelity code with a large range of uses.

Seismic wavelet shape-oriented reflectivity inversion method

Abstract Reflectivity inversion plays a pivotal role in reservoir prediction. Conventional sparse-spike deconvolution assumes that the reflectivity (reflection coefficient) is sparse, which is solved based on the l1 norm. However, the restricted isometry property (RIP) of wavelet matrix and seismic effective bandwidth limits the accuracy of the sparse-spike reflectivity inversion. Consequently, we investigate the connection between seismic amplitude shape and reflectivity. When the reflectivity contains more non-zero values, the wavelet bandwidth within the effective seismic data bandwidth approaches a limit corresponding to the Sinc wavelet, where the main-lobe amplitude closely approximates the reflectivity. Conversely, when the reflectivity has fewer non-zero values, a wavelet with a smaller sidelobe provides a more accurate approximation of the reflectivity. In this paper, we propose a high-resolution inversion optimization method based on joint l2 norm and l1 norm constraints. By parameter tuning, we construct the Sinc wavelet or the wavelet with a weak-sidelobe corresponding to the seismic spectrum. Subsequently, we determine the extremum to approximate the reflectivity. To mitigate the RIP condition's constraints, we employ the l2 norm to balance the l1 norm (joint constraint) by introducing l2 norm with low-pass filtering characteristics. This approach yields more accurate reflectivity estimates. By taking the extremum, this approach yields more accurate reflectivity estimates. The synthetic test demonstrates that our method achieves better reflectivity inversion accuracy compared to sparse-spike inversion with l1–l2 norm constraint. Furthermore, field tests indicate that the proposed reflectivity inversion method not only can better match the well curve, but also exhibits excellent resolution.

Spectral recomposition feature for optimizing seismic velocity model prediction with a neural network

An approach incorporating spectral recomposition results for training a neural network is proposed. The initial procedure is based on an inversion scheme for reconstructing the seismic spectrum of wavelets associated with a reflection event. This allows one to estimate each wavelet's temporal position within a seismogram. Since each calculated wavelet's temporal position is identified, this information is integrated into the seismogram as an additional feature for a trained neural network. A Fully Convolutional Network is trained with models that have features commonly found in offshore hydrocarbon reservoirs. The training step is based on composing a set of an acoustic velocity model set with its seismograms and their position matrices at the time of each wavelet for each seismogram. Next, the network training with a specific number of sets is performed. This approach was able to predict acoustic velocity models more accurately, especially for predicting the shape of salt bodies and the interface of inclined layers, which makes the proposed approach an interesting mean for estimating specific features in offshore hydrocarbon reservoir structures.

Can we quickly retrieve Seismic Source Spectrum characteristics after a large magnitude earthquake? Implementation of a methodology based on Coda waves

After a large magnitude earthquake event, the direct estimation of its Seismic Source Spectrum (SSS) is important to estimate the energy content of the seismic source in broad-band frequency range. This direct knowledge of the SSS, except for the fact that can directly provide information about the Moment Magnitude of the earthquake, constitutes also, in frequency domain, that information, which is required to the Fourier Amplitude Spectra (FAS) simulation of the real-input seismic motion, in several target sites close to the source for which no earthquake recordings exist. In this study, the computation of the SSS of an earthquake is based on a single-station analysis algorithm by applying the spectral factorization method on the coda wave part of a seismic record. An application of this algorithm is implemented here for the Mw = 6.1 Cephalonia Island earthquake of 26/01/2014. The corresponding SSS, computed for several stations away from the source, are compared with the average SSS retrieved by standard applied method. The comparison results strongly encourage application and development of this SSS computation approach.

Calibration of horizontal seismic design spectra of offshore earthquake ground motions by applying improved differential evolution method

Design Response Spectrum (DRS) serves as a crucial cornerstone for seismic design, encapsulating the characteristic parameters of the design spectrum. To investigate the offshore design spectrum required for seismic design of offshore structures, improved differential evolution (DE) methods are first used to determine the characteristic parameters of the horizontal design spectra of offshore ground motions. In assessing the stability and precision of the chosen improved DE methods, we scrutinize the applicability of various renowned DE methodologies in the calibration process. Our findings indicate that differential evolution with global and local neighborhoods (GLDE) exhibits superior stability and accuracy compared to other DE methods, rendering it suitable for calibrating the design spectrum to delineate optimal characteristic parameters of the DRS. Subsequently, the properties of the offshore horizontal design spectra are investigated by applying the recommended GLDE to 6756 seismic data collected from three offshore regions. The site conditions of water depth and sedimentary thickness of the ocean-bottom stations were investigated by the finely divided seismic data with classified earthquake types. The ocean-bottom stations are classified as A-D by the water depth and sedimentary thickness, and the offshore DRS for four site classes with different earthquake types are presented in this study. According to the observed offshore response spectra with different water depth groups, it is found that the water depth should be considered in the offshore design spectra mainly due to the differences between buried and unburied seafloor stations, and the spectral values with deep water layer are considerably larger than those with shallow water. Offshore DRSs are compared with onshore DRSs of seismic codes and different peak ground acceleration (PGA) groups are presented in this study.

A seismic thin‐layer detection factor calculated by integrated S transform with non‐negative matrix factorization

AbstractTime–frequency analysis is one of the effective methods for seismic thin‐layer detection. Conventional time–frequency analysis technology for seismic thin‐layer detection is interfered by the energy of adjacent frequency signals, and there is information redundancy in the frequency‐domain analysis. Therefore, an S transform with improved window factor, which is based on the constrained non‐negative matrix factorization, is constructed to realize seismic thin‐layer detection. First, the seismic data is processed by the S transform of the improved window factor, and then we can obtain the frequency‐domain information with strong time–frequency focus by changing the adjustment factor and attenuation factor in the window function. Furthermore, the key frequency of the seismic data spectrum, which can also be called the key frequency characteristic factor, can be calculated by the non‐negative matrix factorization algorithm. Fortunately, the overthrust model shows a good correspondence between the key frequency characteristic factor and the thin‐layer interface. The field data example shows that this approach provides a new approach for thin‐layer detection.

Adjoint sensitivity kernels for free oscillation spectra

SUMMARY We apply the adjoint method to efficiently calculate sensitivity kernels for long-period seismic spectra with respect to structural and source parameters. Our approach is built around the solution of the frequency-domain equations of motion using the direct solution method (DSM). The DSM is currently applied within large-scale mode coupling calculations and is also likely to be useful within finite-element type methods for modelling seismic spectra that are being actively developed. Using mode coupling theory as a framework for solving both the forward and adjoint equations, we present numerical examples that focus on the spectrum close to four eigenfrequencies (the low-frequency mode, 0S2, and higher frequency modes, namely 2S2, 0S7 and 0S10 for comparison). For each chosen observable, we plot sensitivity kernels with respect to 3-D perturbations in density and seismic wave speeds. We also use the adjoint method to calculate derivatives of observables with respect to the matrices occurring within mode coupling calculations. This latter approach points towards a generalization of the two-stage splitting function method for structural inversions that does not rely on inaccurate self-coupling or group-coupling approximations. Finally, we verify through direct calculation that our sensitivity kernels correctly predict the linear dependence of the chosen observables on model perturbations. In doing this, we highlight the importance of non-linearity within inversions of long-period spectra.

Comparison of Various Input Energy Spectra for the February 6th, 2023, Kahramanmaraş Earthquake Sequence

ABSTRACT This study aims to evaluate the success of various seismic input energy spectra equations in capturing the energy content of the ground motion records of the Türkiye earthquakes since the acceleration response spectra of some records exceeded the design spectra. Although most existing spectra had limited success, especially near the corner period, some recent equations yielded accurate results. Based on the obtained results, it is envisaged that the energy-based seismic design concept will have the maturity to be included in the next-generation seismic design codes as a reliable alternative to the current approaches.

Developing design response spectra for Benghazi city including soil magnification effects

Earthquakes in some countries worldwide cause loss of lives and properties. In Libya, the design of structures to resist earthquake forces was based on a paper published by Mallick in 1976. In 1977, and after small changes in the earthquake zoning map of Libya, the ministry of housing, at that time, adopted it as a draft code of practice for the design of structures to resist earthquake forces. With Benghazi city undergoing significant rehabilitation and development programs, including major national projects, there is a pressing need to estimate updated probabilistic seismic hazard maps and design response spectra specific to the city. This study presented updated probabilistic seismic hazard ground motion for Benghazi city, considering different return periods and accounting for peak ground acceleration (PGA) values with various soil conditions. Proposed design response spectra for Benghazi City unveil substantial PGA amplifications in soft soil areas.

Influence of the Plan Structural Symmetry on the Non-Linear Seismic Response of Framed Reinforced Concrete Buildings

Seismic-resistant design incorporates measures to ensure that structures perform adequately under specific limit states, focusing on seismic forces derived from both the equivalent static and spectral modal methods. This study examined buildings on slopes in densely built urban areas, a common scenario in Latin American cities with high seismic risks. The adjustment of high-rise buildings to sloping terrains induces structural asymmetry, leading to plan and elevation irregularities that significantly impact their seismic response. This paper explores the asymmetry in medium-height reinforced concrete frame buildings on variable inclines (0°, 15°, 30°, and 45°) and its effect on their nonlinear response, assessed via displacements, rotations, and damage. Synthetic accelerograms matched with Chile’s high seismic hazard design spectrum, scaled for different performance states and seismic records from the Chilean subduction zone, were applied. The findings highlight structural asymmetry’s role in influencing nonlinear response parameters such as ductility, transient interstory drifts, and roof rotations, and uncover element demand distributions surpassing conventional analysis and in earthquake-resistant design expectations.

Automatic stack velocity picking using a semi‐supervised ensemble learning method

AbstractPicking stack velocity from seismic velocity spectra is a fundamental method in seismic stack velocity analysis. With the increase in the scale of seismic data acquisition, manual picking cannot achieve the required efficiency. Therefore, an automatic picking algorithm is urgently needed now. Despite some supervised deep learning–based picking approaches that have been proposed, they heavily rely on sufficient training samples and lack interpretability. In contrast, utilizing physical knowledge to develop semi‐data‐driven methods has the potential to efficiently solve this problem. Thus, we propose a semi‐supervised ensemble learning method to reduce the reliance on manually labelled data and improve interpretability by incorporating the interval velocity constraint. Semi‐supervised ensemble learning fuses the information of the estimated spectrum, nearby velocity spectra and few‐shot manual picking to recognize the velocity picking. Test results of both the synthetic and field datasets indicate that semi‐supervised ensemble learning achieves more reliable and precise picking than traditional clustering‐based techniques and the currently popular convolutional neural network method.