Seismic Spectrum Research Articles

Response spectrum-based intensity measure for underground structures

The purpose of this study is to present a novel approach to constructing intensity measures (IMs) for underground structures using seismic response spectrums. The proposed IM takes the form of an integral of the product of the response spectrum and an arbitrary function that reflects the relative importance of each range of period to the seismic response of underground structures. To obtain the arbitrary function, an artificial neural network (ANN) technique is employed. To demonstrate the effectiveness of this method, we develop two different soil-subway station dynamic systems, referred to as Case I and Case II. Based on both cases, the probabilistic seismic demand model (PSDM) for the proposed IM and eight existing IMs are developed. The performance of the proposed IM is compared with that of the existing IMs in terms of their proficiency, practicality, and efficiency, as well as their ability to describe the probabilistic distribution of damage measure (DM). The results indicate that the proposed IM outperforms the existing IMs since it has the highest proficiency for both cases. Moreover, the fragility curves calculated using the proposed IM are more effective than those calculated using traditional IMs, with narrower uncertainty ranges, which can help reduce the uncertainty in evaluating seismic risk. Comparing the function solved by the ANN with the seismic response of subway stations under different periods of harmonic excitation, it can be found that the solved function and the seismic response reach their peak points at the same period. This finding suggests that the proposed IM can account for the interaction between the surrounding soil and underground structures, as well as the softening of soil layers during earthquakes, making it a suitable IM for underground structures.

Estimation of Site Effects and Equivalent Source Parameters of Wenchuan Earthquake Based on Generalized Chaotic Particle Inversion Technique

Abstract Based on the advantages of the chaos particle swarm optimization algorithm and the generalized inversion technology, this article estimates the source parameters and site effects of the Wenchuan earthquake. We used 440 sets of strong-motion records obtained from 43 aftershocks, and the area covered by the records was divided into subregions A and B. Initial separation of source, path, and site from the seismic spectra of subregions A and B using generalized inversion technique and then the source-site optimization model is established using chaotic particle swarm technology. From path-corrected records, we obtained absolute site effects for 33 stations and equivalent source parameters for 43 earthquakes. We made the following conclusions: (1) The moment magnitude Mw was lower than the local magnitude MLdetermined by China Earthquake Network Center. The self-similarity of the Wenchuan earthquake was confirmed. The stress drop averaged 2.31 MPa, and it was independent of the magnitude size and focal depth. (2) In the frequency 1–10 Hz, the quality factor values in subregions A and B are 110.9f0.6 and 116.1f1.2. The decay rate of the crustal medium in the western region of the west Sichuan plateau is significant compared to the eastern part. (3) Bedrock stations 51MXT and L2007 have site effects within a certain frequency. The effect of slope topography on site predominant frequency is not apparent, and the site effects increase with the increase in elevation. The shape of the site amplification curve is more similar in the middle- and low-frequency bands, and different attenuation phenomena will appear in the high-frequency band.

Seasonality of California Central Coast Microseisms

ABSTRACT Linear scattering of ocean wave energy at the ocean–continent transition structure causes the primary microseism at a period of 14 s. Subsequent nonlinear wave–wave interactions produce the secondary microseism signal at half the primary microseism period (Longuet-Higgins, 1950; Haubrich et al., 1963). We use three years (2018–2022) of seismic data from an ongoing microarray deployment in the UC Santa Barbara Sedgwick Reserve, situated in the Santa Ynez Valley, to constrain seasonal and long-term microseismic noise characteristics for this portion of California’s central coast. Ancillary buoy data (spectral data, wave height, wind speed and direction) from the National Oceanic and Atmospheric Administration are used to explore the causal relationship between ocean swell and the generation of microseisms. This region is found to exhibit strong seasonality in the primary and secondary microseism bands (0.05–0.1 and 0.1–0.3 Hz, respectively), with much higher noise levels in the winter compared with the summer, especially for the secondary microseism (15.4 dB). We also observe a systematic shift in the peak frequency of the secondary microseism between the winter (∼0.14 Hz) and summer (∼0.20 Hz) months, which may reflect a difference in sources of secondary microseisms between the two seasons. Local buoy wave height and spectral data are well correlated with seismic power spectra during times of incoming storm swell in winter, indicating locally generated microseisms along the central coast during this season.

Multipath Transfer-Function Correction Method to Predict Site-Specific Amplification at City Scale

Abstract The site-specific amplification of seismic waves is an essential component of local seismic hazard assessment. It can be evaluated from empirical data, but measurements are feasible just in a limited number of locations. Hence, at the city scale, there is a need for the theoretical prediction and interpolation of the amplification. In this article, we introduce a physics-based method to predict the site-specific amplification and duration in a broad frequency range. The method is based on a novel energy-based concept of the multipath propagation of waves in viscoelastic media with random heterogeneities. The amplification is expressed by the surface-outcrop transfer function of the multipath wave propagation, which is defined by expected values of the energy spectral ratio. The method is applied to the near-surface 2D velocity model in the city of Zürich in Switzerland. The predicted amplification is validated by empirical data at a nearby seismic station, and it is compared with the soil class and other site-condition proxies. Finally, the method performance is demonstrated by the prediction of site-specific seismic waveforms and response spectra for the 2022 ML 4.7 Mulhouse earthquake.

Comparative study of seismic spectra of great magnitude occurred in Chile between 2012 to 2022 and the design spectra of seismic standard NCH433

In this document, a study of the spectra of large-magnitude seismic records that occurred in Chile between 2012 and 2022 is presented, comparing them with the design spectra of NCh433 and D. S 61. For this, seismic records greater than Mw = 6 have been used, with different depths to the hypocenter and with different types of soil. The catastrophes caused by earthquakes with magnitudes greater than Mw = 6 in the last decade in seismic zones (Turkey and Syria, 2023; Pakistan, 2013; Iran, 2014; Ecuador, 2016 or, Mexico, 2017; among others), have called into question the requirements structural aspects of earthquake-resistant standards in the world. That is why this work aims to demonstrate that highly seismic areas such as Chile, prone to having earthquakes with magnitudes greater than Mw = 6, have seismic-resistant regulations updated to the existing reality. The aim is to demonstrate whether the design spectra of the Standard have been sufficiently representative to determine the calculation accelerations used in the structural design of buildings. It is concluded that many of the spectral accelerations of the records that occurred in Chile exceed those of the design spectrum of the Standard, especially for short periods. Finally, in this research, new design spectra composed of 3 intervals (the 2nd interval is a plateau) are proposed that are more adjusted to the existing seismic reality in Chile during the last decade, considering the type of soil (A-D) existing in the Code (D.S 61).

A Review on Seismic Analysis of RCC and Steel Structures using Linear and Non-linear Static Analysis

Abstract: An earthquake can cause significant harm to various aspects, including buildings, general life, and particularly multistory structures. In India, structures constructed in earthquake-prone regions, as defined by IS 1893: 2002, must be designed to withstand the loads, stresses, and consequences of earthquakes. Several techniques are available for assessing multi-story structures in this context, such as the Response Spectrum Method, Equivalent Lateral Force Method, Time History Method, and adhering to specific code provisions. Numerous researchers have undertaken studies to analyze multi-story buildings using one or more of these methods. However, there exists still a confusion about an effective and efficient method preferred for seismic design of multi-story buildings. Among the various approaches, the seismic coefficient method and response spectrum method are the most widely used. This comparative investigation aims to review research reports that have employed the Equivalent Lateral Force Method and Response Spectrum Method to analyze multi-story buildings in earthquake-prone areas. The design response spectrum serves as the initial reference point for most established seismic design and assessment procedures. It primarily dictates the inertia forces that buildings and structures must withstand during an earthquake. This paper aims to introduce and discuss contemporary concepts regarding the creation and utilization of earthquake design response spectra. Additionally, the paper highlights the various methods of seismic analysis being investigated in the past literature. It also gives an overview of various investigations being carried out using linear and non-linear static analysis of RCC structures. Many of the ideas presented are specifically aimed at aiding engineers who work in regions with low to moderate seismic activity. The main objective is to inform engineers about modern approaches to developing response spectra. This knowledge can then be applied effectively in both analytical and design contexts when dealing with earthquake-related challenges

Seismic margin assessment of the real dynamic response of nuclear engineering structures based on the response envelope method

The accuracy of response calculations for nuclear structures is directly related to the reliability of margin assessment results. The seismic response envelope (SRE) method, which is more effective than the traditional mode decomposition response spectrum method, has received increasing attention in studies on structural dynamic responses in nuclear engineering. It is able to consider the characteristics of multiple seismic responses occurring simultaneously, but applying it to the seismic margin assessment of structures beyond design-basis earthquakes becomes a challenge and some practical issues remain unaddressed. Focusing on the characteristics of the seismic response spectrum and regularization of the coordinate system, this study derived an SRE concentric circle equation in the regular coordinate system and defined the seismic safety margin level. A seismic margin assessment strategy for nuclear shear wall structures was developed based on the relationship between the bearing capacity surface controlled by the reinforcement ratio and the concentric circle of the SRE. A comparison between the SRE method and other seismic analysis methods for multiple seismic response calculations verified the effectiveness of the proposed method. Moreover, in particular, the emphasis was on the variation characteristics of the seismic safety margin level considering discrete points under the new and old strategies, and the solution accuracy and efficiency of the proposed strategy were discussed. Finally, the SRE method was used to evaluate the seismic margin of a real nuclear engineering structure, providing reliable data support for the solution strategy in practice.

Study on the Influence of a Rubber-Modified Soil Isolation Layer on the Isolation Performance of Frame Structures with Different Foundation Forms

In order to investigate the seismic performance of a rubber-modified soil isolation layer, a three-dimensional finite element model was constructed using finite element analysis software, utilizing a two-story frame structure as the engineering background. Nonlinear dynamic time history analysis and comparisons were performed against the seismic performance of the structure. The evaluation was based on several parameters, including the contact area of the base, the thickness of the rubber-particle-modified soil isolation layer, ground motion records with varying amplitudes, and seismic frequency spectrum characteristics. The research findings indicate that the implementation of a rubber-modified soil isolation layer effectively mitigates the peak acceleration, horizontal displacement, and shear stress of the frame structure. This not only enhances the seismic performance of the structure but also enlarges the contact area of the base. Increasing the thickness of the rubber-modified soil isolation layer will effectively decrease the peak acceleration, horizontal displacement, and shear stress of the structure during seismic events. The effectiveness of the isolation provided by the rubber-modified soil layer improves as the intensity of the ground motion record increases.

Phase‐shift correction of seismic reflections by means of spectral recomposition

AbstractUsing post‐critical reflection data, it is possible to obtain useful information that allows more reliable geological characterization of the subsurface. However, the strong distortion caused by the phase shift in post‐critical wavelets makes the use of post‐critical reflections rather challenging. For this reason, an approach which is capable of estimating the phase shift of each wavelet of a reflection event in a data‐driven manner is desirable. In this vein, in case the frequency spectrum of a wavelet can be correctly estimated, it is possible to estimate the instantaneous phase shift. In this work, we propose an approach which can perform such estimation based on spectral recomposition of seismic data. We design an inversion approach in order to reconstruct the seismic spectrum of the wavelets of a reflection event, which subsequently allows us to estimate the instantaneous phase of each wavelet of the near‐surface reflection events without performing prior velocity analysis and/or critical‐angle estimation. After finding the instantaneous phase for each wavelet of a reflection event, we show next how one can find the respective phase shifts that can then be corrected.

Fuzzy inference system model for the spectrum characteristic periods of the Türkiye Building Earthquake Code (2007)

Seismic design codes define response spectra with crisp numerical classifications of seismic parameters, which mainly affect the spectrum's shape and determination of seismic design loads. The efficiency of structural safety and construction costs depends on the optimum design and accurately determined seismic forces. As presented in the seismic design codes, several parameters are utilized to calculate the seismic design forces with response spectra. This study proposes a rule-based fuzzy inference system (FIS) model with fuzzy set numbers to determine the relevant parameters. By defining the soil profile thickness and shear wave velocity as inputs, the model generates the spectrum characteristic periods specified in the Türkiye Building Earthquake Code (TBEC 2007). The response spectra of twenty different samples with the FIS and crisp models were generated and compared to assess the model's superiority. Unlike crisp seismic code classifications, the proposed FIS model accounts for imperfections in soil group selection and topmost soil layer thickness, offering a more realistic representation of uncertainties and proving to be an effective tool for addressing linguistic vagueness in seismic response spectra analysis. The comparison between fuzzy and crisp output seismic parameters revealed significant differences in response spectra shape and spectrum intensity values. The FIS model-generated spectra were more conservative in certain building locations, while in others, they provided similar or lower values, suggesting potential cost savings in design. The FIS model demonstrates its efficacy in producing more accurate and robust designs by considering the uncertainties inherent in the problem. Furthermore, this approach has the potential to be extended to study seismic parameters of other design codes, although further research is required to comprehensively explore its capabilities and limitations.

Floor Seismic Response Spectrum for the Building Equipped with Visco-Elastic Decouplers

By installing the visco-elastic (VE) decouplers between the floor slab and the beam, the floors of a building are isolated from the primary structure. Such a structural system, termed VE decoupled floors, has an increased damping and a reduced inertial force for mitigating the floor seismic response. These features lead to a significantly improved seismic performance of the important facilities resting (or anchored) on floors. This paper focuses on the floor seismic response spectrum (FSRS) of the building equipped with VE decoupled floors. First, the frequency-dependent property of the structure is dealt with, whereas the time-variant stiffness and damping of the VE decoupler are replaced by a couple of stabilized substitutions, and the appropriation of this substitution is numerically validated. Secondly, given the stabilized substitutive model, the FSRS is derived based on the classic complex modal decomposition process and the stochastic dynamics of linear oscillators. In this process, the input seismic excitation is considered via a specific model that accounts for its non-stationary nature. Lastly, a parametrical analysis is conducted to validate the proposed FSRS model and to reveal some special features of the VE decoupled flooring system. It is shown that the FSRS can be better mitigated if a more flexible VE decoupler and a larger mass (isolation) ratio are incorporated. A VE decoupled floor installed at the level of the roof is more effective than the ones installed at the lower levels. Basically, the peak of FSRS can be reduced by 70% if the VE decoupling system is properly designed.

Simulating Strong Ground Motion from the Great 1923 Kanto Earthquake in the Tokyo Metropolitan Area Based on Source Model Derived from Seismic Intensity Data

ABSTRACT This study simulates strong ground motions in the Tokyo metropolitan area during the 1923 Kanto earthquake using the stochastic Green’s function method. Source characteristics were modeled using seismic intensity inversion analysis, and path and site characteristics were modeled using inhomogeneous attenuation structure and empirical amplification factors. The results of these simulations were consistent with seismic intensities estimated based on the collapse rate of wooden houses. The distribution of pseudovelocity response spectra averaged at periods of 1–2 s was large: ∼200 cm/s in southern Kanagawa and southern Chiba prefectures, ∼100–200 cm/s in eastern Tokyo, and ∼50–100 cm/s in eastern Saitama prefecture despite its distance from strong-motion generation areas (SMGAs). The simulation results were regressed on site characteristics and fault distance, and the residuals were interpolated using the Kriging method to estimate detailed maps of seismic intensity and response spectra on an ∼250 m mesh reflecting site-specific characteristics. The following conclusions can be made: (1) all SMGAs, other than those in northern Tokyo Bay, were located near large slip areas based on coseismic geodetic and seismic waveform data. Although the SMGAs in the northern part of Tokyo Bay exerted little influence on the southern part of the Kanto region, their consideration was required to reproduce the seismic intensity at the northwest Tokyo and Saitama; (2) intense strong motion in central Tokyo occurred at the back marsh, delta, coastal lowlands, and filled lands, whereas low levels of strong motion were determined at terraces covered with volcanic ash soil. Combined with building distribution, this indicates areas of high seismic risk; (3) the seismic intensity and response spectra in the Tokyo metropolitan area obtained through this simulation were larger than those obtained from seismic records of the 2011 Tohoku earthquake—the most recent megathrust earthquake.

Exploring risk-targeted ground motions and seismic design spectra for mainland China

Seismic design under the paradigm of uniform hazard only considers the seismic hazard of building sites, which will lead to inconsistent collapse risks of buildings in different areas. To achieve uniform collapse risk, the paradigm of conventional seismic design with uniform hazard should be shifted to the new framework of uniform risk, which accounts for both seismic hazard of sites and collapse fragility of buildings. In this study, based on the principle of risk targeting, parametric sensitivity analyses of risk-targeted ground motions for mainland China are performed considering different risk categories and site classes. Then, the risk-targeted peak ground accelerations and the uniform-risk seismic design spectra are obtained for mainland China. Seismic risk assessment is conducted for an 8-story reinforced concrete frame structure using the ground motions selected based on the uniform-risk seismic design spectra. The results indicate that the influence of logarithmic standard deviation of the target collapse fragility function on the risk-targeted maximum considered earthquake gradually increases with risk category. The impact of target collapse risk on risk-targeted maximum considered earthquake of a hard site is more remarkable than that of other sites. The effects of the logarithmic standard deviation and the conditional collapse probability under the maximum considered earthquake on the collapse risk gradually increase with the site class. In addition, the construction of uniform-risk seismic design spectra takes into account both seismic hazard and structural fragility. It is reasonable to select ground motions based on uniform-risk seismic design spectra for conducting seismic risk assessment of structures.

Deghosting dual‐component streamer data using demigration‐based supervised learning

AbstractGhost reflections from the free surface distort the source signature and generate notches in the seismic amplitude spectrum. For this reason, removing ghost reflections is essential to improve the bandwidth and signal‐to‐noise ratio of seismic data. We have developed a novel approach that involves training a convolutional neural network to remove source and receiver ghosts from marine dual‐component data. High‐quality training data is essential for the network to produce accurate predictions on real data. We have used the demigration of a stacked depth‐migrated image to create training shot gathers. Demigrated pressure and vertical velocity data are used to train the network. We apply the trained network on real pressure and vertical velocity data with ghosts. The network's output may be either source deghosting and receiver deghosting, or both. We test our method on synthetic Marmousi and real North Sea data with dual‐component streamers. The method is compared with conventional dual‐component deghosting using the summation of pressure and vertical velocity. Results show that the method can accurately remove the ghosts with only minor errors in synthetic data. Based on a decimation test, the method is less affected by spatially aliased data than a conventional method, which could benefit data with high frequencies and/or large receiver or cable separations. On real data, the results show consistency with conventional deghosting, both within and outside the training area. This indicates that the method is a viable alternative to conventional methods on real data.

Reliability-Based Selection of Retrofit Works for Schools under Seismic Hazard

A reliability-based procedure is proposed to assess and compare the economic effectiveness of three retrofit alternatives for actual schools located in three zones with different seismic hazards. The procedure calculates the school failure probability under the damaged conditions, by considering the damages produced by the 2017 earthquake in Mexico, and the failure probability under each retrofit alternative, from the seismic spectra corresponding to the seismic hazard of each site. The best retrofit alternative is the one with the minimum expected life-cycle cost for each school. The global failure probability is calculated according to the Ditlevsen’s bounds, and the limit states consist of the event in which the maximum moment exceeds the bending capacity for beams, and the combined axial and bending forces exceed the capacity of the columns; the maximum responses are obtained through nonlinear analyses. The proposed retrofit alternatives are column and beam jacketing with steel angles and plates, increment of the concrete cross sections of columns and beams, and the addition of bracing. The effectiveness of each alternative, in terms of failure probability reduction and expected life-cycle cost, was assessed for each school. The procedure may be used to update the current retrofit specifications for schools.

Seismic Response Analysis of Secondary Lining Polymer Grouting Debonding Repair for Tunnel Construction Based on Parameter Inversion

The void phenomenon behind the tunnel lining has become the main cause of tunnel disease, easily triggering tunnel lining structure damage, shedding, water seepage, and other diseases that seriously threaten the normal operation of the tunnel. The void area behind the lining seriously reduces the seismic capacity of the tunnel. In this paper, the mechanical parameters of the surrounding rock are calculated by optimizing the inversion of the improved system identification sensitivity analysis method, and the numerical model of the tunnel’s dynamic response is optimized using the improved inversion results to study the repair effect and seismic capacity of the Longmenshan tunnel using polymer grouting to repair the void area behind the lining under the action of a seismic load. The results show that the displacement and stress at the top of the tunnel secondary lining void area are significantly reduced and close to normal after the repair of polymer grouting; however, the stress and displacement at the top of the secondary lining are significantly different under the action of seismic waves at the same peak at different site conditions, which indicates that the dynamic response of this tunnel model has obvious sensitivity to the seismic wave spectrum.

Analysis of seismic time-history effect of single corroded pipeline in seasonally frozen soil region

Based on the pipe-soil thermal-solid coupling analysis method, the single corrosion defect pipeline, insulation layer and seasonally frozen soil were taken as the research object in this paper. Under the specific working conditions of differential frost heave, the seismic time history seismic time history effects were analyzed. The study focused on the axial and vertical velocity responses at the center of the corroded zone of buried pipelines with different corrosion defect characteristics, and then their variations were summarized. The result indicates that the corrosion depth has a greater influence on the axial velocity response than the vertical velocity response. Moreover, the corrosion depth has a larger impact on the maximum vertical and axial displacements at the center of the corroded zone than the corrosion length. The response sensitivity of the corrosion depth to vibratory loading is twice that of the length. When the corrosion length is fixed, the maximum growth rate of axial strain in the corroded zone typically occurs at a corrosion depth ratio between 50% and 75%. Additionally, when the same peak ground motion is considered for pipelines in the same type of site, different seismic wave spectra have significant effects on the dynamic response of buried defective pipelines.

Floor response spectra and seismic design method of electrical equipment installed on floor in indoor substation

Electrical equipment installed on floors is a typical type of nonstructural component in indoor substations, which could be subjected to earthquake loading during seismic events. To investigate the seismic design method of floor electrical equipment in indoor substations, simulation models of four whole-indoor substations comprising main control buildings and their floor electrical equipment were established. Seismic response spectrum analyses of main-attachment structures were performed with a high number of ground motions as inputs. Using mathematical statistics and data fitting methods, this research suggested the calculation formula of amplification factor of floor acceleration response spectrum. Specifically, when the periodic ratio of electrical equipment to main control building is in the range of 0.9–1.1, the system would produce a strong resonance-like effect with a peak spectral amplification factor. The floor response spectrum for seismic design was influenced by four factors: equipment importance category, floor position, damping ratio of electrical equipment, and torsion effect of main control building. Following that, a seismic design method especially applicable for electrical equipment installed on floor in indoor substation, which combines amplification factor and calculation method of seismic action indicated in the relevant specification, was presented. Lastly, a typical 220 kV whole-indoor substation was taken as an example to validate the accuracy of the design method highlighted in this article.

Spectral recomposition for optimizing starting points in Full-Waveform Inversion

By optimizing the wavelet fitting of the arrivals in a reflection event, it is possible to perform significant enhancements for Full-Waveform Inversion (FWI) predictions and its processing time. For this reason, approaches capable of reducing the number of iterations for FWI — without decreasing the quality of the prediction — are of interest. Once the initial guess for FWI is better estimated, it is possible to predict the velocity model within a determined accuracy with fewer iterations. We thus propose an approach which can perform this estimation, based on spectral recomposition of seismic data. We design an inversion scheme to reconstruct the seismic spectrum of wavelets of a reflection event, which subsequently allows estimating the position in time of each wavelet in a seismogram. After finding the position in time of each wavelet, we can guide the calculated wavelet to fit the corresponding observed signal, starting from a closer initial point. Our approach leads to quite accurate predictions of velocity models with fewer iterations.

Critical angle of reflections and Poisson's ratio from spectral recomposition

Using the critical angle information of a reflection event, it is possible to calculate several essential physical parameters that are key to reliable geological characterization of the subsurface. However, estimation of the critical angle usually requires several steps of seismic processing. For this reason, an approach which is capable of estimating the critical angle directly from the data is of interest. Once the critical angle is estimated, it is possible to estimate further the Poisson's ratio and the seismic velocities. In this work, we propose an approach which can perform this estimation, based on spectral recomposition of seismic data. We design an inversion scheme in order to reconstruct the seismic spectrum of wavelets of a reflection event, which subsequently allows us to estimate the critical angle of near-surface reflection events without performing prior velocity analysis. After finding the critical angle, we show next how to estimate the Poisson's ratio and the compressional- and shear-wave velocities of the medium above the reflector. The approach leads to quite accurate values for Poisson's ratio even for noisy data, in case the number of layers is not large.