Seismic Model Research Articles

Three-dimensional density model of the mantle beneath the Ukrainian shield

Purpose. Mantle density models are key tools for understanding the fundamental geological and physical processes occurring within the Earth and are essential to our scientific and applied understanding of the planet. Methodology. The tasks were solved by a complex research method, including analysis and generalization of literary and patent sources, analytical, experimental studies, using computer and mathematical modelling methods. Findings. One-dimensional models simplify the mantle density distribution by assuming that it is uniform only in the vertical direction. This limitation does not allow for horizontal variations in mantle density, which may be important on a regional scale. 3D models are more complex and require more data and computational resources, so their use may be limited. In this study, we present a quasi-three-dimensional model of mantle density beneath the Ukrainian Shield. This 3D model is obtained using a basic set of one-dimensional seismic tomographic velocity models calculated for 21 mantle domains in the depth range from 50 to 2,600 km. The process of converting the P-wave velocity model into a density model includes the following stages: 1) determining seismic boundaries in the mantle based on P-wave velocity curves for each mantle domain; 2) creating a synthetic mantle model beneath the Ukrainian Shield for the P,S-wave velocity curves; 3) solving the Adams-Williamson equation for each domain, considering polynomial corrections to extract heterogeneities during its solution; 4) analysing existing models by comparing the calculated gravitational potential at the central point of the Ukrainian Shield as the standard reference for selecting one of 5 reference models. Here, we focus on the final stages of constructing the mantle density model by: 1) balancing the mass of the upper and lower mantle for each domain when determining density using the Adams-Williamson equation and introducing polynomial corrections; 2) calculating densities for each of the 21 mantle domains and their 3D integration. Originality. The obtained mantle-density model of the Ukrainian Shield aligns well with the division of the mantle into three main layers: lithosphere, upper mantle, and lower mantle. Each of the mantle’s structural layers has its representation pattern in density heterogeneities. Anomalies of decreased density in the lithosphere of the Ukrainian Shield correlate with thermal anomalies, whereas anomalies of increased density correspond to tectonic zones dividing its megablocks. Practical value. Regions of increased density gradient are associated with mantle thrust faults, which in some cases can be boundaries between different petrological formations and serve as channels for magma ascent into the Earth’s crust at certain stages of geological development of the Ukrainian shield and, in turn, be sources of minerals.

Selection of optimal intensity measures for seismic performance evaluation of underground utility tunnel and internal pipeline system

Seismic intensity measures (IMs), which are closely related to both earthquake hazards and structural responses, play a critical role in the performance-based earthquake engineering (PBEE) framework. This paper aims to investigate and define the most representative IMs for probabilistic seismic demand model (PSDM) for the longitudinal utility tunnel and internal pipeline system. Similar to the requirements by the Chinese Code for seismic design of urban rail transit structures, the utility tunnel in this study is assumed being buried in four typical engineering site classes for the analyses. Soil-tunnel-pipeline interactions are simulated using a double-beam system resting on a nonlinear foundation. Soil-tunnel interaction, tunnel-pipeline interaction and joint connections are modeled as nonlinear springs with different mechanical properties. A series of 17 pairs of outcrop ground-motion records and 27 commonly used IMs are selected in the analyses. Engineering demand parameter (EDP) is defined based on the maximum joint opening and the maximum strain of the utility tunnel and internal pipeline, respectively. The selected IMs for predicting the seismic responses of tunnel-pipeline systems are tested using different criteria, i.e., correction, efficiency, practicality, and proficiency. The final decision-making procedure employs a fuzzy multi-criteria decision method. The numerical results indicate that: (1) The velocity-related IMs are the most representative IMs based on the four criteria for structures buried in four sites of different conditions; (2) The optimal seismic IMs vary with different criteria, site classes and structure types. According to the fuzzy multi-criteria decision approach, optimal IMs for the tunnel-pipeline system are PGV, PGV, EPV and HI for site classes I – IV, respectively. The proposed optimal IMs can be utilized to construct seismic fragility curves of utility tunnel, internal pipeline and tunnel-pipeline systems in four different site classes.

On the utility of story loss functions for regional seismic vulnerability modeling and risk assessment

Vulnerability functions relate loss to seismic intensity and can be developed via several approaches. They are a fundamental part of seismic risk assessment on a regional level and support decision-making and intervention strategies aimed at reducing risk. This article discusses a prominent analytical approach to developing seismic vulnerability models for buildings based on equivalent single-degree-of-freedom (SDOF) modeling, fragility function, and damage-to-loss model integration. The fundamental assumptions are scrutinized, and their principal drawbacks are highlighted. An alternative approach also based on an equivalent SDOF modeling approach is discussed but instead capitalizes on story loss functions (SLFs) as a means to more accurately compute economic losses and their sources. The main benefit is that the contribution of floor acceleration-based losses can be directly considered, and the disaggregation of losses is fully represented. A case study comparison is presented to highlight the similarities and key benefits. It is seen that the SLF-based approach can provide a much more comprehensive means to compute and communicate loss contributions among different element groups (i.e., structural, non-structural, and contents) and individual stories along the building height. Existing models can simply be adjusted to this approach and provide a more holistic view of risk. The benefits and potential applications in the (re)insurance sector are also discussed.

Seismic modeling and performance evaluation of seismically isolated building considering large strain effects under near-fault earthquakes

Lead rubber bearings (LRBs) have been widely used in seismically isolated buildings to mitigate earthquake damages in highly earthquake-prone regions. The deformation of the LRBs has been generally recognized to conform to the bilinear model under moderate shear deformation. However, when the bearings are loaded with large strain deformation, LRBs exhibit a significant increase in stiffness and strength due to the hardening characteristics of the rubber. Nevertheless, the dilemma in engineering practice is that most of the existing LRB models in design software cannot capture complex hardening behaviors under large strain loadings. Furthermore, although some LRB models can consider the large strain effects, they require many calibrated parameters. For this reason, a concise generalized Bouc–Wen model was proposed (hereinafter referred to as BoucWenG model) in this work, which can improve the aforementioned limitations of the traditional LRB models while retaining the favorable features of the Bouc–Wen model. The detailed features of the BoucWenG model were introduced first. Then, the generalized model was verified using the experimental results of LRBs with different sizes under cyclic large strain loadings. Furthermore, considering the large strain effects, we examined the seismic performance of the base isolation system using two comparative isolated reinforced concrete frame buildings, in which the base isolation bearings were simulated by the traditional Bouc–Wen and the proposed BoucWenG models. Next, we conducted seismic fragility analyses of these two isolated buildings through incremental dynamic analysis, in which the near-fault (NF) ground motions characterized by large-amplitude velocity pulse were also considered. The comparison results reveal that the proposed BoucWenG model can well represent the large strain hardening and strength degradation properties of LRBs. Furthermore, the dynamic responses of the superstructure and the isolation system significantly tend to vary when the large strain effects of the bearings are considered under strong earthquakes. The traditional LRB model, which ignores the large strain effects, may highly overestimate the shear deformation of the isolation layer and lead to poorer-than-expected seismic isolation effects for the superstructure, especially under strong NF earthquakes.

3D Multiresolution Velocity Model Fusion with Probability Graphical Models

ABSTRACT The variability in spatial resolution of seismic velocity models obtained via tomographic methodologies is attributed to many factors, including inversion strategies, ray-path coverage, and data integrity. Integration of such models, with distinct resolutions, is crucial during the refinement of community models, thereby enhancing the precision of ground-motion simulations. Toward this goal, we introduce the probability graphical model (PGM), combining velocity models with heterogeneous resolutions and nonuniform data point distributions. The PGM integrates data relations across varying resolution subdomains, enhancing detail within low-resolution (LR) domains by utilizing information and prior knowledge from high-resolution (HR) subdomains through a maximum posterior problem. Assessment of efficacy, utilizing both 2D and 3D velocity models—consisting of synthetic checkerboard models and a fault-zone model from Ridgecrest, California—demonstrates noteworthy improvements in accuracy, compared to state-of-the-art fusion techniques. Specifically, we find reductions of 30% and 44% in computed travel-time residuals for 2D and 3D models, respectively, as compared to conventional smoothing techniques. Unlike conventional methods, the PGM’s adaptive weight selection facilitates preserving and learning details from complex, nonuniform HR models and applies the enhancements to the LR background domain.

Scoring and ranking probabilistic seismic hazard models: an application based on macroseismic intensity data

Abstract. A probabilistic seismic hazard model consists of a set of weighted models/branches that describes the center, the body and the range of seismic hazard. Owing to the intrinsic nature of this kind of analysis, the weight of each model/branch represents its scientific credibility. However, practical uses of this model may sometimes require the selection of one or a few hazard curves that are sampled from the whole model, which often consists of thousands of branches. Here we put forward an innovative procedure that facilitates the scoring, ranking and selection of the hazard curves to account for the requirements of a specific application. The approach consists of a careful quality check of the data used for scoring and the adoption of a proper scoring rule. To show the applicability of this approach, we present an example that consists of scoring and ranking a set of multiple models/branches constituting a recent seismic hazard model of Italy. To score these branches, hazard estimates produced by each of them are compared with time series of macroseismic observations available in the Italian macroseismic database for a carefully selected set of localities deemed sufficiently representative, homogeneously distributed in space and complete with respect to time and intensity levels. The proper scoring parameter used for such a comparison is the logarithmic score, which can always be applied independently of the distribution of the data.

On the singularity point in acoustic orthorhombic media

Abstract The acoustic orthorhombic model is widely used in seismic modeling and processing of P-wave data. However, the anisotropic acoustic models have so called S-wave artifacts (1 artifact in transversely isotropic acoustic medium and two artifacts in orthorhombic acoustic medium). I show that S-wave artifacts can have one singularity point that results in complications in polarization field and the group velocity surface. The conditions of the existence of this point are defined in terms of anellipticity parameters. This singularity point and its group velocity image are the objects of my analysis.

Fracture network characterisation of the Balmuccia peridotite using drone-based photogrammetry, implications for active-seismic site survey for scientific drilling

The presence of discontinuities (e.g. faults, fractures, veins, layering) in crystalline rocks can be challenging for seismic interpretations because the wide range of their size, orientation, and intensity, which controls the mechanical properties of the rock and elastic wave propagation, resulting in equally varying seismic responses at different scales. The geometrical characterisation of adjacent outcrop discontinuity networks allows a better understanding of the nature of the subsurface rocks and aids seismic interpretation. In this study, we characterise the discontinuity network of the Balmuccia peridotite (BP) in the Ivrea–Verbano Zone (IVZ), northwestern Italy. This geological body is the focus of the Drilling the Ivrea–Verbano zonE (DIVE), an international continental scientific drilling project, and two active seismic surveys, SEismic imaging of the Ivrea ZonE (SEIZE) and high-resolution SEIZE (Hi-SEIZE), which aim to resolve the subsurface structure of the DIVE drilling target through high-resolution seismic imaging. For fracture characterisation, we developed two drone-based digital outcrop models (DOMs) at two different resolutions (10−3–10 m and 10−1–103 m), which allowed us to quantitatively characterise the orientation, size, and intensity of the main rock discontinuities. These properties affect the seismic velocity and consequently the interpretation of the seismic data. We found that (i) the outcropping BP discontinuity network is represented by three more sets of fractures with respect to those reported in the literature; (ii) the discontinuity sizes follow a power-law distribution, indicating similarity across scales, and (iii) discontinuity intensity is not uniformly distributed along the outcrop. Our results help to explain the seismic behaviour of the BP detected by the SEIZE survey, suggesting that the low P-wave velocities observed can be related to the discontinuity network, and provide the basic topological parameters (orientation, density, distribution, and aperture) of the fracture network unique to the BP. These, in turn, can be used for interpretation of the Hi-SEIZE seismic survey and forward modelling of the seismic response.

Seismic characterisation of the subsoil under a historic building: Cathedral Church of Saint Mary in Murcia case study

This research focuses on the Cathedral Church of Saint Mary in Murcia, Spain, which is located in a moderate-to-high seismic risk zone in the Spanish context. The study uses geophysical techniques and geotechnical investigation to characterise seismic ground models at the building's scale, aiming to understand the real amplification of the ground under seismic effect in historic buildings. Three soil layers (silt, sand with gravel, and gravel) were identified through core borings. Multichannel Analysis of Surface Waves (MASW) profiles and Mini-array profiles revealed Vs values of 305 ± 32 m/s, 296 ± 62 m/s, and 440 ± 38.5 m/s, respectively, for these materials. Seismic Refraction Tomography (SRT) showed Vp values of 586 ± 73 m/s, 700 m/s, and 1466 ± 489 m/s for the corresponding layers. The horizontal-to-vertical spectral ratio (HVSR) approach identified a ground predominant period ranging from 0.37 to 0.38 s. Another significant peak at 2.3 s is observed, probably associated to the Triassic basement. Three seismic events with magnitudes Mw between 4.9 and 5.1 were used as inputs to determine the amplification factor (AF). The results indicate a PGA amplification factor between 1.7 and 2.1. These results contribute to the conservation and mitigation of seismic risk of this cultural heritage generating input data that enables precise computation of the soil-structure interaction.

Seismic capacity models for earth dams and their use in developing fragility curves

This article develops seismic capacity models for earth dams and demonstrates how the proposed seismic capacity models may be used to develop seismic fragility curves that predict the probability of damage as a function of ground shaking intensity. Developing earth dam fragility curves requires two major components: (1) a seismic capacity model that predicts the probability of a damage state given the relative settlement (RS) and (2) an engineering demand model that predicts the RS as a function of ground motion intensity. While seismic demand models for earth dams have been studied by various researchers, there is a scarcity of seismic capacity models. This article focuses first on developing seismic capacity relationships using a dataset of earthquake case histories of dam performance. Different from previously developed relationships, only the damage description for each dam is used when assigning the damage state, which results in statistical variability in the capacity relationship between the damage state and RS. The fragility curve development is demonstrated by combining the seismic capacity relationships with a seismic demand model for RS derived from nonlinear, dynamic finite element analyses for a 20-m generic dam geometry subjected to a suite of earthquake motions from the NGA-West2 database.

Average spectral acceleration (AvgSa) for high-confidence probabilistic seismic demand modeling of urban highway bridge portfolios: What period range and damping ratio shall we use?

The average spectral acceleration (AvgSa), i.e., the geometric mean of spectral accelerations over a period range, has attracted widespread recognition as one of the most promising intensity measures (IMs) for probabilistic seismic demand modeling of structures. As AvgSa is a structure-related spectral IM, a pivotal step in calculating AvgSa is to determine an appropriate period range and damping ratio. Whilst optimal AvgSa has been well documented for buildings, consensus on the period range and damping ratio of AvgSa for urban highway bridges is yet to be reached. To this end, a pool of AvgSa candidates with different combinations of lower and upper period bounds and damping ratios are assessed to identify the optimum combination(s) for straight and curved urban highway bridge portfolios against bidirectional seismic excitations, in terms of peak pier drift ratio, peak bearing displacement, and residual pier drift ratio. Results indicate that for the peak demand parameters, optimal AvgSa is characterized by a damping ratio of 0.2 and a period range of [Tf, 1.5Tf], where Tf is the structural fundamental period, for bridges with relatively short piers; and the optimal period range becomes [Tf, 2Tf] for medium to tall-pier bridges. Besides, the optimal period range for the conventional 5%-damped AvgSa is also detected, where [0.5Tf, 1.5Tf] is the optimal range for bridges with relatively short piers, while [0.5Tf, 2Tf] is recommended for medium to tall-pier bridges. Regarding the residual pier drift ratio, averaging spectral accelerations over any examined period ranges does not outperform traditional spectral accelerations at specific periods.

Seismic wave modeling of fluid-saturated fractured porous rock: including fluid pressure diffusion effects of discretely distributed large-scale fractures

Abstract. The scattered seismic waves of fractured porous rock are strongly affected by the wave-induced fluid pressure diffusion effects between the compliant fractures and the stiffer embedding background. To include these poroelastic effects in seismic modeling, we develop a numerical scheme for discretely distributed large-scale fractures embedded in fluid-saturated porous rock. Using Coates and Schoenberg's local-effective-medium theory and Barbosa's dynamic linear slip model characterized by complex-valued and frequency-dependent fracture compliances, we derive the effective viscoelastic compliances in each spatial discretized cell by superimposing the compliances of the background and the fractures. The effective governing equations for fractured porous rocks are viscoelastic anisotropic and numerically solved by the mixed-grid-stencil frequency-domain finite-difference method. The main advantage of our proposed modeling scheme over poroelastic modeling schemes is that the fractured domain can be modeled using a viscoelastic solid, while the rest of the domain can be modeled using an elastic solid. We have tested the modeling scheme in a single fracture model, a fractured model, and a modified Marmousi model. The good consistency between the scattered waves off a single horizontal fracture calculated using our proposed scheme and the poroelastic modeling validates that our modeling scheme can properly capture the fluid pressure diffusion (FPD) effects. In the case of a set of aligned fractures, the scattered waves from the top and bottom of the fractured reservoir are strongly influenced by the FPD effects, and the reflected waves from the underlying formation can retain the relevant attenuation and dispersion information. The proposed numerical modeling scheme can also be used to improve migration quality and the estimation of fracture mechanical characteristics in inversion.

Toward Tectonic-Type and Global 1D Seismic Models of the Upper Mantle Constrained by Broadband Surface Waves

ABSTRACT The unprecedentedly dense current sampling of the upper mantle with seismic data offers an opportunity for determining representative seismic velocity models for the Earth’s main tectonic environments. Here, we use over 1.17 million Rayleigh- and 300,000 Love-wave, fundamental-mode, phase-velocity curves measured with multimode waveform inversion of data available since the 1990s, and compute phase-velocity maps in a 17–310 s period range. We then compute phase-velocity curves averaged over the globe and eight tectonic environments, and invert them for 1D seismic velocity profiles of the upper mantle. The averaged curves are smooth and fit by VS models with very small misfits, under 0.1%, at most periods. For phase-velocity curves extending up to 310 s, Rayleigh waves resolve VSV structure down to the shallow lower mantle. Love-wave sampling is shallower, and VSH and, thus, radial anisotropy profiles are resolved down to 375–400 km depth. The uncertainty of the VS models is dominated by the trade-offs of VS at neighboring depths. Using the model-space-projection approach, we quantify the uncertainty of VS in layers of different thickness and at different depths, and show how it decreases with the increasing thickness of the layers. Example 1D VS models that fit the data display the expected increase of the lithospheric seismic velocity with the age of the oceanic lithosphere and with the average age of the continental tectonic type. Radial anisotropy in the global and most tectonic-type models show a flip of the sign from positive (VSH>VSV) to negative at 200–300 km depth. Negative anisotropy is also observed in the shallow mantle lithosphere beneath oceans down to 45–55 km depth. We also compute a global model with the minimal structural complexity, which fits the data worse than the best-fitting one but does not include a sublithospheric low-velocity zone, providing a simple reference for seismic studies.

METHODS FOR 3D INVERSION OF GRAVITY DATA IN INDENTIFYING TECTONIC FACTORS CONTROLLING HYDROCARBON ACCUMULATIONS IN THE EL ZEIT BASIN AREA, SOUTHWESTERN GULF OF SUEZ, EGYPT

The Gebel EL-Zeit area in the southwestern Gulf of Suez, Egypt, is an area with a significant hydrocarbon potential in sedimentary basins, so that the three-stage inversion method was proposed for the Bouguer anomalies observed therein. Salt diapirs obscured the deep structure of the main central El-Zeit basin; hence, this method was implemented to overcome challenges in 3D seismic modeling. Our study included direct and inverse parameterization sequences that involved analyzing the inputs and outputs within trial-and-error initiations and inverse estimations to assess whether and how much the constraining parameters used in the calculations could achieve the intended aim. Data reduction, filtering, optimization, and constraint assumptions were used to determine the minimal set of density model parameters needed to set limits on the acceptable range of density contrasts that are required to study the basement depths, swells, troughs, faulting/folding and intra-sedimentary structures, and for direct modeling aimed at creating a simple model to save time. The thirteen constrained wells with a total depth ranging from shallow to deep were not involved in direct modeling but provided quality control over the graphical display of the inverse results for the entire study area. Moreover, many parameter constraints were inverted to regulate the way the calculated data are related to the model’s solution that allowed us to determine which inversion trial provided the best parameterization sequence and, therefore, yielded the most appropriate solution for the depth-density model which is approximating reality with a minimal computation error in the study area.

Comparison of statistical low-frequency earthquake activity models

Slow earthquakes are slow fault slip events. Quantifying and monitoring slow earthquake activity characteristics are important, because they may change before large earthquakes occur. Statistical seismicity models are useful for quantifying seismicity characteristics. However, no standard statistical model exists for slow earthquake activity. This study used a high-quality catalog of low-frequency earthquakes (LFEs), a type of slow earthquake, in the Nankai subduction zone from April 2004 to August 2015 and conducted the first comparison of existing statistical LFE activity models to determine which model better describes LFE activity. Based on this comparison, this study proposes a new hybrid model that incorporates existing model features. The new model considers the LFE activity history in a manner similar to the epidemic-type aftershock sequence (ETAS) model and represents the LFE aftershock rate (subsequent LFE occurrence rate) with a small number of model parameters, as in the Omori–Utsu aftershock law for regular earthquakes. The results show that the proposed model outperforms other existing models. However, the new model cannot reproduce a feature of LFE activity: the sudden cessation of intense LFE bursts. This is because the new model superimposes multiple aftershock activities and predicts extremely high seismicity rates during and after the LFE bursts. I suggest that reproducing and successfully predicting the sudden cessation of intense LFE bursts is critical for the further improvement of statistical LFE activity models. In addition, the empirical equations formulated in this study for the LFE aftershock rates may be useful for future statistical and physical modeling of LFE activity.Graphical

Multi-metric evaluation of the optimal intensity measure for mainshock-aftershock fragility analysis of transmission towers

Identifying the optimal intensity measure (IM) contributes to reducing uncertainties in probabilistic seismic demand models (PSDM) and enhancing confidence of their results. Although many studies have discussed appropriate IMs for mainshocks, relatively less attention is paid to the potential aftershock effect. In particularly, the optimal IMs for developing PSDM of transmission towers subjected to sequential earthquakes has not been well studied previously. Therefore, this paper conducts a multi-metric evaluation to identify the optimal IM in the context of mainshock-aftershock (MSAS) fragility analysis of transmission towers. This evaluation process includes collecting a set of ground motions recorded with varying magnitudes and fault distances to construct MSAS sequences, followed by comprehensive discussions on their seismic characteristics by comparing thirty-six potential IMs candidates. Additionally, a finite element model of a transmission tower is established to numerically investigate different engineering demand parameters (EDP) of the tower under the selected MSAS sequences. The optimal PSDM of the transmission tower is determined by evaluating each couple of IM−EDP on a logarithmic space using multiple evaluation metrics. Through this analysis, the first-mode spectral acceleration Sa(T1,ξ) is identified as the optimal IM as it exhibits excellent correlation, efficiency, practicality and proficiency with the EDPs of the transmission tower, especially with the inter-segment displacement ratio. Consequently, seismic fragility curves of the transmission tower are developed using the optimal IM. The research outcome can contribute to improving the understanding of the probabilistic assessment of transmission towers in the MSAS scenario.

A novel machine learning approach for interpolating seismic velocity and electrical resistivity models for early-stage soil-rock assessment

A novel machine learning approach for interpolating seismic velocity and electrical resistivity models for early-stage soil-rock assessment

Forecasting the Long-Term Spatial Distribution of Earthquakes for the 2023 U.S. National Seismic Hazard Model Using Gridded Seismicity

ABSTRACT Probabilistic seismic hazard analyses such as the U.S. National Seismic Hazard Model (NSHM) typically rely on declustering and spatially smoothing an earthquake catalog to estimate a long-term time-independent (background) seismicity rate to forecast future seismicity. In support of the U.S. Geological Survey’s (USGS) 2023 update to the NSHM, we update the methods used to develop this background or gridded seismicity model component of the NSHM. As in 2018, we use a combination of fixed and adaptive kernel Gaussian smoothing. However, we implement two additional declustering methods to account for the fact that declustering is a nonunique process. These new declustering methods result in different forecasts for the locations of future seismicity, as represented by spatial probability density functions that are later combined with a rate model to produce a full gridded earthquake rate forecast. The method updates, particularly in the separation of the spatial and rate models as well as revised regional boundaries, in some places cause substantive changes to the seismic hazard forecast compared to the previous 2018 NSHM. Additional updates to catalog processing and induced seismicity zones also contribute to changes in the gridded seismicity hazard since 2018. However, these changes are well understood and reflect improvements in our modeling of gridded seismicity hazard.

Seismic risk model for regional buildings that considers the influence of temperature and intensity measures

Probability-based seismic risk and random ground motion theories are used to develop high-precision seismic risk functions and models of regional building portfolios. Seismic intensity measures and structural demand parameters are critical in developing seismic fragility models for building clusters. Earthquake damage data indicate that ambient temperature may influence structural fragility, but the effect of temperature on seismic risk is commonly ignored. A method for quantifying seismic intensity is proposed in this study and optimized using 450,000 acceleration records detected by 15 stations during the Luding earthquake in Sichuan, China, on September 5, 2022. Considering the influence of different temperature fields, the proposed seismic intensity quantification method was used to evaluate structural damage during two destructive earthquakes in Xinjiang, China (the Aktao earthquake on September 2, 2003 and the Zhaosu earthquake on December 1, 2003). Three structural empirical seismic risk matrices and cloud maps were developed, and a vulnerability membership curve was generated using fuzzy decision-making, a membership algorithm, and nonlinear regression. A structural seismic risk index function was proposed, and vulnerability cloud diagrams and curves based on actual structural seismic vulnerability datasets were generated. Together, these analyses demonstrated the impact of temperature and intensity measures on the seismic risk to regional buildings. A model was established to evaluate the seismic risk to typical structures and was validated using historical earthquake damage data from China. This method improves the accuracy of earthquake risk and vulnerability assessments for typical building clusters given the influence of temperature. The developed seismic risk prediction model enables the evaluation of vulnerability and resilience of typical structures under low and high temperatures.

Truncated pseudo-differential operator √−▽2 and its applications in viscoacoustic reverse-time migration

SUMMARY The pseudo-differential operator with symbol |k|α has been widely used in seismic modelling and imaging when involving attenuation, anisotropy and one-way wave equation, which is usually calculated using the pseudo-spectral method. For large-scale problems, applying high-dimensional Fourier transforms to solve the wave equation that includes pseudo-differential operators is much more expensive than finite-difference approaches, and it is not suitable for parallel computing with domain decomposition. To mitigate this difficulty, we present a truncated space-domain convolution method to efficiently compute the pseudo-differential operator $\sqrt{-\nabla ^2}$, and then apply it to viscoacoustic reverse-time migration. Although $\sqrt{-\nabla ^2}$ is theoretically non-local in the space domain, we take the limited frequency band of seismic data into account, and constrain the approximated convolution stencil to a finite length. The convolution coefficients are computed by solving a least-squares inverse problem in the wavenumber domain. In addition, we exploit the symmetry of the resulting convolution stencil and develop a fast spatial convolution algorithm. The applications of the proposed method in Q-compensated reverse-time migration demonstrate that it is a good alternative to the pseudo-spectral method for computing the pseudo-differential operator $\sqrt{-\nabla ^2}$, with almost the same accuracy but much higher efficiency.