Earthquake Magnitude Research Articles

Hydroacoustic sensing of seismic events during the Tajogaite volcanic eruption (La Palma, Spain)

Volcanic processes generate a variety of seismic events that can be detected by both on-land and underwater sensors. During the 2021 subaerial eruption of the Tajogaite volcano on La Palma Island (Canary Islands, NW Africa), an underwater acoustic sensor was strategically deployed to monitor seismic activity. This study presents marine passive acoustic monitoring data from a moored hydrophone deployed offshore at a depth of 77 m and 7 km from the volcanic vent, both during and after the eruption. We compare hydrophone recordings with island’s seismic network and earthquake database from the Instituto Geográfico Nacional (IGN). By calculating acoustic metrics and analyzing low-frequency bands (< 100 Hz), we identified 712 impulsive acoustic signals consistent with seismic events recorded in the seismic catalogue. These acoustic signals were double-pulsed, low-frequency (≤ 50 Hz with peak frequencies ≤ 15 Hz) and exhibited sound levels that well correlated with earthquake magnitudes. Our findings demonstrate that shallow-water hydro-acoustics can detect and estimate the magnitude of volcano-tectonic earthquakes in the studied scenario. These results encourage for the integration of hydro-acoustic monitoring in conjunction with on-land seismic stations to enhance the overall monitoring of the investigated volcanic area seismic activity.

HEM NAEMP: a novel hybrid ensemble model for North Anatolian Fault zone earthquake magnitude prediction

Abstract The application of machine learning in predicting earthquake magnitudes is crucial due to its ability to process extensive data sets and identify intricate patterns, thereby enhancing the accuracy and timeliness of predictions. This capability is essential for improving readiness and relief techniques against seismic activities. This study introduces a novel hybrid ensemble model, the HEM NAEMP, specifically evolved for predicting earthquake magnitudes along the North Anatolian Fault zone. The model integrates data from both the North Anatolian and San Andreas fault zones-the latter selected due to its tectonic similarity-to develop a comprehensive dataset that includes newly extracted features. The novelty of this study lies in the combination of data from two different fault lines to create a new dataset, the extraction of novel features, and the development of a previously unused model leveraging this dataset and its features. The HEM NAEMP model employs a several of regression algorithms, including k-nearest neighbors, random forest, support vector machine, decision tree and extreme gradient boosting, to effectively predict earthquake magnitude. The evaluation metrics for the model are as follows: mean squared error (MSE) of 0.011, mean absolute error (MAE) of 0.064, root mean squared error (RMSE) of 0.108, mean absolute percentage error (MAPE) of 0.268, R Square $$(\text {R}^2)$$ ( R 2 ) of 0.92 and training time of 2.44 sec. These results are compared against those from a Long-Short Term Memory (LSTM), Convolutional Neural Network (CNN) and AutoRegressive Integrated Moving Average (ARIMA) models, demonstrating that HEM NAEMP has mostly lower error rates in MAE and MAPE and high score in $$\text {R}^2$$ R 2 , as well as reduced training time, thereby confirming its viability and efficiency.

Upgrading a Low-Cost Seismograph for Monitoring Local Seismicity

The use of a dense network of commercial high-cost seismographs for earthquake monitoring is often financially unfeasible. A viable alternative to address this limitation is the development of a network of low-cost seismographs capable of monitoring local seismic events with a precision comparable to that of high-cost instruments within a specified distance from the epicenter. The primary aim of this study is to compare the performance of an advanced, contemporary low-cost seismograph with that of a commercial, high-cost seismograph. The proposed system is enhanced through the integration of a 24-bit analog-to-digital converter board and an optimized architecture for a low-noise signal amplifier employing active components for seismic signal detection. To calibrate and assess the performance of the low-cost seismograph, an installation was deployed in a region of high seismic activity in Evgiros, Lefkada Island, Greece. The low-cost system was co-located with a high-resolution 24-bit commercial digitizer, equipped with a broadband (30 s—50 Hz) seismometer. An uninterrupted dataset was collected from the low-cost system over a period of more than two years, encompassing 60 local events with magnitudes ranging from 0.9 to 3.2, epicentral distances from 5.71 km to 23.45 km, and focal depths from 1.83 km to 19.69 km. Preliminary findings demonstrate a significant improvement in the accuracy of earthquake magnitude estimation compared to the initial configuration of the low-cost seismograph. Specifically, the proposed system achieved a mean error of ±0.087 when benchmarked against the data collected by the high-cost commercial seismograph. These results underscore the potential of low-cost seismographs to serve as an effective and financially accessible solution for local seismic monitoring.

Machine learning for predicting earthquake magnitudes in the Central Himalaya

Human intervention cannot halt natural disasters like earthquakes, but machine learning application expertise can be utilized to detect patterns in data and increase understanding and predictive power. Recent development of machine learning models has increasingly developed interest in forecasting and predicting the magnitude of earthquakes. In this work, Random Forest Regressor (RFR), Multi-Layer Perceptron Regressor(MLPR), and Support Vector Regression (SVR) models were employed to predict the magnitude of greater than 6 mb earthquakes that occurred in the year 2015 in the central Himalaya. We noticed RFR method had been able to predict the magnitude of the Gorkha earthquake (6.9mb), and the Kodariearthquake (6.7 mb) in comparison with the other two models. We also checked the performance of these models by three parameters Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE) and noticed the better performance of RFR model. The findings illustrate that RFR is achieving better performance than the other two algorithms, as the predicted magnitudes are close to the actual magnitudes.

Importance sampling of seismic tsunami sources with near-field emphasis for inundation PTHA: benchmarking with complete ensembles

Summary Site-specific Probabilistic Tsunami Hazard Assessment (PTHA) is a powerful tool for coastal planning against tsunami risk. However, its typically high computational demands led to the introduction of a Monte Carlo Stratified Importance Sampling (SIS) approach, which selects a representative subset of scenarios for numerical inundation simulations. We here empirically validate this sampling approach, for the first time to our knowledge, using an existing extensive dataset of numerical inundation simulations for two coastal sites in the Mediterranean Sea (Catania and Siracusa, both located in Sicily, Italy). Moreover, we propose a modified importance sampling function to prioritise seismic tsunami scenarios based on their arrival time at an offshore point near the target site, in addition to their wave amplitude and occurrence rate as leveraged in the previous work. This sampling function is applied separately in each earthquake magnitude bin, and allows denser sampling of near-field earthquakes to whose variations tsunamis are very sensitive. We compare the confidence intervals of the offshore PTHA estimates obtained with the new and the original importance sampling functions. Then, we benchmark our onshore PTHA estimates obtained with both functions against the inundation PTHA calculated using the full set of scenarios. We also test the assumption that onshore random errors follow a normal distribution, as found previously for the offshore case. As a result of the benchmarks, we find that the SIS approach works satisfactorily. Introducing the arrival time as an additional sampling factor enhances the precision of the estimates of both the mean and the percentiles for the two coastal sites considered. With this modification it is possible to deal efficiently with heterogeneous near-field earthquake sources involving coastal deformation at Catania and Siracusa, in addition to regional crustal and subduction sources. By comparing the sampling errors with the model (epistemic) uncertainty, an optimal trade-off between the number of simulations employed and the uncertainty of the PTHA model can be found, even for such a complex situation. A relatively small number of scenarios, on the order of a few thousand, is sufficient to perform site-specific PTHA for practical applications. These numbers correspond to 4–8% of the already reduced ensembles used in previous assessments at the same sites.

Automatic speech recognition predicts contemporaneous earthquake fault displacement

Significant progress has been made in probing the state of an earthquake fault by applying machine learning to continuous seismic waveforms. The breakthroughs were originally obtained from laboratory shear experiments and numerical simulations of fault shear, then successfully extended to slow-slipping faults. Here we apply the Wav2Vec-2.0 self-supervised framework for automatic speech recognition to continuous seismic signals emanating from a sequence of moderate magnitude earthquakes during the 2018 caldera collapse at the Kīlauea volcano on the island of Hawai’i. We pre-train the Wav2Vec-2.0 model using caldera seismic waveforms and augment the model architecture to predict contemporaneous surface displacement during the caldera collapse sequence, a proxy for fault displacement. We find the model displacement predictions to be excellent. The model is adapted for near-future prediction information and found hints of prediction capability, but the results are not robust. The results demonstrate that earthquake faults emit seismic signatures in a similar manner to laboratory and numerical simulation faults, and artificial intelligence models developed for encoding audio of speech may have important applications in studying active fault zones.

Bibliometric Analysis in the Context of Earthquake and Türkiye

Türkiye has experienced many earthquakes of different magnitudes throughout history. Since the destructive consequences of these earthquakes lead to disasters, they have an important place in terms of disaster management. Considering the seismicity of Türkiye, this study aims to present a bibliometric analysis of the studies on earthquakes and Türkiye from the Web of Science (WOS) database. In the study, filters were applied within the framework of various criteria, and analyses were made in the VOSviewer program. Within the scope of the study, it was determined that studies on Earthquake &amp;amp; Türkiye have increased in recent years, the journal with the most publications is Geophysical Journal International, and the most cited study is “Progressive failure on the North Anatolian fault since 1939 by earthquake stress triggering”.It was determined that Barka, Aykut stand out among the authors regarding total link strength and citations, and Ergintav, Semih regarding number of documents and co-authorship. In terms of countries, the USA is the country with the most publications after Türkiye. In terms of keywords, earthquake, Türkiye and the North Anatolian Fault Zone came to the fore. It is thought that this study will be an important reference for researchers who want to study earthquakes in Türkiye.

Empirical regressions for distributed faulting of dip-slip earthquakes

Probabilistic Fault Displacement Hazard Analysis (PFDHA) is pivotal in assessing the probability of surface fault displacement during seismic events, with critical implications for infrastructure systems like pipelines and lifelines. Recent earthquakes have underscored the importance of fault displacement as a cause of damage. This study aims to improve predictive models and regression analyses to assess the probability and expected amount of throw on distributed ruptures (DR) from normal and reverse earthquakes. The research leverages the SURE 2.0 database, which classifies ruptures into different ranks, including primary and various typologies of distributed ruptures. Logistic regression models are employed to assess the probability of DR occurrence, considering factors such as earthquake magnitude, proximity to the principal fault, faulting style, and DR location (hanging wall/footwall) as predictor variable. In addition, a fault displacement model is formulated to estimate the median throw on DRs based on these parameters and on a mean throw on the principal fault. The outcomes offer valuable insights into the characteristics and likelihood of DRs, carrying implications for PFDHA applications. The study introduces a decision-tree algorithm designed to assist PFDHA practitioners in selecting the most suitable approach based on the available geological knowledge. This study contributes to an improved understanding of fault displacement hazard analysis and provides a versatile framework for its application across diverse geological contexts.

Earthquake induced liquefaction hazard analysis for Chittagong City using machine learning

Liquefaction hazard analysis is crucial in earthquake-prone regions as it magnifies structural damage. In this study, standard penetration test (SPT) and shear wave velocity ( V s ) data of Chittagong City have been used to assess the liquefaction resistance of soils using artificial neural network (ANN). For a scenario of 7.5 magnitude (Mw) earthquake in Chittagong City, estimating the liquefaction-resistance involves utilizing peak horizontal ground acceleration (PGA) values of 0.15 and 0.28 g. Then, liquefaction potential index (LPI) is determined to assess the severity of liquefaction. In most boreholes, the LPI values are generally higher, with slightly elevated values in SPT data compared to V s data. The current study suggests that the Valley Alluvium, Beach and Dune Sand may experience extreme liquefaction with LPI values ranges from 9.55 to 55.03 and 0 to 37.17 for SPT and V s respectively, under a PGA of 0.15 g. Furthermore, LPI values ranges from 25.55 to 71.45 and 9.55 to 54.39 for SPT and V s correspondingly. The liquefaction hazard map can be utilized to protect public safety, infrastructure, and to create a more resilient Chittagong City.

Limitations of earthquake coseismic deformation measurements using InSAR

ABSTRACT Interferometric Synthetic Aperture Radar (InSAR) is commonly used to measure earthquake coseismic deformation. However, InSAR cannot be used to effectively measure all types of coseismic deformation, and it is influenced by numerous factors. Currently, for the limitations of InSAR coseismic deformation measurement, only empirical judgements are used to address these issues, and quantitive descriptions are lacking. To determine the limits of coseismic deformation that can be measured using InSAR, we assessed the effects of satellite parameters, earthquake magnitude, and earthquake depth on such measurements through coseismic deformation simulations and fault parameter traversals. By comparing the absolute deformation magnitudes, we identified the fault parameters that were most and least sensitive to coseismic deformation measurements using InSAR. We then quantitatively analysed the upper and lower limits of earthquake magnitude and depth for InSAR coseismic deformation measurements. The lower limit was determined by comparing noise and deformation, whereas the upper limit was determined from the phase gradient ambiguity. We used the least squares method to derive an empirical equation that can be used to screen earthquake catalogues for further inversion with InSAR measurements. We found that coseismic deformation measurements using satellites are limited by their sensitivities to fault strike, rake, and dip angles. Additionally, the smallest earthquake magnitude that can be measured by InSAR varies with depth. These findings can be used to improve our understanding of the limitations and capabilities of InSAR for measuring coseismic deformation.

Revealing Channelized Features Through Multi-Scale Workflows in A Mixed Carbonate Siliciclastic Setting, Grayburg and San Andres Formations, Midland Basin, TX.

Mixed carbonate-siliciclastic channelized systems pose significant challenges for geological characterization due to their high lithological variability. Understanding the lithological distribution is crucial for deciphering basin evolution and guiding ongoing drilling operations.#xD;An example of such a mixed channel system is identified in the San Andres and Grayburg Formations in the Midland Basin, TX. These units feature siliciclastic-infilled channels cutting across predominantly carbonate shelves. An integrated study of core, well-log, and seismic data was conducted to analyze the lithological variability of the channelized interval and understand its geomorphological evolution. Seismic attributes such as coherent energy, sweetness, and spectral decomposition proved to be the most efficient at enhancing the contrast between clastic and carbonate elements, demonstrating the feasibility of depicting lithological heterogeneity at a seismic scale. Additionally, conventional seismic interpretation and geometric attributes revealed two categories of channel incisions: type I, characterized by V-shaped bases, straight, and mostly oriented in a NE-SW direction; and type II, characterized by U-shaped bases, slightly sinuous, and a NW-SE orientation. Well-log based litho-density techniques and core descriptions corroborated the seismic observations by illustrating heterogeneity and the siliciclastic nature of the channel infills.#xD;A 3D lithology model constrained by the previous analyses shows a dominance of siliciclastics in the Lower San Andres, while the Upper San Andres and Grayburg are limestone-rich with episodic siliciclastic events (i.e., channel incisions) and dolostone (in the Upper Grayburg). Geomorphological and stratigraphic variations were correlated to changes in sea level and source rock composition. Overall, these insights improve our understanding of siliciclastic deposition in these formations within the Midland Basin, potentially serving as analogs for the Brushy and Cherry Canyon formations in the Delaware Basin.#xD;

Analysis of borehole strain anomalies before the 2017 Jiuzhaigou Ms 7.0 earthquake based on a graph neural network

Abstract. On 8 August 2017, a strong earthquake of magnitude 7.0 occurred in Jiuzhaigou, Sichuan Province, China. To assess pre-earthquake anomalies, we utilized variational mode decomposition to preprocess borehole strain observation data and combined them with a graph WaveNet neural network model to process data from multiple stations. We obtained 1-year data from four stations near the epicenter as the training dataset and data from 1 January to 10 August 2017 as the test dataset. For the prediction results of the variational mode decomposition–graph WaveNet model, the anomalous days were extracted using statistical methods, and the results of anomalous-day accumulation at multiple stations showed that an increase in the number of anomalous days occurred 15–32 d before the earthquake. The acceleration effect of anomalous accumulation was most obvious 20 d before the earthquake, and an increase in the number of anomalous days also occurred in the 1 to 3 d post-earthquake. We tentatively deduce that the pre-earthquake anomalies are caused by the diffusion of strain energy near the epicenter during the accumulation process, which can be used as a signal of pre-seismic anomalies, whereas the post-earthquake anomalies are caused by the frequent occurrence of aftershocks.

Generating Input Ground Motions for Seismic Risk Assessment Using Recorded Ground Motions from the Moderate Magnitude Earthquake

To secure the seismic performance of structures, seismic risk assessment is necessary to quantify safety against beyond-design-based earthquakes and seismic design. For the seismic risk assessment of structures, the input ground motions corresponding to the seismic intensity for evaluation are required as seismic loads, which must reflect the tectonic characteristics and site conditions. In this study, ground motions recorded in regions of low to moderate seismicity were used to generate examples of input ground motions for seismic risk assessment. A uniform hazard spectrum (UHS) was used as the target spectrum for risk assessment, following the guidelines. The magnitude and distance parameters of the scenario earthquake for seismic risk assessment were determined via hazard de-aggregation. The empirical Green’s function method (EGFM) was used to match the ground motion recorded at the site with the seismic intensity required for seismic risk assessment. In addition, a spectral matching process was applied to ensure that the input ground motion was compatible with the response spectrum used in seismic risk assessment. In this process, the convergence characteristics of the spectral matching to the target spectrum were analyzed. Consequently, the spectral conditions for selecting the ground motion for the seismic risk assessment were determined.

Comparison of coseismic velocity changes estimated by cross-correlation of ambient seismic noise for earthquakes in south Korea and Japan

Ambient noise cross-correlation has been widely used to observe post-earthquake temporal velocity variations. Comparative studies are essential for assessing seismic hazards and clarifying the relationship between velocity variation and magnitude. However, very few comparative studies by earthquake magnitude have been conducted, particularly for magnitudes smaller than 6. In 2016 and 2017, southeastern Korea experienced the two most damaging earthquakes of the past 250 years: the Pohang earthquake (M 5.4) and Gyeongju earthquake (M 5.8). This study compared the coseismic velocity variations of these earthquakes with those observed in the M 7.3 Kumamoto and M 6.6 Tottori earthquakes, which occurred in Japan in 2016. In this study, the moving window cross-spectral analysis revealed different curves for bidirectional cross-correlations, a difference that has not been addressed in previous studies. This discrepancy was most likely caused by data deficiencies due to prolonged aftershocks or by instability from small-magnitude earthquakes recorded by surface seismometers in Korea. The average velocity decrease between forward and reverse order pairs correlated well with earthquake magnitude, except in the case of the Korean earthquake. Our devised measure based on aftershock activity suggests that the large decrease in the Pohang earthquake was due to non-coseismic noise in addition to instability.

Seismic and GNSS strain-based probabilistic seismic hazard evaluation for northern Chile using DAS Magnitude Scale

BackgroundProbabilistic Seismic Hazard Assessment (PSHA) is a leading methodology for determining key ground motion parameters such as Peak Ground Acceleration (PGA) and spectral acceleration (SA), essential for structural design. This approach uses extensive earthquake data, typically spanning over a century, leveraging frequency and magnitude statistics. However, long-term ground shaking probabilities may not always be accurately captured by traditional data-driven methods. To address these limitations, this study develops a PSHA map for Northern Chile using both seismic and GNSS (Global Navigation Satellite System) data. A curated homogeneous earthquake catalog, based on the advanced seismic moment magnitude scale Mwg(Das Magnitude Scale), replaces the traditional Mw scale to ensure superior accuracy, particularly for intermediate and smaller earthquakes.ResultsUsing the earthquake catalog, seismicity parameters ‘a’ and ‘b’ from the Gutenberg-Richter relationship were derived. Seismogenic modeling and Ground Motion Models (GMMs) were applied to estimate ground motion probabilities for a 475-year return period. Additionally, a PSHA map was constructed using GNSS strain rates, translating velocity-derived strain rates into seismic moment rates and ground shaking probabilities for seismic source zones. Comparative analyses revealed higher PGA values from GNSS strain data compared to seismic catalog data. GNSS strain data proved invaluable for refining seismic segmentation in Northern Chile, enhancing the precision of PSHA calculations.ConclusionsA PSHA map for Northern Chile, synthesizing seismic catalog data and GNSS strain rates using a Logic Tree-based algorithm, has been developed for a 475-year return period. This map provides a critical tool for generating seismic hazard assessments aligned with building codes and emergency planning protocols. By integrating GNSS strain rates and seismic data, this study advances the reliability and accuracy of long-term ground shaking predictions.

Suggestions and Applications for Evaluating Seismic Functionality for Railway Infrastructure Network Based on Fragility Curve

This study proposes a novel model to quantitatively evaluate functionality loss in railway network systems during earthquakes and assesses its applicability to a hypothetical railway network system. The model combines seismic fragility functions and restoration curves to assess functionality loss, deriving a time-dependent recovery function to propose a functionality loss model based on earthquake magnitude. The proposed model uses a hypothetical railway network to calculate the overall functionality loss of the network under various earthquake scenarios. The hypothetical railway network was designed with three lines, allowing different routes to remain operational depending on the damaged sections and increasing the diversity of network impact scenarios based on the functionality loss. This model provides a framework for analyzing the functionality loss and recovery processes of railway networks during seismic events and assessing the socioeconomic impacts of earthquakes.

Duration of the Occurrence of Mw ≥ 4.5 Aftershocks of the 2 April 2024 Mw 7.4 Hualin, Taiwan Earthquake

ABSTRACT Taiwan was shaken in the early morning of 2 April 2024 by an Mw 7.4 earthquake. Earthquakes of magnitude 7 and above are normally followed by damaging aftershocks. It is useful to have an estimate as to how long such aftershocks will continue. This knowledge helps in the recovery process. The duration of occurrence of the aftershocks of certain magnitudes can be estimated using Omori’s Law. Using the data of the aftershocks of the first 14 days after the Hualien earthquake, we estimated that the Mw ≥ 4.5 aftershocks shall continue for 80 days. Now, we are presenting analysis of recently available catalog up to 80 days to check and validate the prediction. Our analysis suggests that the rate of Mw ≥ 4.5 aftershocks in the region has gone down to the background seismicity rate after the estimated period of time.

Seismotectonic and Geological Mapping around the High and Middle Atlas Junction: Integration of Satellite Imagery and Seismic Analysis in the Tizi N’Isly Basin, Morocco

The Tizi N’Isly basin, located between the Central High Atlas and Middle Atlas of Morocco, features a complex geological and seismic profile. This study aims to precisely identify areas of vulnerability, seismic zones, and regions exhibiting seismic amplification. The High Atlas is known for its seismic activity, with a notable earthquake of magnitude 6.8 occurring on September 8, 2023, at a depth of 10 km, attributed to an unidentified fault. This event, followed by significant aftershocks, represents the most substantial seismic activity in Morocco since the 1960 Agadir earthquake (magnitude 5.9). Our research combines geological mapping, lineament extraction from satellite imagery, and seismic analysis is to understand the surface and subsurface geology and tectonics. Processed satellite images enhance geological features, facilitating the identification of faults and fractures. Geostatistical analysis of meso-Cenozoic terrain fracturing reveals that lineaments predominantly align with NNE-SSW to NE-SW directions, with additional minor fracture directions. The seismic activity observed is closely linked to faults within this zone, highlighting regional weaknesses.

Relationship Between Near-Fault Strong Ground Motion and Earthquake Magnitude of Crustal Earthquake Using Dynamic Rupture Simulation

Relationship Between Near-Fault Strong Ground Motion and Earthquake Magnitude of Crustal Earthquake Using Dynamic Rupture Simulation

Testing Driving Mechanisms of Megathrust Seismicity With Explainable Artificial Intelligence

AbstractThe correlation between subduction zone features and megathrust seismicity provides relevant clues on what controls the generation, location and clustering of mega‐earthquakes (magnitudes Mw ≥ 8.0). Thus far, weak correlations are found between subduction zone parameters and seismicity through bivariate statistical analyses. Here, we used Explainable Artificial Intelligence (XAI) to assess the relevance of geophysical properties and tectonic motions along major subduction zones, paired with novel proxies of slab stress from calculations of buoyancy‐driven subduction. The features derived from these data sets, describing the physical state, kinematics, and dynamics, served as inputs to a Fully Connected Network (FCN) trained to classify segments according to the largest earthquake magnitude that ruptured it. The subsequent use of Layer‐wise Relevance Propagation, an XAI technique, on a trained FCN provides an estimate of the relevance of the input, identifying the features most relevant to the classification. The XAI procedure confirmed the importance of subduction interface curvature, sediment thickness, long wavelength bathymetric roughness, and free‐air gravity anomalies, as previously proposed. Interestingly, our procedure revealed the importance of slabs extending to the upper mantle as well as the trench‐parallel slab stress, showing how three‐dimensional subduction forces may control large earthquakes. This suggests the preferential occurrence of large earthquakes on megathrust segments around slab steps and edges, where the slab depth measured along trench varies abruptly. At these steps, the trench‐parallel forcing is maximized by the excess load of neighboring deeper slabs.