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The contribution of the Antarctic Ice Sheet to barystatic sea-level rise could be as high as eight metres around 2300 but remains deeply uncertain. Ice sheet retreat causes bedrock uplift, which can exert a stabilising effect on the grounding line. Yet, sea-level projections exclude bedrock adjustment, use simplified Earth structures or omit the uncertainty in climate response and Earth structure. We show that the grounding line retreat is delayed by 50 to 130 years and the barystatic sea-level contribution reduced by 9–23% when the heterogeneity of the solid Earth is included in a coupled ice – bedrock model under different emission scenarios till 2500. The effect of the solid Earth feedback in ice sheet projections can be twice as large as the uncertainty due to differences between climate models. We emphasise that realistic Earth structures should be considered when projecting the Antarctic contribution to barystatic sea-level rise on centennial time scales. This study finds that Antarctica’s ground uplift slows ice retreat. More realistic Earth models show future sea-level rise could be up to about 20% lower than estimates that ignore this effect.

The dynamics of the ice sheets on glacial timescales are highly controlled by interactions with the solid Earth, i.e., the glacial isostatic adjustment (GIA). Particularly at marine ice sheets, competing feedback mechanisms govern the migration of the ice sheet's grounding line (GL) and hence the ice sheet stability. For this study, we developed a coupling scheme and performed a suite of coupled ice sheet–solid Earth simulations over the last two glacial cycles. To represent ice sheet dynamics we apply the Parallel Ice Sheet Model (PISM), and to represent the solid Earth response we apply the 3D VIscoelastic Lithosphere and MAntle model (VILMA), which, in addition to load deformation and rotation changes, considers the gravitationally consistent redistribution of water (the sea-level equation). We decided on an offline coupling between the two model components. By convergence of trajectories of the Antarctic Ice Sheet deglaciation we determine optimal coupling time step and spatial resolution of the GIA model and compare patterns of inferred relative sea-level change since the Last Glacial Maximum with the results from previous studies. With our coupling setup we evaluate the relevance of feedback mechanisms for the glaciation and deglaciation phases in Antarctica considering different 3D Earth structures resulting in a range of load-response timescales. For rather long timescales, in a glacial climate associated with the far-field sea-level low stand, we find GL advance up to the edge of the continental shelf mainly in West Antarctica, dominated by a self-amplifying GIA feedback, which we call the “forebulge feedback”. For the much shorter timescale of deglaciation, dominated by the marine ice sheet instability, our simulations suggest that the stabilizing sea-level feedback can significantly slow down GL retreat in the Ross sector, which is dominated by a very weak Earth structure (i.e., low mantle viscosity and thin lithosphere). This delaying effect prevents a Holocene GL retreat beyond its present-day position, which is discussed in the scientific community and supported by observational evidence at the Siple Coast and by previous model simulations. The applied coupled framework, PISM–VILMA, allows for defining restart states to run multiple sensitivity simulations from. It can be easily implemented in Earth system models (ESMs) and provides the tools to gain a better understanding of ice sheet stability on glacial timescales as well as in a warmer future climate.

The bedrock deformation in response to a melting ice sheet provides negative feedback on ice mass loss. When modelling the future behaviour of the Antarctic Ice Sheet, the impact of bed deformation on ice dynamics varies but can reduce projections of future sea-level rise by up to 40 % in comparison with scenarios that assume a rigid Earth. The rate of the solid Earth response is mainly dependent on the viscosity of the Earth's mantle, which varies laterally and radially with several orders of magnitude across Antarctica. Because modelling the response for a varying viscosity is computationally expensive and has only recently been shown to be necessary over centennial time scales, sea-level projection ensembles often exclude the Earth's response or apply a globally constant relaxation time or viscosity. We use a coupled model to investigate the accuracy of various approaches to modelling the bedrock deformation to ice load change. Specifically, we compare the sea-level projections from an ice-sheet model coupled to (i) an elastic lithosphere, relaxed asthenosphere (ELRA) model, with either uniform and laterally varying relaxation times, (ii) a glacial isostatic adjustment (GIA) model with a radially varying Earth structure (1D GIA model), and (iii) a GIA model with laterally varying earth structures (3D GIA model). Furthermore, using the 3D GIA model we determine a relation between relaxation time and viscosity which can be used in ELRA and 1D models. We conduct 500-year projections of Antarctic Ice Sheet evolution using two different climate models and two emissions scenarios: the high emission scenario SSP5-8.5 and the low emission scenario SSP1-2.6. Using a rigid Earth model, this results in ∼3–7.5 m of barystatic sea-level rise with significant retreat in various basins due to marine ice sheet instability. The results show that using a uniform relaxation time of 300 years in an ELRA model leads to a total sea-level rise that deviates less than 40 cm (6 %) from the average of the 3D GIA models in 2500. This difference in the projected sea-level rise can be further reduced to 20 cm (4 %) by using an upper mantle viscosity of 1019 Pa s in the 1D GIA model, and to 10 cm (2 %) in 2500 by using a laterally varying relaxation time map in an ELRA model. Our results show that the Antarctic Ice Sheet contribution to sea-level rise can be approximated sufficiently accurate using ELRA or a 1D GIA model when the recommended parameters derived from the full 3D GIA model are used.

Ocean tide loading (OTL) displacements are sensitive to the shallow structure of the solid Earth; hence, the high-resolution spatial pattern of OTL displacement can provide knowledge to constrain the shallow Earth structure, especially in coastal areas. In this study, we investigate the sensitivity of the modeled M2 OTL displacement over Taiwan Island to perturbations of three physical quantities, namely, the density, bulk modulus, and shear modulus in the upper mantle and crust. Then, we compare the sensitivity of the modeled M2 OTL displacement to Earth models with the sensitivity to ocean tide models using root mean square (RMS) differences. We compute the displacement Green’s function and OTL displacement relative to the center of mass of the solid Earth (CE) reference frame, analyze the sensitivity to the three physical quantities in the CRUST1.0 model and the Preliminary Reference Earth Model (PREM), and present their spatial patterns. We find that displacement Green’s functions and OTL displacements are more sensitive to the two elastic moduli than the density in the upper mantle and crust. Moreover, their distinctive sensitivity patterns suggest that the three physical quantities might be constrained independently. The specific relationships between the perturbed structural depths and the distance ranges of peak sensitivities from the observation points to the coastline revealed by the shear modulus can mitigate the nonuniqueness problem in inversion. In particular, the horizontal tidal components observed by the Global Positioning System (GPS) can yield better results in inversions than the vertical component owing to the smaller OTL model errors and the higher structural sensitivity (except for the shear modulus in the asthenosphere).

The growing industrialism has led to the generation of unmanageable waste, which is usually dumped in landfills. Utilizing these materials in reinforced earth structures will not only help in large-scale recycling of the materials but also restrict the overutilization of geo-materials. The aim of the present study is to assess the interaction of biaxial geogrid with two different solid waste materials namely, steel slag (SS) and construction and demolition waste (CDW) and compare its performance with the conventional backfill material, sand. To achieve this, direct shear tests and pullout tests were conducted at various normal stress levels ranging from 25 to 200 kPa. The direct shear results revealed that both steel slag and CDW exhibits higher shear strength compared to sand. Similarly, the pullout test results indicated that the pullout resistance of the geogrid is higher in steel slag and CDW than in sand. The pullout resistance factor ( F ∗ ) was evaluated to quantify the interaction of the geogrid with backfills. F ∗ values were found to be greater than 1 at lower normal stress (25 kPa), and less than 1 at higher normal stress (200 kPa), indicating a stronger interaction at lower normal stresses. According to interaction coefficient ratio (ICR) values, the interaction of the geogrid with steel slag and CDW at 25 kPa normal stress was 38% and 33% higher, respectively, than that with sand. Furthermore, an artificial neural network (ANN) model was developed using data from the current study as well as data gathered from previous studies to predict the pullout resistance of geogrids in a wide range of geomaterials. An excellent prediction capability was observed with coefficient of determination ( R 2 ) value more than 0.9.

Heat provides the energy that drives almost all geological phenomena and sets the temperature at which these phenomena operate. This book explains the key physical principles of heat transport with simple physical arguments and scaling laws that allow quantitative evaluation of heat flux and cooling conditions in a variety of geological settings and systems. The thermal structure and evolution of magma reservoirs, the crust, the lithosphere and the mantle of the Earth are reviewed within the context of plate tectonics and mantle convection - illustrating how theoretical arguments can be combined with field and laboratory data to arrive at accurate interpretations of geological observations. Appendices contain data on the thermal properties of rocks, surface heat flux measurements and rates of radiogenic heat production. This book can be used for advanced courses in geophysics, geodynamics and magmatic processes, and is a reference for researchers in geoscience, environmental science, physics, engineering and fluid dynamics.

Seismic arrays, first introduced in the late 1950s to detect underground nuclear explosions, have helped to improve our knowledge about the structure of the Earth for the last 40 years. During these years, numerous array processing methods have been developed that use the high signal coherence and accurate timing of array data to generate high-resolution images of Earth structure. Here, we present an overview of resolution issues related to seismic array studies of Earth structure by first introducing basic array processing techniques and then discussing more advanced techniques applied to array data recently. The increase of seismic stations deployed in experiments or permanently in many regions of the globe allows a much denser sampling of the seismic wavefield. This dense sampling enables the adaptation of controlled source analysis techniques for the study of Earth structure using earthquakes with higher resolution than previously possible. Here we will discuss different migration methods of teleseismic data that use the incidence angle information of scattered arrivals to obtain images of Earth structure. Finally, we show data examples how these methods can be used to increase our knowledge of the structure of the Earth’s deep interior.

Optimization models for reinforced earth structures such as foundation pads, bridge abutments, and embankments based on the Eurocode standard are presented. The developed optimization models, which take into account construction costs and environmental footprint, are used to determine an optimal design for each earth structure. The optimization model uses discrete variables, making the results more suitable for actual construction practice and fully exploiting the geotechnical and structural capacity of earth structures with geosynthetic reinforcement. The multi-objective optimization was performed to find a set of solutions that represent the best trade-off between construction cost and environmental footprint. The results show that the correct selection of geosynthetics leads to a significant reduction in costs and environmental impact. The general observation that emerges from the multi-objective optimization is that when designing the earth structures using geosynthetic reinforcements, due to the discrete set of variables, there are not so many optimal solutions that the designer can choose from. The entire optimization process is illustrated with the help of a numerical example. This study can help engineers to select earth structure and geosynthetic reinforcements that are economical and sustainable.

The dynamic response of earth-retaining structures is a complex issue. The design of these structures under seismic loading conditions is, therefore, quite challenging. Because there are not many case histories on field performance of earth-retaining structures, the theory of dynamic response has been based on the results from both model tests and numerical analyses. The most common approach to the seismic design of retaining walls, especially where the expected ground acceleration is less than or equal to 0.29g, involves estimating the loads imposed on the wall during earthquake shaking and then ensuring that the wall can resist those loads. Because the actual loading on retaining walls during earthquakes is extremely complicated, seismic pressures are usually estimated using the Mononobe-Okabe pseudo-static method. The Mononobe-Okabe equation is an extension of the Coulomb’s classical solution, which accounts for inertial forces. Another approach for designing against seismic loading is to allow for an “acceptable permanent deformation” and determine the dimensions of the structure accordingly. This approach is typically more appropriate for retaining structures to be built in highly seismic regions, where the peak ground acceleration for the design earthquake is larger than 0.29g. Neither the Mononobe-Okabe method nor the displacement method accounts for the characteristics of the ground motion. More realistic dynamic response analysis can be performed using the results from laboratory studies and numerical models. This paper presents the state-of-the-art for the design of earth-retaining structures under dynamic loading conditions. The commonly used simplified design procedures were presented. Relatively recent laboratory studies and numerical solutions were reviewed. Some case histories regarding the seismic performance of retaining walls were also listed.

Seismic waves preceding the core phase PKIKP, known as PKP precursors, have been used to map small scatterers near the core‐mantle boundary (CMB). However, their low signal‐to‐noise ratio has required manual identification, hindering systematic and comprehensive analysis. Here, we develop GraphCursor, a model based on Graph Neural Networks (GNNs), to detect PKP precursors across multiple stations. Trained on manually picked precursors, GraphCursor identifies 37,512 precursor waveforms from 5,499 global earthquakes (2000–2024). We locate scatterers by stacking multistation probability functions and estimate their strengths relative to global averages. Our exhaustive search produces unprecedentedly abundant scatterers, including new discoveries of those beneath Antarctica. The distribution of most global scatterers largely correlates with ultra‐low velocity zones (ULVZs). GraphCursor's potential extends to identifying other deep seismic phases and aids in promoting the discovery of new deep Earth structures.