Earth Model Research Articles

A robust numerical method based on a deep-learning operator for solving the 2D acoustic wave equation

The numerical solution of a wave equation plays a crucial role in computational geophysics problems, which forms the foundation of inverse problems and directly impacts the high-precision imaging results of earth models. However, common numerical methods often lead to significant computational and storage requirements. Due to the heavy reliance on forward-modeling methods in inversion techniques, particularly full-waveform inversion, enhancing the computational efficiency and reducing the storage demands of traditional numerical methods have become key issues in computational geophysics. We develop the deep Lax-Wendroff correction (DeepLWC) method, a deep-learning-based numerical format for solving 2D hyperbolic wave equations. DeepLWC combines the advantages of traditional numerical schemes with a deep neural network. We provide a detailed comparison of this method with the representative traditional Lax-Wendroff correction method. Our numerical results indicate that the DeepLWC significantly improves the calculation speed (by more than 10 times) and reduces the space needed for storage by more than 10,000 times compared with traditional numerical methods. In contrast to the more popular physics-informed neural network method, DeepLWC maximizes the advantages of traditional mathematical methods in solving partial differential equations and uses a new sampling approach, leading to improved accuracy and faster computations. It is particularly worth pointing out that DeepLWC introduces a novel research paradigm for numerical equation solving, which can be combined with various traditional numerical methods, enabling acceleration and reduction in the storage requirements of conventional approaches.

Conformal mapping at elevation with implications for low-distortion projections

This article develops the theory of the conformal mapping of the surface of constant height above the ellipsoid (ChS), which has implications for the design of low-distortion projections. This paper gives a development of the Mercator, polar stereographic, Lambert conformal conic (LCC) and transverse Mercator (TM) projections based on the ChS, a better Earth model than the reference ellipsoid (RE) for positions at height. This article provides new formulas for the LCC and TM inverse scale problems – when given a value for the local scale function, where does it occur? These formulas apply to both traditional mapping on the RE and novel mapping on the ChS.

1 g shake table study on seismic strengthening of low-cost rammed earthen houses built of silt enriched soil using natural fiber reinforcement

Earthen houses are practiced as a traditional and low-cost housing in many countries around the globe. These houses were exposed to unacceptable earthquake (EQ) risks despite their environmental benefits. Past earthquakes including the recent past 2017 Tripura EQ has evidenced significant damages mostly in earthen/masonry houses which are built in a non-engineered manner. In this context, the current study aims to investigate the seismic behavior and failure patterns of both unreinforced and using proposed retrofitted rammed earth model houses (with and without openings) built using typical Tripura soils having higher silt content using unidirectional shake table experiments on total 26 physical models. Besides, both seismic strength and structural stability are also examined for retrofitted earthen houses. The study indicates that, proposed novel low-cost natural fiber made textile encasing reinforcement technique has exhibited promising seismic performance of such houses from the view point of structural strength and ductile behavior as compared to traditional cementitious additives and fiber blended stabilized retrofitted houses as well untreated houses. The fundamental lateral period of model unreinforced and reinforced houses found within the range of 0.08 to 0.15 s respectively which indicates increased stiffness of walls due to strengthening may decrease the lateral period maximum up to 46.67%. On the other hand, the maximum increase in seismic strength was observed in order of 4.50 to 6.31 times in the case of bitumen treated bamboo fiber textile based encased houses with L-shaped bamboo splint corner reinforcement whereas traditional cementitious stabilized method has offered maximum 1.13 to 1.83 times increment in lateral strength. Further, the effect of different parametric variations such as area of openings (doors and windows), thickness to height ratio, variation in compaction methodologies on seismic performances of unreinforced rammed earthen houses were also studied in detail. Finally, regression based closed form predictive expressions for seismic strength of rammed earthen houses and without retrofitting are proposed herein. The performed cost analysis study will also help to assess the effectiveness of proposed strengthening techniques.

Noise source localization using deep learning

Summary Ambient noise source localization is of great significance for estimating seismic noise source distribution, understanding source mechanisms and imaging subsurface structures. The commonly used methods for source localization, such as the matched field processing and the full-waveform inversion, are time-consuming and not applicable for time-lapse monitoring of the noise source distribution. We propose an efficient alternative of using deep learning for noise source localization. In the neural network, the input data are noise cross-correlation functions and the output are matrices containing the information of noise source distribution. It is assumed that the subsurface structure is a horizontally layered earth model and the model parameters are known. A wavefield superposition method is employed to efficiently simulate ambient noise data with quantities of local noise sources labelled as training datasets. We use a weighted binary cross-entropy loss function to address the prediction inaccuracy caused by a sparse label matrix during training. The proposed deep learning framework is validated by synthetic tests and two field data examples. The successful applications to locate an anthropogenic noise source and a carbon dioxide (CO2) degassing area demonstrate the accuracy and efficiency of the proposed deep learning method for noise source localization, which has great potential for monitoring the changes of the noise source distribution in a survey area.

Transcriptomic evidence of erythropoietic adaptation from the International Space Station and from an Earth-based space analog

Space anemia affects astronauts and the underlying molecular alterations remain unknown. We evaluated the response of erythropoiesis-modulating genes to spaceflight through the analysis of leukocyte transcriptomes from astronauts during long-duration spaceflight and from an Earth model of microgravity. Differential expression analysis identified 50 genes encoding ribosomal proteins with reduced expression at the transition to bed rest and increased during the bed rest phase; a similar trend was observed in astronauts. Additional genes associated with anemia (15 genes), erythrocyte maturation (3 genes), and hemoglobin (6 genes) were down-regulated during bed rest and increased during reambulation. Transcript levels of the erythropoiesis transcription factor GATA1 and nine of most enriched erythrocyte proteins increased at reambulation after bed rest and at return to Earth from space. Dynamic changes of the leukocyte transcriptome composition while in microgravity and during reambulation supported an erythropoietic modulation accompanying the hemolysis of space anemia and of immobility-induced anemia.

Studying long term relationship between carbon Emissions, Soil, and climate Change: Insights from a global Earth modeling Framework

The persistent increase in greenhouse gas (GHG) emissions, notably carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O), since the mid-20th century has been a key driver of significant climate alterations. This study investigates the complex feedback mechanisms that both influence and are influenced by global climate dynamics, soil processes, and GHG emissions. Our statistical approach incorporates correlation measures, highlighting the limitations of such analyses, namely their inability to confirm causality, sensitivity to outliers, and the exclusive capture of linear relationships. Geographically Weighted Regression (GWR) models reveal spatial variations in the relationship between environmental factors and GHGs, while Path Analysis aids in delineating direct and indirect influences among variables. The research pinpoints significant spatial heterogeneity in the impacts of economic and environmental factors on GHGs, underscoring the necessity of localized strategies for climate change mitigation and sustainable land management. This study also identifies potential threats to agricultural productivity due to soil degradation, which hinder climate adaptation efforts. Our findings advocate for a concerted global response to reduce GHG emissions and address the challenges posed by the interplay of climate change, soil dynamics, and GHG emissions.

The Impact of the Three-Dimensional Structure of a Subduction Zone on Time-dependent Crustal Deformation Measured by HR-GNSS

Accurately modeling time-dependent coseismic crustal deformation as observed on high-rate Global Navigation Satellite System (HR-GNSS) lends insight into earthquake source processes and improves local earthquake and tsunami early warning algorithms. Currently, time-dependent crustal deformation modeling relies most frequently on simplified 1D radially symmetric Earth models. However, for shallow subduction zone earthquakes, even low-frequency shaking is likely affected by the many strongly heterogeneous structures such as the subducting slab, mantle wedge, and the overlying crustal structure. We demonstrate that including 3D structure improves the estimation of key features of coseismic HR-GNSS time series, such as the peak ground displacement (PGD), the time to PGD (tPGD), static displacements (SD), and waveform cross-correlation values. We computed synthetic 1D and 3D, 0.25 Hz and 0.5 Hz waveforms at HR-GNSS stations for four M7.3+ earthquakes in Japan using MudPy and SW4, respectively. From these synthetics, we computed intensity-measure residuals between the synthetic and observed GNSS waveforms. Comparing 1D and 3D residuals, we observed that the 3D simulations show better fits to the PGD and SD in the observed waveforms than the 1D simulations for both 0.25 Hz and 0.5 Hz simulations. We find that the reduction in PGD residuals in the 3D simulations is a combined effect of both shallow and deep 3D structures; hence incorporating only the upper 30 km of 3D structure will still improve the fit to the observed PGD values. Our results demonstrate that 3D simulations significantly improve models of GNSS waveform characteristics and will not only help understand the underlying processes, but also improve local tsunami warning.

Multisource information fusion model for deformation safety monitoring of earth and rock dams based on deep graph feature fusion

Constructing a long-term deformation monitoring model for earth–rock dams that integrates multisource monitoring information is highly important for enhancing the safety state evaluation and monitoring effectiveness of such dams. In this paper, we propose a new health monitoring model named the deformation–seepage–water level multimeasurement point health monitoring (DSW-MPHM) model for earth–rock dams based on deep graph feature fusion. This model fuses coupled seepage, deformation, and water level features from different monitoring sites of the dam body, base, and shoulder. To achieve this goal, we first establish a new module to fuse spatial and temporal features using graph convolutional networks and long short-term memory. Seepage features and water level features are then extracted using graph attention mechanisms. Subsequently, we employ the feature fusion technique, which incorporates principal component analysis and gated fusers, to construct the DSW-MPHM model, which effectively fuses information from multiple sources. This novel approach successfully addresses the issues of information redundancy and the limited reliability of monitoring models. To verify the validity of the model, it is applied to an endoscopic deformation monitoring program of a panel rockfill dam with a height of 185.5 m. The results demonstrate the superior stability and effectiveness of the proposed method compared to those of 10 baseline prediction models. Additionally, the characterization of the seepage and water level features extracted from the model is verified for its reasonableness. Thus, our proposed model is well suited for practical engineering applications.

Wellbore Instability Analysis to Determine the Safe Mud Weight Window for Deep Well, Halfaya Oilfield

Wellbore instability is one of the most common issues encountered during drilling operations. This problem becomes enormous when drilling deep wells that are passing through many different formations. The purpose of this study is to evaluate wellbore failure criteria by constructing a one-dimensional mechanical earth model (1D-MEM) that will help to predict a safe mud-weight window for deep wells. An integrated log measurement has been used to compute MEM components for nine formations along the studied well. Repeated formation pressure and laboratory core testing are used to validate the calculated results. The prediction of mud weight along the nine studied formations shows that for Ahmadi, Nahr Umr, Shuaiba, and Zubair formations ranges between 12.5 to 15 ppg. The predicted safe mud weight value seems to be narrow with a well deviation higher than 350. Therefore, for Ahmadi, Nahr Umr, Shuaiba, and Zubair formations, the wellbore appears unstable compared to other formations. The results of stability analyses indicate that the breakout mud weight wasn’t affected by wellbore azimuth because of low-stress contrast. Furthermore, shear failure can be prevented by drilling the well with an inclination of less than 350. As well as, to prevent breakdown the well should be drilled with an inclination between 25o to 65o in the direction of minimum horizontal stress. These outcomes could be used to prevent wellbore instability and determine a safe mud-weight window when planning to drill nearby wells in the future.

1D Geomechanical Model and Wellbore Stability Analysis for Kafr El-Sheikh Formation at Sapphire Field, West Delta Deep Marine, Egypt

The Messinian Abu Madi Formation considered the most prospective reservoir target in the Nile Delta, is situated under the Pliocene Kafr El-Sheikh Formation, where most non-productive time takes place. Nevertheless, reaching the desired reservoir presents a greater level of complexity than first perceived. To mitigate the occurrence of significant non-productive time caused by wellbore instability problems, including stuck pipes, tight holes, pack-offs, and jarring or fishing operations, there has been an increased focus on geomechanical analysis. Therefore, this work aims to offer a comprehensive 1D mechanical earth model for a specific set of wells situated in the sapphire field, which is situated inside the West Delta Deep Marine region. The mechanical parameters of the rock were determined by the use of empirical equations, since the absence of core sample data necessitated reliance on wireline data. The analysis of the borehole image has provided clarification that the orientation of the maximum horizontal stress is aligned with the NNE-SSW direction. The calibration of this model was conducted using data obtained from wellbore stability events that occurred during the drilling operations of these wells. This model would be valuable in forecasting and minimizing prospective problems by predicating the proper safe mud window. Sapphire-Da, the primary key, is utilized in this particular piece of writing.

On the Stability of Mantle‐Sensitive P‐Wave Interference During a Secondary Microseismic Event

AbstractBody wave extraction from oceanic secondary microseismic sources with seismic interferometry provides alternative information to better constrain the Earth's structure. However, sources' spatiotemporal variations raise concerns about travel time measurement robustness. Therefore, we study the cross‐correlations’ stability during a single oceanic event. This study focuses on 3 days of data and three seismic arrays' combinations between 8 and 11 December 2014 during storm Alexandra, a “weather bomb” event in southern Greenland. We use the WAVEWATCH III hindcast to model P‐wave noise sources and assess the impact of short‐term source variations on cross‐correlations. Model‐based cross‐correlations compared to data show coherent delays to reference 3D Earth models (∼0–3 s) confirming the robustness of the source model which could explain minor travel time variations (≤1 s).

Sedimentary environment of basal Ediacaran barite growth on Baltica in E. Finnmark, N. Norway, and subsequent dissolution/reprecipitation

Basal Ediacaran barite, which has mass-anomalous depleted 17O, supporting Snowball Earth models, likely grew in shallow-marine settings, but sedimentological constraints lack details. Environmental conditions in the Varanger Palaeovalley during the basal Ediacaran are well preserved in the Nyborg Formation, where barite forms < 15 mm high synsyn-sedimentary crystal fans on Archean basement or thin intervening sediments. Sedimentary evidence suggests crystal fans formed in low-energy, very shallow-marine to subaerial facies. Rare earth element and yttrium signatures in associated carbonates suggest non-saline growth environments. Post-depositional fluid-flow replaced crystal fan barite with silica (now quartz) and redeposited barite as: <1 × 0.2 mm “dispersed” grains in sediments below fans; <5 mm grains replacing calcite filling desiccation cracks; <1 mm grains in basement fissures; <3 µm grains replacing matrix calcite; irregular grains in detrital sheet-silicate + calcite grains. Caledonian dissolution-reprecipitation reworked barite into brittle fractures and stylolites. Barite Δ17O values are amongst the most negative (-0.9 – -1.25 ‰) and δ18O values the lowest recorded (9.9 – 16.9 ‰) anywhere, consistent with a high latitude Baltica at ∼ 635 Ma. δ34S values (17.7 – 24.5 ‰) lie within the known range for basal Ediacaran barite.

Estimating elastic properties of sediments by pseudo-wells generation utilizing simulated annealing optimization method

The hydrate concentration model considerably affects elastic properties, including bulk and shear modulus. Defining seismic properties of sediments, such as compressional and shear wave velocity and density, provides valuable information to identify rock facies and fluid types. This information commonly results from pre-stack seismic inversion, while post-stack seismic information provides acoustic impedance as a layer-based property. Traditionally, seismic inversion requires well logs to produce an initial guess of inversion routines and provide a low-frequency part of the amplitude spectrum. Eventually, seismic inversion methods could not be performed in the areas without well-log data, such as deep sea areas. In such cases, pseudo-well logs derived from pre-stack seismic data are a solution. Pseudo-well generation is a title used to estimate the elastic parameters of sediments in areas, such as deep marine environments, where drilled wells are absent or sparse. Metaheuristic optimization algorithms are suitable tools for minimizing the cost function as they best match real and synthetic seismic data. In this study, the SEAM earth model has been used as a reference to investigate the quality of pseudo-well generation utilizing a simulated annealing (SA) algorithm as an optimization method of property model change, which minimizes the cost function of seismic inversion. As a result, considering an initial model type of the SEAM model, simultaneous seismic inversion introduced the best compressional and shear wave velocities and density logs, which provide the best real and synthetic seismic data match when synthetic data is calculated from the simplified Zoeppritz equation.

REVEAL: A Global Full-Waveform Inversion Model

ABSTRACT We present REVEAL, a global-scale, transversely isotropic full-waveform inversion model. REVEAL builds upon the earlier construction of the long-wavelength Earth (LOWE) model by lowering the minimum period from 100 to 33 s and by more than doubling the number of included earthquakes to 2366. In the course of 305 quasi-Newton iterations, REVEAL assimilated a total of 6,005,727 unique three-component waveforms. The inversion method rests on the combination of a stochastic mini-batch optimization and wavefield-adapted spectral-element meshes. Although the former naturally exploits redundancies in the data set, the latter reduces the cost of wavefield simulations by reducing the effective dimension of the numerical mesh. As a consequence, the average cost of an iteration in this inversion is only around 0.62% of an iteration that uses the complete data set with a standard cubed-sphere-type mesh. We calculated 3D synthetic seismograms using a graphics processing unit-accelerated spectral-element wave propagation solver, accommodating the effects of anelasticity, topography, bathymetry, ocean loading, and ellipticity. For a diverse range of global wavepaths, REVEAL predicts complete three-component seismograms at 33 s period that have not been included in the inversion. This generalization to unseen data suggests applications of REVEAL in event location and characterization, as well as in ground-motion modeling.

Crustal carbonate build-up as a driver for Earth’s oxygenation

Oxygenation of Earth’s atmosphere and oceans played a pivotal role in the evolution of the surface environment and life. It is thought that the rise in oxygen over Earth’s history was driven by an increasing availability of the photosynthetic limiting nutrient phosphate combined with declining oxygen-consuming inputs from the mantle and crust. However, it has been difficult to assess whether these processes alone can explain Earth’s oxygenation history. Here we develop a theoretical framework for the long-term global oxygen, phosphorus and carbon cycles, incorporating potential trajectories for the emergence of continents, the degassing of mantle volatiles and the resulting increase in the size of the crustal carbonate reservoir. We find that we can adequately simulate the Earth’s oxygenation trajectory in both the atmosphere and oceans, alongside reasonable reconstructions of planetary temperature, atmospheric carbon dioxide concentration, phosphorus burial records and carbon isotope ratios. Importantly, this is only possible when we include the accumulation of carbonates in the crust, which permits ever-increasing carbon recycling rates through weathering and degassing. This carbonate build-up is a missing factor in models of Earth’s coupled climate, nutrient and oxygen evolution and is important for reconstructing Earth’s history and potential exoplanet biogeochemistry.

A time-domain SGFD-FK hybrid method for 2D teleseismic elastic wave modeling and inversion

AbstractFull waveform inversion (FWI) has proved to be a reliable tool for high-resolution imaging of lithospheric structures at various depths down to the upper mantle. However, when the size of the model is large, the computational burden is significative and applications are restricted to low frequencies. To tackle this issue, we developed a new 2D time-domain hybrid method to simulate high-frequency teleseismic body waves propagating through a local heterogeneous elastic Earth model: The frequency-wavenumber (FK) integration method is coupled with the staggered grid finite difference method (SGFD). The FK method is used to compute the wavefield due to obliquely incident plane P and SV waves in a 1D multilayered half space that excites a local heterogeneous region. Inside this region, the velocity-stress staggered grid FD method (SGFD) is used to accurately deal with wave propagation in heterogeneous media. Spurious waves that might be generated at the boundaries of the local region are avoided using convolutional perfectly matched layers (CPML). This new hybrid method inherits the low-memory requirements of the FK method and the accuracy, efficiency and easy implementation of the SGFD. The new hybrid method is benchmarked against the analytical FK method for some canonical models and shows good agreement with analytical solutions. Subsequently, our modeling tool is incorporated into a full waveform inversion algorithm adapted for teleseismic configurations to invert the incident P wave and its coda. The inversion is carried out using a gradient approach that is efficiently implemented via the adjoint-state method. The results suggest that our hybrid method and FWI algorithm represent a valuable tool for 2D forward and inverse regional applications using teleseismic data sets.

Surface loading on a self-gravitating, linear viscoelastic Earth: moving beyond Maxwell

SUMMARY Constitutive laws are a necessary ingredient in calculations of glacial isostatic adjustment (GIA) or other surface loading problems (e.g. loading by ocean tides). An idealized constitutive law governed by the Maxwell viscoelastic model is widely used but increasing attention is being directed towards more intricate constitutive laws that, in particular, include transient rheology. In this context, transient rheology collectively refers to dissipative mechanisms activated in addition to creep modelled by the Maxwell viscoelastic model. Consideration of such viscoelastic models in GIA is in its infancy and to encourage their wider use, we present constitutive laws for several experimentally derived transient rheologies and outline a flexible method in which to incorporate them into geophysical problems, such as the viscoelastic deformation of the Earth induced by surface loading. To further motivate this need, we demonstrate, via the Love number collocation method, how predictions of crustal displacement depart significantly between Earth models that adopt only Maxwell viscoelasticity and those with transient rheology. Throughout this paper, we highlight the differences in terminology and emphases between the rock mechanics, seismology and GIA communities, which have perhaps contributed towards the relative scarcity in integrating this broader and more realistic class of constitutive laws within GIA. We focus on transient rheology since the associated deformation has been demonstrated to operate on timescales that range from hours to decades. With ice mass loss enhanced at similar timescales as a consequence of anthropogenically caused climate change, the ability to model GIA with more accurate constitutive laws is an important tool to investigate such problems.

Statistical appraisal of geothermal heat flow observations in the Arctic

Abstract. Geothermal heat flow is an important boundary condition for ice sheets, affecting, for example, basal melt rates, but for ice-covered regions, we only have sparse heat flow observations with partly high uncertainty of up to 30 m W m−2. In this study, we first investigate the agreement between such pointwise heat flow observations and solid Earth models, applying a 1D steady-state approach to perform a statistical analysis for the entire Arctic region. We find that most of the continental heat flow observations have a high reliability and agreement to solid Earth models, except a few data points, such as, for example, the NGRIP (North Greenland Ice Core Project) point in central Greenland. For further testing, we perform a conditional simulation with focus on Greenland in which the local characteristics of heat flow structures can be considered. Simple kriging shows that including or excluding the less reliable NGRIP point has a large influence on the surrounding heat flow. The geostatistical analysis with the conditional simulation supports the assumption that NGRIP might not only be problematic for representing a regional feature but likely is an outlier. Basal melt estimates show that such a local spot of high heat flow results in local high basal melt rates but leads to less variation than existing geophysical models.

A mechanism for reconciling the synchronisation of Heinrich events and Dansgaard-Oeschger cycles

The evolution of the northern hemispheric climate during the last glacial period was beset by quasi-episodic iceberg discharge events from the Laurentide ice sheet, known as Heinrich events (HEs). The paleo record places most HEs into the cold stadial of the Dansgaard-Oeschger cycle. However, not every Dansgaard-Oeschger cycle is associated with a HE, revealing a complex interplay between the two modes of glacial variability. Here, using a coupled ice sheet-solid earth model, we introduce a mechanism that explains the synchronicity of HEs and Dansgaard-Oeschger cycles. Unlike earlier studies, our mechanism does not require a trigger during the stadial. Instead, the atmospheric warming signal during the interstadial of the Dansgaard-Oeschger cycle causes enhanced ice stream thickening that leads to the HE during the late interstadial. We demonstrate that this mechanism reproduces the key HE characteristics and provides an explanation for synchronous HEs from different regions of the Laurentide ice sheet.

Apparent Non-Double-Couple Components as Artifacts of Moment Tensor Inversion

Compilations of earthquake moment tensors from global and regional catalogs find pervasive non-double-couple (NDC) componentswith a mean deviation from a double-couple (DC) source of around 20%. Their distributions vary only slightly with magnitude, faulting mechanism, or geologic environments. This consistency suggests thatfor most earthquakes, especially smaller ones whose rupture processes are expected to be simpler, the NDC components are largely artifacts of the moment tensor inversion procedure. This possibility is also supported by the fact that NDC components for individual earthquakes with Mw&lt;6.5 are only weakly correlated betweencatalogs. We explore this possibility by generating synthetic seismograms for the double-couple components of earthquakes around theworld using one Earth model and inverting them with a different Earth model. To match the waveforms with a different Earth model, the inversion changes the mechanisms to include a substantial NDC component while largely preserving the fault geometry (DC component). The resulting NDC components have a size and distribution similar to those reported for the earthquakes in the Global Centroid Moment Tensor (GCMT) catalog. The fact that numerical experiments replicate general features of the pervasive NDC components reported in moment tensor catalogs implies that these components are largely artifacts of the inversions not adequately accounting for the effects of laterally varying Earth structure.