The research focuses on so-called coherency functions, statistical tools that quantify how strongly ground motions at two separated points on the ground surface are correlated as a function of frequency and distance. When waves propagate through the heterogeneous Earth, scattering, differences in arrival times known as wave passage effects, and local site conditions all erode this correlation, particularly at high frequencies. Because engineers cannot know the exact ground motion at every foundation point in advance, they rely on empirical coherency models fitted to dense instrument arrays, such as the SMART-1 array in Taiwan and the Lotung large-scale seismic experiment, to generate statistically consistent sets of spatially varying ground motion time histories for analysis.

A central motivation of the study is to validate the spectral correction factors recommended in ASCE Standard 4-98, the American Society of Civil Engineers standard for the seismic analysis of safety-related nuclear structures, and the coherency model developed by Norman Abrahamson in 2005 for the Electric Power Research Institute. These corrections account for the fact that the motion actually experienced by a large foundation is smoother, and generally weaker at high frequencies, than the free-field motion recorded in the soil away from the structure. This averaging effect, sometimes called the foundation input motion reduction, depends on the size and stiffness of the foundation, the properties of the underlying soil, and the assumed degree of incoherency in the incoming wave field.

To carry out the investigation, the team implemented several widely used coherency functions in code_aster, the open-source finite element software developed by EDF for advanced structural analysis. The models compared include classical formulations such as the Harichandran-Vanmarcke model, the Hao-Oliveira-Penzien model, the Der Kiureghian model and the Abrahamson and co-workers empirical functions derived from the Lotung experiment. Using these functions, the researchers generated ensembles of spatially varying ground motions compatible with target free-field response spectra for both rock and soil site profiles, following established simulation techniques for multivariate stochastic processes.

In the first part of the study, the authors analysed a rigid square foundation subjected to spatially varying ground motion that includes wave incoherency. From the computed foundation motions they derived foundation response spectra, which describe the maximum response a single-degree-of-freedom oscillator would experience at the base of the structure. By comparing these spectra with the corresponding free-field response spectra, they determined reduction factors, that is, ratios quantifying how much the foundation motion is attenuated relative to the free field at each frequency. These numerically derived factors were then benchmarked against the spectral corrections prescribed in the EPRI 2005 methodology and ASCE Standard 4-98.

The results reveal a striking sensitivity: the foundation response spectra can change considerably depending on which coherency model and which ground motion parameters are assumed. Because each empirical model was calibrated on different arrays, site conditions and frequency ranges, they do not produce identical descriptions of the wave field, and these differences propagate directly into the computed reduction factors. For practitioners, this means that the choice of incoherency model is not a technical detail but a decision that can materially influence the seismic demand calculated for safety-critical structures, particularly in the frequency range above a few hertz where incoherency effects are strongest.

The second part of the paper extends the analysis to a full reactor building of a nuclear power plant, coupling the spatially varying excitation with a soil-structure interaction model. Soil-structure interaction refers to the mutual influence between the flexibility of the supporting soil and the dynamic response of the structure: soft soils can lengthen the effective period of the building system and dissipate energy through radiation damping, while the massive foundation filters and averages the incoming wave field. When the ground motion is also spatially incoherent, these two mechanisms interact, and the resulting structural response can differ substantially from what a conventional analysis with identical motion at all support points would predict.

The findings show that the effect of incoherency is remarkable for secondary systems within the reactor building that are sensitive to frequencies larger than 10 hertz. Secondary systems include piping, cable trays, equipment and other components anchored to the structure, whose response is governed by the floor motion spectra at their attachment points rather than by the ground motion itself. Because incoherency predominantly suppresses high-frequency content in the foundation input motion, floor response spectra at these higher frequencies can be reduced, which may ease the design burden for high-frequency equipment, but the magnitude of this reduction depends again on the coherency model selected.

The work was carried out within an international collaborative framework, with support from the German Academic Exchange Service (DAAD), the European Commission’s METIS program under Horizon 2020, and the German Federal Ministry for the Environment, Nature Conservation, Nuclear Safety and Consumer Protection through the CRUAS-19 project. This combination of academic and industrial partners reflects the practical stakes of the research: nuclear regulators and operators in Europe and elsewhere are increasingly requiring that wave incoherency be explicitly accounted for in site-specific seismic assessments, and reliable, validated modelling tools are essential for that task.

For the earthquake engineering community, the study delivers a clear message about uncertainty and standardisation. The spectral corrections embedded in ASCE Standard 4-98 and the EPRI methodology represent decades of accumulated empirical knowledge, but the new results show that they should be applied with an awareness of the sensitivity of the outcome to the underlying coherency assumptions. As dense seismic arrays continue to record data worldwide, and as site-specific coherency functions are developed for individual nuclear sites, the authors’ open-source implementation in code_aster offers a transparent pathway for engineers to test alternative models, quantify the spread of predicted foundation and floor response spectra, and ultimately make more robust safety decisions for the large semi-rigid structures that society depends upon most.

Subject of Research: Effect of spatial ground motion coherency models on soil-structure interaction analysis of large semi-rigid structures such as nuclear reactor buildings

Article Title: Influence of different spatial coherency models in soil-structure interaction analyses of large semi-rigid structures

Article References: Soyluk, K., Zouatine, M., Sadegh-Azar, H., Zentner, I., Kudawoo, D., & Khemakhem, A. (2026). Influence of different spatial coherency models in soil-structure interaction analyses of large semi-rigid structures. Bulletin of Earthquake Engineering. https://doi.org/10.1007/s10518-026-02664-w

Image Credits: AI Generated

DOI: 10.1007/s10518-026-02664-w

Keywords: spatial variability, soil-structure interaction, coherency model, nuclear power plant, reactor building, seismic analysis, ground motion, wave incoherency, foundation response spectra, ASCE Standard 4-98, code_aster, earthquake engineering

The research team, led by Arshdeep Singh Atwal and Aarush Lal of CSK Himachal Pradesh Krishi Vishvavidyalaya, Palampur, focused on cauliflower, a nutrient-hungry cool-season crop that dominates the vegetable economy of the Shivalik foothill zone. Indora block, spanning roughly 298 square kilometres between elevations of 261 and 765 metres, receives about 1000 millimetres of rain annually and enjoys a semi-humid subtropical climate that has made it an important vegetable belt. Yet the region’s agriculture is constrained by tiny landholdings, erratic water availability, and fertiliser use that is often both low and imbalanced. Continuous cropping, excessive tillage, residue removal and skewed fertiliser regimes have accelerated nutrient mining and organic matter depletion, making systematic soil characterisation an urgent priority rather than an academic luxury.

Between August 2022 and 2023, the researchers sampled the top 20 centimetres of soil from ninety-nine farming households growing the Megha cauliflower variety on plots of at least 500 square metres, covering twenty-two village councils and thirty-seven villages. The samples, air-dried and sieved, were subjected to a full battery of standard analyses: bulk density by core sampler, texture by hydrometer, water holding capacity by the Keen and Raczkowski box method, pH by glass electrode, organic carbon by dichromate wet oxidation, available nitrogen by alkaline potassium permanganate, phosphorus by Olsen’s method, potassium by flame photometry, and sulphur by turbidimetry, alongside exchangeable calcium and magnesium. The result was one of the most comprehensive physico-chemical datasets ever assembled for this corner of the lower Himalayas.

The descriptive statistics painted a picture of generally healthy but unevenly distributed fertility. Soil pH ranged from 6.34 to 7.56 with a mean of 7.16, placing the soils in the neutral to slightly alkaline range that suits vegetable production well. Electrical conductivity, averaging 0.26 decisiemens per metre, stayed safely below the 0.8 threshold considered problematic for crops. Organic carbon ranged from 7.00 to 13.60 grams per kilogram, a medium-to-high level the authors attribute to the regular addition of farmyard manure and plant residues by local growers. Available nitrogen averaged 284 kilograms per hectare, phosphorus a modest 12.15 kilograms per hectare, and potassium 280 kilograms per hectare, while sulphur, calcium and magnesium varied considerably, with phosphorus showing the highest relative variability of all measured properties at a coefficient of variation of 38.28 percent.

Correlation analysis revealed the web of interdependencies that governs how these soils behave. Bulk density, a measure of compaction, correlated positively with particle density and available potassium, the latter likely reflecting potassium-bearing minerals such as feldspars and micas that simultaneously increase particle packing and nutrient supply. It correlated strongly and negatively with porosity, as expected, since denser soils have less pore space. Most strikingly, organic carbon correlated strongly and positively with available nitrogen at 0.65, confirming that organic matter is the engine of nitrogen supply in these systems, releasing mineralisable nitrogen in proportion to its abundance. Sulphur tracked positively with pH, consistent with enhanced mineralisation of organic sulphur under near-neutral conditions, while exchangeable calcium and magnesium rose together with indicators of improved fertility and microbial activity.

To compress this multivariate complexity into interpretable structure, the team applied principal component analysis, which extracted six components with eigenvalues above one that together explained 69.43 percent of the total variance. The first component, dominated by bulk density alone, signalled that soil structural condition, shaped by management decisions about tillage and compaction, is the single strongest axis of differentiation across the landscape. The second was driven by organic carbon, reflecting the heavy reliance of smallholders on organic manure as their primary nutrient pathway. Later components captured particle density with phosphorus and potassium, the pH-sulphur-calcium-magnesium cluster tied to base saturation and leaching dynamics, electrical conductivity, and finally nitrogen with porosity. A complementary hierarchical cluster analysis grouped the ninety-nine sampling sites into seven major clusters, whose long branch linkages pointed to substantial multivariate dissimilarity driven by topography, parent material and divergent management environments.

The study’s most innovative contribution came from spatial statistics. Using Global Moran’s I, a measure of spatial autocorrelation computed in the GeoDa software with a six-nearest-neighbour weight matrix and 999 permutations, the researchers tested whether each soil property was randomly distributed or spatially structured. Six properties passed the significance test: pH, electrical conductivity, organic carbon, porosity, nitrogen and sulphur. Positive Moran’s I values for these attributes mean that similar values cluster together on the map, so high-pH fields neighbour high-pH fields and nitrogen-poor patches form coherent zones rather than isolated points. The remaining properties, including bulk density, water holding capacity, phosphorus, potassium, calcium and magnesium, appeared spatially random, a finding the authors link to the region’s complex topography, which creates microclimatic and edaphic variation over short distances, and to individual farm management decisions that override natural gradients.

Local Indicator of Spatial Association analysis then pinpointed exactly where the clusters lie. Sulphur expressed the strongest clustering of any property, with 47 significant sampling sites and 23.23 percent of the study area falling into the high-high category, concentrated toward the north, a pattern the authors attribute to gypsiferous parent material, higher organic matter and fertilisers such as single superphosphate. Electrical conductivity formed high-value clusters in the north, where erratic and low rainfall allows salts to accumulate, while nitrogen showed high clusters in the central and northern regions and low clusters toward the south-west, a patchiness that implicates nutrient management practices as the dominant driver rather than any natural gradient. The team even notes that naturally occurring Acacia catechu trees, which fix atmospheric nitrogen, may act as local nitrogen hotspots. Porosity was the only variable with more low-low than high-high area, with compacted zones in the northern half pointing to the cumulative effect of seasonal tillage and field traffic.

Translated into practice, the cluster typology becomes a management blueprint. Low-low zones, where a property is significantly depressed and surrounded by similarly depleted neighbours, are the highest-priority targets: nitrogen-poor clusters call for increased fertilisation or green manures such as Sesbania or Trifolium, organic-carbon-poor zones for farmyard manure, compost and legume cover crops between cauliflower seasons, and sulphur-deficient patches for sulphur-coated urea and oilseed cakes. Porosity low-low zones indicate compaction that could be remedied with subsoiling or deep tillage combined with organic amendments. High-high clusters, by contrast, may need optimisation to avoid toxicity-like conditions, while high-low outliers, anomalously enriched sites within deficient neighbourhoods, deserve investigation to understand how they arose. To visualise all of this, the team generated continuous fertility surfaces using inverse distance weighting in QGIS with a weighting power of two and a fine spatial resolution of 0.0001 degrees, producing thematic maps of every measured property clipped to the block boundary.

The authors are candid about the limitations: the survey covered a single block, a single season, and only the surface layer, so the findings cannot be generalised to other agro-climatic zones without further work. Even so, the framework is deliberately replicable, and the maps now serve as a baseline against which future soil health monitoring, climate-driven fertility shifts and the effects of changing nutrient regimes can be measured. For a region where farmers manage fragments of land under unpredictable monsoon rainfall, the message is quietly transformative: soil fertility in the lower Himalayas is not a uniform backdrop but a structured, mappable landscape of hotspots and deficits, and knowing where those zones lie is the first step toward feeding crops precisely what they need, where they need it, while protecting fragile mountain soils for the long term.

Subject of Research: Spatial variability and geostatistical mapping of soil physico-chemical properties in vegetable-cultivated Himalayan soils

Article Title: Spatial characterization and geostatistical analysis of soil properties in vegetable cultivated soils of Indora block (Kangra district), Himachal Pradesh, India

Article References: Atwal, A. S., Lal, A., Kapoor, R., Sandal, S. K., Sharma, R., Sepehya, S., & Kumari, P. (2026). Spatial characterization and geostatistical analysis of soil properties in vegetable cultivated soils of Indora block (Kangra district), Himachal Pradesh, India. Discover Soil, 3(1), Article 116. https://doi.org/10.1007/s44378-026-00271-4

Image Credits: AI Generated

DOI: 10.1007/s44378-026-00271-4

Keywords: soil science, spatial variability, geostatistics, Moran's I, LISA, precision agriculture, Himalayan farming, cauliflower, soil fertility, nutrient management, Himachal Pradesh, organic carbon

The research team, led by Mukesh P. Chaudhari of Gujarat University’s Department of Chemistry together with Ruchi Nair, Pratik Chavda, Dharmik Patel and Divya R. Mishra, combined systematic field sampling with Geographic Information System (GIS) mapping and multivariate statistics. Their goal was straightforward but ambitious: to measure the spatial distribution of the major soil fertility indicators across all fourteen talukas of Banaskantha and to translate those measurements into practical guidance for sustainable land management in a region where salinity, nutrient depletion and drought are intensifying pressures.

To capture the district’s variability, the researchers collected 46 geo-referenced composite soil samples from agricultural fields using a systematic 15 by 15 kilometer grid, an approach aligned with internationally accepted spatial sampling guidelines from the Food and Agriculture Organization and the USDA-NRCS Soil Survey Manual. At each sampling point, five sub-samples were taken in a zig-zag pattern within a 10 to 15 meter radius and homogenized into a single representative composite. All samples came from the 0 to 15 centimeter plough layer, the zone most responsive to nutrient availability and management. Each sample was then analyzed in the laboratory for soil moisture, pH, electrical conductivity (EC), organic carbon (OC), and available nitrogen, phosphorus and potassium.

Turning those numbers into pictures required spatial interpolation. Using ArcGIS version 10.8.1, the team applied the Inverse Distance Weighting (IDW) technique, a deterministic method that estimates unknown values from the weighted average of nearby sampling points, assuming that closer observations carry more influence than distant ones. The resulting raster layers, classified into concentration ranges and overlaid on the district boundary, produced district-scale thematic maps of every fertility indicator. The authors are candid that these maps are intended for regional visualization rather than precise field-level prediction, and that formal cross-validation statistics were not performed; they recommend denser sampling networks and geostatistical validation in future work.

The findings reveal dramatic heterogeneity. Soil moisture ranged from less than 1 percent to more than 20 percent, with the highest values in Suigam (24.74 percent), Vav (13.92 percent) and Lakhani (12.87 percent), where finer clay- and silt-rich soils retain water through greater surface area and capillary action, and where shallow groundwater or capillary rise may contribute. In contrast, the coarse sandy soils of Dhanera, Deesa, Kankrej and parts of Tharad and Palanpur drain rapidly and lose moisture to intense evapotranspiration, leaving almost nothing in reserve. Soil pH spanned from slightly acidic (6.34) in the forest-influenced taluka of Danta, where higher rainfall leaches basic cations, to strongly alkaline (8.65) in Vav, Suigam and parts of Lakhani, where aridity and carbonate-rich parent materials drive salt accumulation.

Electrical conductivity told perhaps the starkest story. While some soils in Deesa, Palanpur and Vadgam showed EC values as low as 0.01 dS/m, samples from Suigam and Lakhani exceeded 200 dS/m, indicating severe salinity likely driven by saline groundwater, an arid climate and evaporitic concentration of salts at the surface. Such salinity lowers osmotic potential, hampers water uptake by plants and damages soil structure. The study also identified a persistent district-wide phosphorus deficit: available phosphorus ranged from just 0.25 to 7.97 mg/kg, with most talukas below 3 mg/kg, because alkaline conditions cause phosphorus to precipitate as insoluble calcium phosphates. Available potassium, by contrast, swung from 49 to 884 mg/kg, with very high values in Bhabhar, Deesa and Danta, likely reflecting mica-rich parent material or heavy fertilizer input. Available nitrogen ranged even more widely, from 78 to 2,100 mg/kg, with the highest levels in Bhabhar, Kankrej and Lakhani, probably tied to farmyard manure, nitrogen fertilizers and clay that retains ammonium.

Organic carbon emerged as a central thread running through the district’s fertility story. Levels ranged from a very low 0.10 percent to a high 3.50 percent, with the richest soils found in Danta’s forest-edge environments, where cooler microclimates, better moisture and greater biomass return slow decomposition and build humus. The intensively farmed alluvial plains of Deesa, Dhanera, Palanpur and Kankrej showed very low organic carbon, a consequence of sandy textures, rapid oxidation under high temperatures and continuous cropping with minimal residue return. Correlation analysis reinforced carbon’s pivotal role: organic carbon was positively associated with available phosphorus (r = 0.499) and available potassium (r = 0.444), while the strongest relationship in the entire matrix linked available phosphorus and potassium (r = 0.778), suggesting shared parent materials or similar fertilization histories.

Principal Component Analysis then distilled the district’s complexity into two dominant processes. Validated by a Kaiser-Meyer-Olkin statistic of 0.61 and a highly significant Bartlett’s test (p < 0.001), the PCA extracted two components with eigenvalues greater than 1 that together explained over 72 percent of the total variance. The first, accounting for 55.42 percent, loaded heavily on electrical conductivity, available potassium, available nitrogen and soil moisture, representing a salinity-nutrient enrichment factor typical of semi-arid regions where evapotranspiration exceeds precipitation and soluble ions accumulate at the surface. The second, explaining 17.32 percent, was dominated by pH, organic carbon and available phosphorus, capturing the organic matter-fertility relationship in which carbon-rich soils maintain more stable pH and better phosphorus availability.

The practical implications are as uneven as the soils themselves. The authors conclude that a single, uniform fertilizer recommendation is unlikely to optimize productivity across the district. Eastern and northeastern areas, including Danta, Bhabhar, Amirgadh and parts of Vav, show comparatively better soil health and should focus on conservation practices to maintain fertility. Nutrient-deficient zones in the central plains call for integrated nutrient management combining organic amendments, residue retention, biochar or farmyard manure with balanced fertilization. The severely saline talukas of Suigam and Lakhani require reclamation through gypsum application, improved drainage, optimized irrigation and salt-tolerant crops. In high-pH zones, phosphorus-solubilizing biofertilizers, split phosphorus doses and organic matter additions could unlock trapped nutrients, while high-nitrogen areas should be monitored to prevent nitrate leaching into groundwater.

The researchers emphasize that their nutrient management strategies remain preliminary decision-support recommendations. The agronomic effectiveness and economic feasibility of the proposals have not yet been tested through crop response experiments, fertilizer trials or cost-benefit analyses, and the study did not include indicators such as soil texture, cation exchange capacity, micronutrients or biological properties. Still, by fusing laboratory chemistry, GIS interpolation and multivariate statistics into a single framework, the study establishes an important baseline dataset for regional soil fertility assessment. In a state that contains some of India’s largest extents of saline and alkaline land, and a country where roughly 175 million hectares of agricultural area face soil-related constraints, showing precisely where a district’s soils are thriving and where they are failing may prove to be the first, indispensable step toward farming that fits the ground it stands on.

Subject of Research: Spatial variability of soil fertility indicators assessed with GIS and multivariate statistics for sustainable land management in a semi-arid Indian district

Article Title: Spatial variability of soil fertility indicators using GIS for sustainable land management in Banaskantha district western India

Article References: Chaudhari, M. P., Nair, R., Chavda, P., Patel, D., & Mishra, D. R. (2026). Spatial variability of soil fertility indicators using GIS for sustainable land management in Banaskantha district western India. Discover Soil, 3(1), Article 161. https://doi.org/10.1007/s44378-026-00320-y

Image Credits: AI Generated

DOI: 10.1007/s44378-026-00320-y

Keywords: soil fertility, spatial variability, GIS, Inverse Distance Weighting, soil salinity, organic carbon, soil pH, available nutrients, principal component analysis, precision agriculture, sustainable land management, semi-arid India