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Abstract Largescale volcanic eruptions and earthquakes are occurring frequently in the Philippines, and research has shown that slab metamorphism and diversity alter the impacts of subducted oceanic plates by changing water‒carbon productivity and interplate stability. Within the framework of the thermal evolution history of subducting slabs, the relationships between subduction zone seismicity characterized by both regular megathrust earthquakes and slow slip events of various magnitudes and long-term slab dehydration–decarbonation evolution in the Philippines remain poorly understood. Here, we constructed a comprehensive thermal model incorporating 3-D slab geometric data for the incoming plate and a 3-D subduction velocity field based on the MORVEL plate motion dataset for the Philippine subduction zone with high spatial and temporal resolutions. Our findings reveal that subduction seismicity and arc volcanism are prominent in belt-shaped regions with high thermal gradients (> 5 °C/km) and large-scale slab dehydration (> 0.05 wt%/km). Dehydration of serpentinite in ultramafic rocks in the subducting slab and decarbonation of carbonate minerals preferentially contribute to the generation and transport of fluids and carbonate melts, thus facilitating seismicity and carbon-rich magmatism. Our results suggest that slab geometry diversity-induced juxtaposed slab dehydration-decarbonation processes play a vital role in the generation of megathrust earthquakes below the forearc.

Abstract Changing thermal regime is one of the key mechanisms driving seismogenic behaviors at cold megathrusts, but it is difficult to interpret warm subduction zones such as Vanuatu for the temperatures are higher than that accommodates shallow brittle failures. We construct a 3-D thermomechanical model to clarify the thermal structure that controls tectonic seismicity in Vanuatu and predict a warm circumstance associated with abundant seismicity. Results reveal a heterogeneous slab ranging from 300 °C to over 900 °C from the Moho to subvolcanic depth. The subduction seismicity corresponds well to the plate interface where dynamic thermal dehydration is focused. The transformation from hydrated basalts to eclogites along the slab facilitates the occurrence of intense earthquakes and slips. Multistage mineralogical metamorphism affects the dynamic stability of megathrusts and favors the generation of active interplate large events. Therefore, slab thermal dehydration plays a greater role than slab temperature condition in influencing the subduction earthquake distribution in warm subduction systems.

Compelling evidence has shown that geomagnetic disturbances in vertical intensity polarization before great earthquakes are promising precursors across diverse rupture conditions. However, the geomagnetic vertical intensity polarization method uses the spectrum of smooth signals, and the anomalous waveforms of seismic electromagnetic radiation, which are basically nonstationary, have not been adequately considered. By combining pulse amplitude analysis and an experimental study of the cumulative frequency of anomalies, we found that the pulse amplitudes before the 2022 Luding M6.8 earthquake show characteristics of multiple synchronous anomalies, with the highest (or higher) values occurring during the analyzed period. Similar synchronous anomalies were observed before the 2021 Yangbi M6.4 earthquake, the 2022 Lushan M6.1 earthquake and the 2022 Malcolm M6.0 earthquake, and these anomalies indicate migration from the periphery toward the epicenters over time. The synchronous changes are in line with the recognition of previous geomagnetic anomalies with characteristics of high values before an earthquake and gradual recovery after the earthquake. Our study suggests that the pulse amplitude is effective for extracting anomalies in geomagnetic vertical intensity polarization, especially in the presence of nonstationary signals when utilizing observations from multiple station arrays. Our findings highlight the importance of incorporating pulse amplitude analysis into earthquake prediction research on geomagnetic disturbances.

Electromagnetic indices play a potential role in the forecast of short-term to imminent M ≥ 5.5 earthquakes and have good application prospects. However, despite possible progress in earthquake forecasting, concerns remain because it is difficult to obtain accurate epicenter forecasts based on different forecast indices, and the forecast time span is as large as months in areas with multiple earthquakes. In this study, based on the actual demand for short-term earthquake forecasts in the Gansu–Qinghai–Sichuan region of western China, we refined the construction of earthquake forecast indicators in view of the abundant electromagnetic anomalies before moderate and strong earthquakes. We revealed the advantageous forecast indicators of each method for the three primary earthquake elements (time, epicenter, magnitude) and the spatiotemporal evolution characteristics of the anomalies. The correlations between the magnitude, time, intensity, and electromagnetic anomalies of different M ≥ 5.5 earthquakes indicate that the combination of short-term electromagnetic indices is pivotal in earthquake forecasting.

Geomagnetic vertical intensity polarization is a method with a clear mechanism, mature processing methods, and a strong ability to extract anomalous information in the quantitative analysis of seismogenic geomagnetic disturbances. The existing analyses of geomagnetic vertical intensity polarization are all based on the 5~100 s frequency band without refinement of the partitioning process. Although many successful results have been obtained, there are still two problems in the process of extracting anomalies: the geomagnetic anomalies that satisfy the determination criteria are still high in occurrence frequency; and the anomalies are distributed over too large an area in space, which leads to difficulties in determining the location of the epicenter. In this study, based on observations from western China, where fluxgate observation points are positioned in areas with frequent, densely distributed medium-strength earthquakes, we refined the frequency bands of geomagnetic vertical intensity polarization, recalculated the spatial and temporal evolution characteristics of geomagnetic disturbances before earthquakes, and improved the crossover frequency anomaly prediction index while promoting the application of the method in earthquake forecasting.

Summary: Slow earthquakes predominant in Costa Rica indicate unstable faulting of segmented Central American megathrusts, but the recurrence of episodic tremors and slips reported to precede a giant earthquake remains still enigmatic. The underlying mechanism is related to the variation in the coupling along the heterogeneous subduction interface which is poorly understood. In this study, we used up-to-date 3D thermal modeling to provide insights into the along-strike variation in the thermal state and hydraulic distribution beneath the Central American subduction zone. Our results show that the subducted Cocos Plate is much warmer than previously estimated, and the slab geometry exhibits remarkable perturbations along the trench. We found that the regions of large dehydration rate along the slab are consistent with the seismicity occurrence depth beneath the Moho. Below the Nicoya Peninsula and the Guatemala-Nicaragua segment of megathrusts, fluids derived from subducted slab result in increased pore fluid pressures and subsequent recurrence of slow slip events and regular earthquakes.

Abstract Because of the steep subduction of a highly concave slab, researchers have characterized megathrusts under the Marianas as among the coldest and curviest plate coupling interfaces in various circum-Pacific subduction zones. Seismic tomography indicates that the heterogeneous underlying plate varies markedly in its subduction angle, velocity, and flexure along the strike and dip, while their effects on the thermal structure and intraslab earthquake occurrence remain enigmatic. By incorporating the 3-D MORVEL velocity and state-of-the-art slab geometry into thermomechanical modeling, we estimated the 3-D subduction thermal state and hydrothermal regime below the Marianas. We find that (1) the concave slab geometry and the complexity of the intraslab velocity variation in the Marianas are associated with a heterogeneous along-strike thermal regime and a cold mantle wedge beneath the central Marianas; (2) amphibolitization and eclogitization of subducted oceanic crust cause variations in fluid pressure and fluid release from the subduction interface, which may influence the distribution of interface seismicity in the Mariana system; (3) the concentration of active hydrothermal vents in the trench > 8 km deep is accompanied by a large temperature gradient and subsequent remarkable slab dehydration in the southern Marianas; and (4) slab dehydration (> 0.02 wt%/km) from 30 to 80 km indicates notable fluid release and potential fluid migration in subduction channels, which may correspond to the large water flux at depth beneath the Marianas.

Summary: Previous subduction thermal models are inconsistent with the values of forearc heat flow (50–140 mW/m2) and global P‒T conditions of exhumed rocks, both suggesting a shallow environment 200–300°C warmer than model predictions. Here, we revaluate these problems in Kuril-Kamchatka using 3D thermomechanical modeling that satisfies the observed subduction history and slab geometry, while our refined 3D slab thermal state is warmer than that predicted by previous 2D models and better matches observational constraints. We show that warmer slabs create hierarchical slab dehydration fronts at various forearc depths, causing fast and slow subduction earthquakes. We conclude that fast-to-slow subduction earthquakes all play a key role in balancing plate coupling energy release on megathrusts trenchward of high P-T volcanism.

A powerful volcanic eruption that occurred in Tonga on 15 January 2022, produced strong vibrations in the atmosphere, ocean, and solid Earth. We identify infrasound waves traveling with an apparent velocity of 0.31 km/s up to 10,000 km from Tonga in seismic and tsunami recordings. Clear signals of these infrasound waves with a fundamental model of Lamb wave are evident before the shallow-water gravity wave and after the Rayleigh and body waves. The pressure amplitudes of the infrasound waves at stations of 400–1000 km from the eruption are 5–10 hPa. The infrasound wave generated trans-Pacific tsunami waves to arrive 4–5 h earlier than the gravity waves of regular tsunami in the populated countries near the Pacific oceans. We use numerical simulation methods for the oceanic plate subduction zone in Tonga to estimate the pressure-temperature fields and the desulfurization at shallow depths. The simulated total sulfur dioxide released during the eruption ranges from 0.4 to 2.0 Tg. This is small in comparison with previous studies of comparable infrasound pressures. The total emission and sulfur dioxide amounts may have been controlled by the amount of sulfur contained in the subducted plate as well as the pressure and temperature conditions of the subduction zones.

Seismic quiescence or enhanced phenomena are anomalous changes against the background of normal seismic activity. Preliminary studies have found that earthquakes with a magnitude of ML≥4 often occur at a low occurrence frequency before giant earthquakes in Tibet. This study analyzed the catalog of ML≥4 earthquakes from 2008 to 2022 and examined the anomalous occurrence of ML≥4 earthquakes preceding most ML≥6 earthquakes. When the monthly occurrence frequency of ML≥4 earthquakes was lower than 4 times over six consecutive months, the subsequent occurrence of ML≥6 earthquakes was highly likely as evidenced by observations. The anomalous characteristics of low-intensity activities were analyzed as a medium- and short-term forecasting index for large earthquakes in the Tibetan area.

Tectonic extrusion bypassing the eastern Himalayan syntaxis results in a significant increase in regional stress instability and the associated frequent occurrence of earthquakes in southern Yunnan, China. However, the stress field, and the relationship between the focal mechanism of earthquakes and stress evolution in southern Yunnan, remain enigmatic. In this paper, using a modified grid point test method, we calculated the focal mechanism of ML ≥ 2.5 earthquakes in southern Yunnan (22–25° N, 100–104° E) from January 2009 to June 2023. Utilizing the solutions of historical earthquake focal mechanisms, we obtained the present-day regional tectonic stress field in southern Yunnan via inversion. The results indicate complex and diverse seismic focal mechanisms, and the main types of earthquakes are strike-slip events, followed by normal fault and reverse fault events. The orientations of the maximum and minimum principal stress axes rotate in a clockwise direction from northeast to southwest. The internal stress orientation distribution of the rhombic Sichuan–Yunnan block in the study area is consistent, and the block boundary zone is the site where stress deflection occurs, and the regional tectonic stress field is influenced by the interaction among different blocks. The distribution of R-value in the Lamping–Simao block gradually increases from north to south, indicating that the compressive stress required for material transport becomes relatively small. Combined with the geological and tectonic background of the study area, our results suggest that the speed of block movement gradually decreases from north to south; the distribution of R-value in the South China block is significantly smaller than that of the interior of the Sichuan–Yunnan rhombus, and the proportion of compressive stresses is larger, indicating a stronger extrusion in this region, which may be related to the fact that the Sichuan–Yunnan rhombus is strongly resisted by the South China block in the east.

Abstract Several interplate seismic events, such as short-term slow slip events (S-SSEs) and low-frequency earthquakes (LFEs), have been identified in the Ryukyu Trench, southwestern Japan. As one of the specific characteristics of this seismicity, the depths at which S-SSEs occur at the plate interface beneath Okinawa Island are approximately 5–10 km shallower than those beneath the Yaeyama Islands. To elucidate the cause of this difference in depth, we constructed a three-dimensional, Cartesian thermomechanical subduction model and applied the subduction history of the Philippine Sea (PHS) plate in the model region. As a result, the interplate temperatures at which S-SSEs take place were estimated to range from 350 to 450 °C beneath Okinawa Island and from 500 to 600 °C beneath the Yaeyama Islands. The former temperature range is consistent with previous thermal modelling studies for the occurrence of slow earthquakes, but the latter temperature range is by approximately 150 °C higher than the former. Therefore, explaining how the depth difference in S-SSEs could be caused from the aspect of only the thermal regime is difficult. Using phase diagrams for hydrous minerals in the oceanic crust and mantle wedge, we also estimated the water content distribution on and above the plate interface of the PHS plate. Near the S-SSE fault planes, almost the same amount of dehydration associated with phase transformations of hydrous minerals from blueschist to amphibolite and from amphibolite to amphibole eclogite within the oceanic crust were inferred along Okinawa Island and the Yaeyama Islands, respectively. On the other hand, the phase transformations within the mantle wedge were inferred only beneath the Yaeyama Islands, whereas no specific phase transformation was inferred beneath Okinawa Island around the S-SSE occurrence region. Therefore, we conclude that dehydrated fluid derived from the oceanic crust at the plate interface would play a key role in the occurrence of S-SSEs.

Abstract In repeating seismic event sequences within a specialized horizontal area, the moment magnitude is usually scaled with the recurrence interval. In addition to two horizontal dimensions, the vertical dimension plays a certain role in affecting the scaling law. However, whether and how the changing depth influences the scaling law remain enigmatic. Based on a large number of earthquake records with high-resolution epicenter locations in recent decades in Japan, we focus on a comparison between the 3-D seismic moment and seismic interval, which recognize the vertical dimension as the same dimension as the horizontal distances. The results show that (1) the seismic moment scaling law is applicable in the multiparameter 3-D models by visiting the 1.8 million events collected during a period of 15 years; (2) the vertical dimension of depth plays an important role in the Mo–SI relationship as well as in the variance in the 3-D seismic moment–interval magnitudes; and (3) the seismic moment rate, attributable to the plate convergence rate, varies with area and depth in influencing the regional earthquake recurrence frequency.

The data include the 3-D temperature field (degrees Celsius), water content (wt%), dehydration rate (wt%/km), and subduction velocity field (cm/yr) of the subducting plate, as well as the coastline and volcano distribution in Alaska. The data of the model region have dimensions of 800 × 1600 × 400 km (length × width × depth). The geometry of the subducted plate is well constrained by Slab2.0, and the plate ages are provided by EarthByte. The subduction velocities inside a prescribed 3-D constrained volume of the oceanic lithosphere are given based on the kinematic plate subduction modeling method and the MORVEL plate motion data. The observation of surface heat flow and Curie point depths are used to constrain the model thermal regime. The geophysical calculation is ensured after the subduction thermal regime reaches a steady state. Data are deposited in the TPDC repository, which has granted a persistent identifier https://data.tpdc.ac.cn/en/disallow/8b266d22-fea7-4259-9a5f-8ac0bd9e7869/. Data include (1) paraview_eq_USGS.vtk (earthquake catalog by IRIS, 2000-2010, Trabant et al., 2012), (2) paraview_slab.vtk (3-D thermal regime, slab water content and slab dehydration), (3) paraview_volcano.vtk (global volcanoes at NCEI, Siebert et al., 2010), and (4) paraview_map.vtk (coastline, GMT).

On 12 June 2021, an earthquake with MS 5.0 occurred in Yingjiang, adjacent to eastern Myanmar, where seismic activity is frequent due to plate collision. To explore the mechanism of this earthquake, the regional stress field of the Yingjiang zone was inverted using the focal mechanisms of 187 historical earthquakes in this area. Furthermore, based on the obtained orientation of the principal stress axes and the stress shape ratio, the fault slip tendency (Ts) was also estimated to evaluate fault instability in the study area. The stress variation results show that the diffusion and migration of the aftershocks suggested strike–slip-type stress accumulation in Yingjiang with a principal compressive stress axis direction-oriented NNE–SSW. Fault slip tendency results show that the seismogenic faults feature strikes within the ranges of 40~80° and 110~150° and dips of 60~90° and exhibit enhanced stress coupling. The distribution of the aftershock sequence is conjectured to have a high correlation with local fluid migration and was likely controlled by the hydrated rock-induced ruptures of the stressed fault systems near the source region. This study provides insights into potential earthquake risks in this region.

Well water levels can reflect the stress placed on a confined subsurface aquifer system in a similar manner to a strain meter. Based on observations of the geophysical field in Lhasa combined with digital data recorded at an underground fluid well at the Lhasa geomagnetic station in recent years, we comprehensively analyzed the characteristics of co-seismic changes caused by 14 different-magnitude M ≥ 5 earthquakes recorded in the well. The results show that (1) the co-seismic changes in water temperature and water level are different; the water level exhibits oscillation-type changes, while the water temperature variations indicate first heating and subsequent recovery. (2) The co-seismic changes are related to the epicentral distance, magnitude and focal depth of the earthquake. The closer the epicenter is to the well, the earlier the co-seismic responses occur, but the time interval between the co-seismic changes in the water level and temperature differs. (3) The co-seismic ratio of the water temperature is higher than that of the water level; this may be related to faulty water level instrumentation or segmented records.

Fast and slow earthquakes are predominantly generated along faults constituting active plate boundaries. Characterized by repeated devastating earthquakes and frequent slow slip events and tremors, the Alaska megathrust presents a chance to understand the complicated dynamics of a subduction system changing from steep to shallow dips associated with enigmatically abundant fast and slow seismic events. Based on three-dimensional thermal modeling, we find that the downgoing metamorphosed oceanic crust containing bound water releases a large amount of fluid and causes the recurrence of fast and slow earthquakes by elevated pore fluid pressure and hydrofracturing. The seismogenic interface and the slow slip events (SSEs) identified beneath the Upper Cook Inlet coincide well with the slab metamorphic dehydration regions. The observed slow earthquakes with quasi-stable fault slips preferentially occur, accompanied by high dehydration and temperature downdip along the transition zone.

The probabilistic seismic hazard analysis (PSHA) method is effectively used in an earthquake risk probability evaluation in seismogenic regions with active faults. In this study, by focusing on the potential seismic source area in Najin Lhasa, southern Tibet, and by incorporating the PSHA method, we determined the seismic activity parameters and discussed the relationship of ground motion attenuation, the seismic hazard probability, and the horizontal bedrock ground motion acceleration peak value under different transcendence probabilities in this area. The calculation results show that the PSHA method divides the potential source area via specific tectonic scales and detailed tectonic markers, which reduces the scale of the potential source area and better reflects the uneven spatial distribution of seismic activity in the vicinity of Najin. The corrected attenuation relationship is also in line with the actual work requirements and is suitable for earthquake risk analysis. In addition, the major influences on the peak acceleration of ground motion in the study area are mainly in the potential source areas of Qushui (M7.5), Dangxiong (M8.5), and Kangma (M7.5). The peak horizontal ground motion acceleration (PGA) with a transcendence probability of 10% in 50 years is 185.9 cm/s2, and that with a transcendence probability of 2% in 50 years is 265.9 cm/s2.

Long-term stress accumulation influenced by coseismic stress changes and postseismic viscoelastic relaxation is considered critical to triggering giant earthquakes. Nevertheless, how the stress increase is interrupted by aftershocks and how it influences the megaseismic cycle remain enigmatic. In this study, based on the Mohr–Coulomb failure criterion at the nucleated segments of the 2008 great Sichuan earthquake, the stress variation associated with four M > 6 aftershocks was calculated for the period from 2010 to 2017. The results show that (1) the spatial distribution of coseismic stress change is correlated with the rupture pattern of large events and has a fundamental impact on triggering subsequent earthquakes and (2) postseismic viscoelastic relaxation leads to increased Coulomb stress accumulation at the northern and southern edges of the seismogenic Longmenshan fault, which results in enhanced fault instability and the potential for future large events.

Single-stationed geomagnetic vertical intensity polarization (GVIP) anomalies have demonstrated good predictions of the occurrence of large earthquakes in Japan. Nonetheless, due to the lack of a previously densified geomagnetic network, how the multistationary GVIP anomaly (MGVIPA) corresponds to impending earthquakes remains poorly understood. Based on the newly constructed geomagnetic network from 2014 in Qinghai, China, which is composed of 23 electromagnetic stations, we suggested an MGVIPA method to analyze the correlation with large earthquakes since 2015. The results show that (1) the occurrence of MGVIPA is characterized by clusters in time that continue in a short period; (2) the spatial distribution of MGVIPA usually occurs with high values synchronously at several places over the same period; and (3) the Mw ≥ 6 earthquakes occurred in the regions indicated by MGVIPA within a period ranging from 3 months to 1 year from 2015 to 2021 in Qinghai, China.

Precursory earth tidal triggering is believed to influence earthquake timing preferentially when a region is critically stressed. However, whether and how the recurrence of aftershocks after a giant earthquake is affected by tidal triggering remains perplexing. To provide insight into this study, we utilized the Schuster test to explore the tidally induced stress variation correlated with the 2011 Mw 9.0 Tohoku earthquake aftershock sequence by determining the tidal phase angle at the occurrence time of events and the periodic characteristics of the aftershocks. Our results show that the aftershocks were triggered by short-period tides, including semidiurnal and diurnal tides. The rupture associated with the mainshock likely resulted in a critical stress state in the focal region, which is conducive to tidal triggering. We subdivided the aftershock catalog into several subsets, using a depth of 30 km and a magnitude of 5 as discriminators. The analysis of these subsets reveals that weaker and deeper earthquakes are best correlated with Earth tides, which will be helpful to investigate the mechanisms of tidal correlation.

Himalayan orogenesis remains enigmatic in terms of Tibetan Plateau geodynamics originating from the Cenozoic India–Eurasian continental collision. India underthrusts below Tibet to the Yarlung–Tsangpo suture, which has been identified as the northernmost boundary for underplating. However, the way in which the historical evolution of continental subduction induces plateau uplift and the way it controls the variation in uplift between outboard and inboard areas is still unclear. To interpret the evolutionary mechanisms involved in the Himalayan growth history, we constructed different 3-D dynamic models at important stages to address these questions related to the formation of the Himalayas on the basis of paleoenthalpy evidence encoded in fossil leaves from recently documented assemblages in southern Tibet. The results show that (1) the effect of crustal thickening was the predominant factor in the early evolution from the Paleocene to the early Eocene, which resulted in a moderate growth rate. (2) The consecutive slab break-off eastward from the western syntaxis and the associated slab rebound significantly accelerated orogenesis from the late Eocene to the Oligocene. The upwelling asthenospheric flow was a key control of increasing crustal buoyancy, which resulted in the fastest growth of the Himalayas during the early Miocene. (3) Thereafter, the gradually enhanced monsoon and surface erosion during accompanying the increasing mountain height resulted in a slowdown of the orogenic rate, which counterbalanced the buoyant force produced by asthenospheric flow driving continuous Himalayan growth.

Abstract Dual subduction represents an unusual case of subduction where one oceanic plate subducts on top of another, creating a highly complex tectonic setting. Because of the complex interaction between the two subducted plates, the origin of seismicity in such region is still not fully understood. Here we investigate the thermal structure of dual subduction beneath Kanto, central Japan formed as a consequence of a unique case of triple trench junction. Using high-resolution three-dimensional thermo-mechanical models tailored for the specific dual subduction settings beneath Kanto, we show that, compared with single-plate subduction systems, subduction of double slabs produces a strong variation of mantle flow, thermal and fluid release pattern that strongly controls the regional seismicity distribution. Here the deepening of seismicity in the Pacific slab located under the Philippine Sea slab is explained by delaying at greater depths (~150 km depth) of the eclogitization front in this region. On the other hand, the shallower seismicity observed in the Philippine Sea slab is related to a young and warm plate subduction and probably to the presence of a hot mantle flow traveling underneath the slab and then moving upward on top of the slab.

Accretionary wedge earthquakes usually occur in the overriding crust close to the trench or above the cold nose of the mantle wedge. However, the mechanism and temperature properties related to the slab dip angle remain poorly understood. Based on 3D thermal models to estimate the subduction wedge plate temperature and structure, we investigate the distribution of wedge earthquakes in Alaska, which has a varying slab dip angle along the trench. The horizontal distance of wedge-earthquake hypocenters significantly increases from the Aleutian Islands to south–central Alaska due to a transition from steep subduction to flat subduction. Slab dehydration inside the subducted Pacific plate indicates a simultaneous change in the distances between the intraslab metamorphic fronts and the Alaskan Trench at various depths, which is associated with the flattening of the Pacific plate eastward along the strike. The across-arc width of the wedge-earthquake source zone is consistent with the across-arc width of the surface high topography above the fully dehydrated megathrust, and the fluid upwelling spontaneously influences wedge seismotectonics and orogenesis.

Based on an analysis of connotation and extension of the concept of the orthogonal curvilinear coordinates, we have deduced a platform of strain tensor expression of Cartesian coordinates, which turns out to be a function of Lame coefficient and unit vector. By using transform matrix between Cartesian coordinates and orthogonal curvilinear coordinates, we have deduced a mathematical expression for correcting displacement vector differential in orthogonal curvilinear coordinates, and given a general expression of strain tensor in orthogonal curvilinear coordinates.

Abstract Background Cancer-testis antigens (CTAs) have emerged as potential clinical biomarkers targeting immunotherapy. KK-LC-1 is a member of CTAs, which has been demonstrated in a variety of tumors tissues and been found to elicit immune responses in cancer patients. However, the expression level and immune infiltration role of KK-LC-1 in lung adenocarcinoma (LUAD) remains to be elucidated. Methods In this study, the mRNA expression and overall survival rate of KK-LC-1 were evaluated by the TIMER and TCGA database in LUAD tissues and KK-LC-1 expression was further validated by clinical serum samples using quantitative RT-PCR. The relationship of KK-LC-1 with clinicopathologic parameters was analyzed. ROC curve result showed that miR-1825 was able to distinguish preoperative breast cancer patients from healthy people and postoperative patients. Then, the ROC curves were used to examine the ability of KK-LC-1 to distinguish preoperative LUAD patients from healthy and postoperative patients. The correlation between KK-LC-1 and infiltrating immune cells and immune marker sets was investigated via TIMER, TISIDB database, and CIBERSORT algorithm. The Kaplan-Meier plotter was used to further evaluate the prognostic value based on the expression levels of KK-LC-1 in related immune cells. Results The results showed that KK-LC-1 was significantly over-expressed in LUAD, and high levels of expression of KK-LC-1 were also closely correlated with poor overall survival. We also found that KK-LC-1 associated with TMN stage, NSE and CEA. The ROC curve result showed that KK-LC-1 was able to distinguish preoperative LUAD cancer patients from healthy people and postoperative patients. Moreover, KK-LC-1 had a larger AUC with higher diagnostic sensitivity and specificity than CEA. Based on the TIMER, TISIDB database, and CIBERSORT algorithm, the expression of KK-LC-1 was negatively correlated with CD4+ T cell, Macrophage, and Dendritic Cell in LUAD. Moreover, Based on the TIMER database, KK-LC-1 expression had a remarkable correlation with the type markers of Monocyte, TAM, M1 Macrophage, and M2 Macrophage. Furthermore, KK-LC-1 expression influenced the prognosis of LUAD patients by directly affecting immune cell infiltration by the Kaplan-Meier plotter analysis. Conclusions In conclusion, KK-LC-1 may serve as a promising diagnostic and prognostic biomarker in LUAD and correlate with immune infiltration and prognosis.