Sinkholes or dolines are ground subsidence phenomena that occur worldwide due to both natural and anthropogenic causes e.g.. They are enclosed depressions with internal drainage that are characteristic features of terrains underlain by soluble rocks and may span less than a metre to several hundreds of metres in diameter and tens to hundreds of metres in depth . estimated that karst rocks such as limestone, dolomite, anhydrite, gypsum, and salt underlie about 20 % of the Earth's ice-free continental surface. Thus, the capability for solution and mass transfer by meteoric or groundwater exists. Two main categories of sinkholes have been distinguished: solution and subsidence sinkholes e.g.. The first group results from differential dissolutional weakening of exposed or merely soil-covered karst rocks. The subsequent slow subsidence forms sagging or suffosion sinkholes and is considered to be less hazardous from an engineering point of view . The second group represents a wide spectrum of dolines generated by subsurface chemical dissolution or mechanical erosion, termed subrosion in the following. It is further classified by the affected material (cover, cap rock, or bedrock), the process of subsidence mechanism (collapse, suffosion, or sagging), and the dissolution rate . Subrosion and the development of sinkholes may be influenced by numerous anthropogenic factors such as mining , tunnelling , water abstraction , water impoundment , and other large-scale hydrological projects in karst regions, which enhance the natural process of dissolution . In karst environments, collapse sinkholes are often related to gravitational subsurface cavity collapse , where stress conditions exceed the material stability of the surrounding rocks, which may be related to sudden water-level changes e.g. or seismic activity e.g..

If very fast suffosion takes place or sinkholes suddenly collapse in urban areas, they are a severe hazard for residents, economical and residential buildings, and infrastructure in general e.g.. Hence, ongoing urbanization and the growth of the world's population increase the requirement for detailed investigation of subrosion processes and sinkhole development for risk assessment.

Several geophysical and geodetic methods are applicable for the investigation of potentially unstable ground, subrosion processes, and the accompanied development of sinkholes. Surface deformation and sinkhole development can be monitored by airborne lidar e.g., photogrammetry e.g., and interferometric synthetic aperture radar (InSAR) e.g., or ground-based geodetic methods such as high-precision levelling e.g., ground-based lidar , Global Navigation Satellite System (GNSS) applications e.g., and ground-based InSAR , which are more suitable for small-scale studies and local investigations. Information on, e.g. morphology of cavities, sinkhole fills, or fissures can be investigated by ground-penetrating radar, electrical resistivity tomography, (micro)gravity surveys e.g., or nuclear magnetic resonance e.g., as well as magnetometry e.g.. Due to electromagnetic noise and ferrous materials, electromagnetic methods and magnetometry are often not feasible in urban areas. Information about underground structures and physical rock parameters can be obtained by shear-wave seismic reflection profiles that are especially suitable to resolve shallow geological structures with high resolution e.g.. Furthermore, seismic reflection and seismic refraction give information about deeper layers e.g.. Another valuable tool for the understanding of the development and propagation of collapse sinkholes is numerical modelling e.g.. The use of tiltmeters , borehole strainmeters , or borehole measurements in general are sparse and not applicable in densely built-up urban areas due to high costs and strict approval procedures . Some multidisciplinary field studies include gravimetry e.g. but focus structural interpretations of the Bouguer anomaly above and around assumed subrosion features. Hence, and with sparse exceptions , the majority of the mentioned ground-based methods are applied to localize sinkholes, image the actual state of sinkhole development, and concentrate on their spatial extent or physical parameters at a certain point of time.

In contrast, the time-lapse gravity method can deliver enhanced information about the variable local gravity field over time. It is non-invasive and directly sensitive to temporal mass movements on different spatial and temporal scales. Time-lapse gravity observations were successfully applied to monitor, e.g. subsurface water storage changes in general and in karst regions , CO2 storage changes , or withdrawal or intrusions beneath volcanic edifices .

We present a study that reveals potential subrosion-related mass transfer in the subsurface using spring gravity meters for a time-lapse survey over 4 years. A special focus is placed on the hydrological correction, which strongly means soil water content and changes in groundwater level. Both are challenging impacts on gravity variations e.g., especially in urban areas and where no special hydrological monitoring sites exist. We introduce the survey area of Bad Frankenhausen, located in Thuringia in Germany (Sect. ), and the monitoring concept, including data processing and a hydrological soil water correction approach (Sect. ). The results show constant gravity decrease, as well as continuous subsidence at specific points inside of our measurement network (Sect. ), which is assumed to be caused by underground mass redistribution. This is also discussed in Sect. , such as the feasibility of the time-lapse gravity method for sinkhole monitoring under urban conditions.

Sinkholes in Germany occur over the whole country due to the dissolution of various soluble rocks in the subsurface (Fig. a). These are mainly near-surface salt diapirs in northern Germany , and carbonates and sulfates in the central and southern parts of the country .

Our study area is located in the centre of Bad Frankenhausen (BF), a small city in northern Thuringia in central Germany, which is located in the transition zone of soluble rock packages Fig. a;. It is bounded by the Kyffhäuser hill range to the north (Fig. b) and the Thuringian Basin to the south (an extensive geological overview of Thuringia is given by ). Geological units in the working area were deposited in the Permian and the Triassic, and are divided by the W–E-trending and northwards-dipping Kyffhäuser Southern Margin Fault (KSM Fault) .

The sediments to the north of the KSM Fault are mainly Zechstein evaporites developed from seven evaporation-transgression cycles of the epicontinental Zechstein sea in the Upper Permian (258–250 Ma). These are alternating layers of conglomerates, carbonates, sulfates, and rock salt . The main occurrent marine formations in the research area are termed Werra, Staßfurt, and Leine (Fig. b). Extensive units of anhydrites, carbonates, copper shales, and conglomerates, mainly from the Werra and Staßfurt formations, can be found in the Kyffhäuser hill range. Scattered Leine Formation deposits consisting of salt clays, anhydrites, and carbonates cover the region to the northwest of BF .

The sediments to the south of the KSM Fault are mainly sandstones, claystones, and shales that were deposited during the Triassic terrestrial sedimentation phase after the marine sedimentation phase of the Permian. Triassic Buntsandstein, Muschelkalk, and Keuper overlay the Permian evaporites (for thickness values of the rock units, see ). Quaternary deposits are floodplain sediments, claystones, and siltstones, as well as glacial gravels and aeolian silt deposits.

The whole region is prone to subrosion, as proven by many features on the surface (Fig. ). This is predominant along the KSM Fault (Fig. a) and part of an about 250 km long tourist trail – the “Karst Trail” – along the southern Harz hill range. Several studies show that the Upper Permian in this region is strongly fractured, and therefore the mechanical integrity of the subsurface is disturbed. used a combination of different geophysical methods and joint inversion to show that the fractured zones can serve as pathways for meteoric and groundwater, and hence accelerate the underground dissolution. Proven by salt springs and about 20 000 subrosion structures, which shape the landscape south of the Harz Mountains , the Upper Permian provides the solvable material in the near-surface area , especially along the KSM Fault, where the southward-draining groundwater from the Kyffhäuser hill range ascends (Reuter, unpublished data). The different types and ages of the subrosion features document the ongoing subrosion processes over time. Underground cave growth (Fig. b; a description of the Barbarossa Cave is given by ) and weakening of the rock units lead and led to the development of collapse (Fig. c, d) and sagging sinkholes, which strongly affect urban constructions in and around BF. The most famous subrosion feature in the area is the leaning church tower of BF that currently has an inclination of 4.93∘ (Fig. e) and has been stabilized by a steel pylon construction. Since the last collapse of the Quellgrund sinkhole in 1908, the tower's inclination has been increasing rapidly due to disturbances within the drainage system beneath the building (Sven Schmidt, Thuringian State Institute for Environment and Geology (TLUG), personal communication, 2016). Several cavities and disrupted zones were investigated by three research core drillings (depth: 100–458 m) between 2013 and 2015 around the leaning church tower and mainly in the upper 100 m of the cap rock, which mainly consists of Zechstein anhydrites and gypsum (Sven Schmidt, TLUG, personal communication, 2016). Other investigations show similar results; e.g. the company SOCON Sonar Control found and surveyed a large cavity (volume: 95.5 m3, depth: 14.5–20.5 m, radius: 8 m) directly beneath the tower by using an ultrasonic sound method through an older drill hole beside the tower walls. In addition, the bigger part of infrastructure and buildings shows cracks and damage, which led, e.g. to the necessity to rebuild the leaking swimming pool in the city centre, several building renovations, and reconstruction work.

Sinkhole development and ongoing subsidence in urban regions such as BF represent severe hazard. Therefore, we aim to detect mass redistribution caused by subrosion by applying time-lapse gravity monitoring to improve the understanding of subrosion processes.

Our general approach is the high-precision monitoring of subrosion-induced time-variable gravity and height changes using regular repeated measurement campaigns. Including March 2014, when a 2-week long reference campaign was performed, a total of 17 time-lapse gravimetry (1 week of measurement time) and 18 levelling campaigns were carried out quarterly. The frequency of the campaigns has been reduced to half-yearly intervals since the beginning of 2018. The observed temporal components provide the possibility to derive evidence for ongoing subrosion and afford a quantification of the mass relocation in the subsurface. Therefore, the time-lapse measurements have to be close mesh and of high quality. Potential error sources have to be avoided as much as possible. Realistic error estimations are required when considering the results with respect to significance. All this must be taken into account during planning, measurement, and data analysis. The key requirements in this context are appropriate instrumentation, the local stability of the individual measurement locations, their long-term availability in variable infrastructural surroundings, and a method (measurement and data analysis), which must be robust against inner-city noise (pedestrians, cars, construction work) and systematic errors. In the following, we describe our implemented conception for the monitoring and the data analysis.

The approach presented here combines repeated levelling and time-lapse gravimetric surveys in a local measurement network in BF, Thuringia, central Germany. The aim is to identify surface deformation and mass transfer in the subsurface, in an area that is prone to subrosion, as several features on the surface reveal. After 4 years (17 gravimetry and 18 levelling campaigns) of regular quarterly measurements, we have obtained convincing and meaningful results, implications, and limits. Plausible surface deformation (subsidence) and gravity changes (gravity decrease) were detected in subrosion-prone areas of BF, which means mass transport in the subsurface. Although the temporal changes are small, i.e. a few µGal in gravity over 4 years, the surveys and later data analysis were realized at high effort to gain gravity observations with high precision. This includes a suitable measurement concept and data analysis (LSA), error estimation and propagation, and finally, a new, simple, but effective, method applied for hydrological correction of gravity differences (Sect. ). The results discussed below were achieved in spite of challenging urban area conditions.

Levelling. Vertical deformation of several mma-1 was found around the historical sinkhole areas in the measurement network. The deformation rates vary with time and strongly decrease for the campaigns in 2017, which was a rainy year. The origin of non-linear surface deformation in BF is not well understood and requires continuous observation, further research, and comparison with other data. The seasonal height variations due to ground frost would be reduced by installing holes drilled below the depth of frost and filled with longer steel piles than we did to mark levelling points (Sect. ).

The sources of subsidence in BF can be a combination of geogenic and anthropogenic origin. Evidence of leaching of soluble rocks is the occurrence of two natural brine sources inside of Quellgrund, which extract approximately 250 t of salt per day from the subsurface (Sven Schmidt, TLUG, personal communication, 2017). Thus, subrosion processes and the corresponding subsidence could be affected by human activities due to water extraction. As another example, we found extensive subsidence of 7.5–30.5 mma-1 at three points northwards of the leaning church tower of BF, including gravity point G07 (Fig. b). These subsidence rates are significantly higher than those displayed by the levelling profiles in Fig. . In the church area, several cavities were found at depths up to 100 m through several research core drillings (one of these was surveyed using borehole-based ultrasonic sonar; see Sect. ), which also reveals evidence for underground leaching. Partially, the high subsidence rates could be affected by compaction loading due to intensive construction and recultivation work, which were carried out northwards of the leaning church tower between 2014 and 2016. The load of the northeastward sagging tower itself has an effect on the subsidence rates in this area as well. However, the ongoing subsidence seems to show slightly lower rates after the reconstruction work ended.

Time-lapse gravity. Besides stable gravity differences in obviously stable areas, several gravity differences and certain points in the network have been detected to show significant gravity decrease of up to about 2 µGala-1 with SD of 1–2 µGal over the whole period of 4 years. This is an indication of local mass redistribution and has been observed mainly in and close to known historical sinkhole areas, which could be evidence for ongoing subrosion processes in the subsurface. The order of gravity decrease of 1–2 µGala-1 is small compared to the results of other studies that have investigated underground mass transfer, e.g. greater two-digit µGal range observed by in a volcanic environment. However, the significance of the results is given by the high precision level of our gravity results (SD ≈1 µGal) after LSA and error propagation in our local network, as shown in Sect.  and Table , and by rather continuous rates of found gravity decrease. This has been proven to be due to the use of a highly accurate instrumentation and its appropriate use at measurement site conditions with a sophisticated concept of network configuration and high number of observations, as well as the regular control of their calibration stability. The SD level of the adjusted gravity differences was improved by an extensive preprocessing for data quality improvement and the high sophisticated application of LSA (e.g. drift control, required corrections, and weighting of gravity meters; see Sect. ). Here, the accuracies of the gravity meters indeed have an effect as the used combinations of instruments show (Sect.  and Table ). Hence, the data quality was further increased by using exclusively the newer Scintrex CG5 and ZLS Burris gravity meters, which achieve SD in the range of 3–4 µGal for one observed gravity difference.

We were able to emphasize and interpret subrosion-induced signals for several gravity differences on several survey points by applying a first attempt of correction for seasonal hydrological variations. We have used the global GLDAS Noah model to estimate the effect of a varying soil water content to each single gravity difference in our monitoring network. A regression coefficient for each gravity difference was determined and used to correct it for local soil water content. The regression coefficient represents temporal and spatial deviations in hydrology between two different measurement points, dependent on their geological, topographical, and infrastructural conditions. Although this correction works successfully, the remaining seasonal signals suggest that groundwater has to be considered additionally and the global soil water model may not be completely compatible for local studies. For future and similar studies, we propose to test repeated in situ measurements of the soil water content using ground-penetrating radar or nuclear magnetic resonance, which is especially appropriate to determine local soil water content within the vadose zone . Both methods provide spatial information for soil water distribution. In this context, time-domain reflectometry in drill holes for point-specific 1-D profiles of water content can only be a first approximation because of the heterogeneity of soils, and furthermore drill holes are needed. Additionally, the remaining signal contains groundwater changes. In particular, in 2015, where soil water had an extreme minimum, the signals suggest further “mass loss” (Fig. ). Here, the gravity minimum also can hint at very low groundwater levels and hydrological mass deficits in the aquifer layers. Unfortunately, groundwater gauges are not available in the measurement area; i.e. due to the lack of information about groundwater mechanisms, it is currently not possible to make any assumption about the effect of groundwater on the time-lapse gravity records and thus on the subrosion processes. Therefore, groundwater recordings at high precision level or hydrological models at best should be taken into account for future and similar studies.

An idea, in which way our results could be explained by underground mass transfer, is given in Fig.  as a simple approximation. The gravity effect of a 1 m thick layer of different densities with horizontal dimensions of 10 m in both the x and y directions, which is located and centred beneath a single surface point, is displayed. For example, a cavity similar to the one surveyed beneath the leaning church tower (Sect. ) would have to propagate for 1 m towards Earth's surface, with a density of disappearing rocks of 2600 kgm-3 (density measured by LIAG Hanover using drill cores from the 458 m deep research drilling at the leaning church tower of BF), to explain a gravity decrease of 6.5 µGal (red curve). This could fit to the found gravity decrease at gravity points G07 and G12 (Fig. ), which are located very close to the leaning church tower, after about 3–4 years. Erosion rates known from literature can vary from 0.1 mma-1 for limestone to 0.5–1.0 ma-1 for gypsum under favourable subrosion conditions . The erosion rates determined by the approximation of our simple model are on the order of about 0.25 ma-1. This fits to favourable geological subrosion conditions in our measurement area, in which the caprock mostly consists of anhydrite and gypsum. The erosion itself is proven by several small cavities (Sect. ). Also, it can be discussed if the mass loss is only according to dissolution processes or if, e.g. a roof collapse of a cavity, i.e. breccia, can result in larger rate of mass loss. However, such estimations are indeed subject to the principle of ambiguity in gravity investigations, which has to be considered during interpretation. For an extensive modelling of subrosion processes based on gravity data, very long gravity time series as well as a detailed geological model of the study area are required, which is subject to future work. In addition, and for similar studies, we propose to dense up the measurement network for areas that are demonstrably not gravitationally stable (in our case, around the leaning church tower) and thus to give up few points in stable areas due to high measurement effort. Especially in local studies, which investigate shallow structures, it is required to derive detailed information about the spatial dimension of areas that are prone to gravity decrease due to underground mass redistribution.

In this study, we show the feasibility and the success of an approach that combines levelling and time-lapse gravimetric surveys in the urban area of Bad Frankenhausen in Germany, which is intensely prone to subrosion. We used ground-based time-lapse gravimetry, which is a non-invasive and powerful geophysical tool to monitor mass movements in the subsurface, and precise levelling to investigate the accompanied subsidence. A total of 17 time-lapse gravimetry and 18 levelling campaigns were carried out over 4 years in a local combined network. Despite challenging measurement conditions and the lack of permanent monitoring sites for environmental or hydrological parameters, we identified subrosion-related signal content in our measurements. To our knowledge, the presented field study is the first long-term, high-resolution time-lapse gravity study in a subrosion-prone area. Furthermore, it is the first attempt to quantify mass movements related to underground leaching, as well as to correct time-lapse gravity records for varying soil water content using a regression coefficient. The main results and modifications for future work based on the findings can be summarized as follows:

Subsidence in Bad Frankenhausen, on the order of millimetres up to several centimetres per year, is an ongoing process with possible non-linear periods, which is evidence of ongoing leaching.

Besides ongoing data acquisition, the next step is to create a geological model of the study area based on close-mesh Bouguer anomalies, physical rock parameters derived from other studies in this area e.g., and borehole measurements. On the basis of this model, we aim to identify depth and thickness of potential sinkhole areas in BF and to investigate additional structures which are not being resolved by our time-lapse observations yet. The time-variable subrosion-induced mass transports will be then investigated related to their depth and extent by adapting the geological model for each survey period.

In the future and for similar studies, it is recommendable to focus on the investigation of the role of hydrology and its parameters (e.g. flow intensity, flow path, flow direction) for sinkhole development.