Atomic clocks went through tremendous evolutions and ameliorations since their invention in the middle of the twentieth century. The constant amelioration of their accuracy and stability permitted numerous applications in the field of metrology and fundamental physics. For a long time cold atom Caesium fountain clocks remained unchallenged in terms of accuracy and stability. However, this is no longer true with the recent development of optical clocks. This new generation of atomic clock opens new possibilities for applications in chronometric geodesy.

With this progress in clock technology heading towards a relative clock accuracy of 10⁻18, geodetic applications become feasible, such as determining gravity potential differences over large distances at the level of 0.1 m2 s⁻2. In this context, the effect of temporal gravity field variations on the new observable has to be considered. In addition, the clocks could provide results with a high temporal resolution (e.g. 7 to 1 h or less) for understanding the daily to annual evolution of corresponding phenomena, which makes the clocks unique in their ability to continuously monitor regional variations of the gravity potential field, especially when using a well-distributed clock network.

The goal of this paper is firstly to present an extensive review on the contribution of chronometric geodesy to the study of geodynamic phenomena. The second one is to present and analyze the mathematical framework for the estimation of the spatial-temporal variations of the gravity potential field using temporal networks of clocks. The mathematical background of this analysis was inspired from the 4-dimensional integrated geodesy developed in the last decades of the twentieth century.

How to cite: Chatzinikos, M., Delva, P., and Lion, G.: The contribution of atomic clocks to the study of spatial-temporal variations of the earth's gravity potential field, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13573, https://doi.org/10.5194/egusphere-egu23-13573, 2023.

We derive exact expressions for the relativistic redshift and timing between observers in various configurations in stationary spacetimes for the purpose of chronometry, i.e., relativistic gravimetry based on clocks. These observers are assumed to be equipped with standard clocks and move along arbitrary worldlines. It is shown how redshift observations can be used to infer the (mass) multipole moments of the underlying spacetime, i.e., a decomposition of the gravito-electric potential. In particular, an Earth-bound observer is considered that is meant to model a standard clock on the Earth's surface (or on the geoid).  Its clock is continuously compared with a clock on a satellite to determine from redshift measurements a relativistic gravity potential in the vicinity of the Earth. Results shown here are in agreement with the Newtonian potential determination from the so-called energy approach. The framework is intended for applications within relativistic geodesy and is exemplified in different exact vacuum spacetimes for illustration.

How to cite: Philipp, D., Hackmann, E., and Laemmerzahl, C.: Chronometry: On the redshift and relativistic gravity potential determination in GR, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5312, https://doi.org/10.5194/egusphere-egu23-5312, 2023.

One major objective of Geodesy is the observation of the Earth, its gravity field and climate. To study subtle but impactful changes in the gravitational field, novel paradigms and high-precision measurement schemes are emerging.

According to Einstein’s Theory of General Relativity, the proper time of a clock is the four-dimensional length of its worldline through curved spacetime. Thus, the comparison of clocks always is a comparison of local spacetime geometries. Thereupon, clock comparison could be used as a new method, termed chronometry, for gravity field recovery (GFR) via high-precision timing and redshift measurements. With the fast development of new, better, and smaller time measurement devices, optical clocks are a promising tool for GFR. Such clocks can be compared using, e.g., a light signal propagating in free space. For the determination of all gravitational degrees of freedom, it is necessary to relocate at least one clock around the planet. This can be done via moving clocks on satellites. To interpret these precise measurements correctly, it is essential to consider all influences on the laser signal used.

For this purpose, DLR and ZARM developed a simulation platform called XHPS in the scope of the DFG Collaborative Research Center 1464 TerraQ to model the environmental effects on satellites. It is used to study the influences on the laser signal between a ground station and satellites (or between two satellites). In particular, we want to simulate the signal loss caused by the Earth’s atmosphere, as well as other influences such as the relativistic redshift. It might also be interesting to compare the magnitude of redshift and atmospheric perturbations. This work will present the current state of our research.

How to cite: Wassermann, N., Leipner, A., Philipp, D., Scheumann, J., Bremer, S., and List, M.: Simulation of relativistic and environmental influences on laser signals used for gravity field recovery with spaceborne optical clocks, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12980, https://doi.org/10.5194/egusphere-egu23-12980, 2023.

Within the G4S_2.0 (Galileo for Science) project, funded by the Italian Space Agency (ASI), two activities in the field of Fundamental Physics are under investigation and development: a new measure of the Gravitational Red Shift (GRS) and a search for possible Dark Matter (DM) candidates in the form of domain walls. Both researches are based on data from high-accuracy clocks aboard the satellites.

The GRS measurement exploits the two Galileo satellites DORESA and MILENA injected in 2014 into a wrong orbit characterized by a too high eccentricity. The corrected orbit, still has a relatively high eccentricity (about 0.16) suitable for gravitational measurements. Consequently, the clocks frequency of these two satellites is modulated with the changes of the Earth’s gravitational potential at the height of the satellite.

The search for DM matter is done by looking for the expected rapid perturbations in on-board clocks when a structure like a domain wall crosses Earth’s orbit and the Galileo constellation.  If this occurs, on-board clocks would have to change their frequency relative to a reference clock on Earth.

For both targets, a careful knowledge of the satellite’s position is required, to be obtained with a Precise Orbit Determination (POD) in which the main non gravitational perturbations, such as direct solar radiation pressure, are adequately modeled and accounted for. Furthermore, the clock data needs to be cleaned up by removing long-term drift and fast time jumps unrelated to the effects we want to measure.

We will present the preliminary results obtained within these activities.

How to cite: Visco, M., Di Marco, A., Sapio, F., Lucchesi, D., Cinelli, M., Fiorenza, E., Lefevre, C., Loffredo, P., Lucente, M., Magnafico, C., Peron, R., Santoli, F., Gatto, N., and vespe, F.: Measures in Fundamental Physics within the Galileo for Science (G4S_2.0) project using the data of the Galileo Satellite Constellation, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-11934, https://doi.org/10.5194/egusphere-egu23-11934, 2023.

How to cite: Struckmann, C., Rasel, E. M., Wolf, P., and Gaaloul, N.: Simulating space-borne atom interferometers for Earth Observation and tests of General Relativity, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-13280, https://doi.org/10.5194/egusphere-egu23-13280, 2023.

The aliasing problem in gravity field recovery arises from the under-sampling of geophysical signals which have a period less than twice the sampling period of the mission. This temporal aliasing problem matters even more for future gravity missions when assessing the actual improvement provided by using new technologies such as cold atom gradiometers or flying drag-free with a laser interferometer. The level of errors caused by temporal aliasing is significantly higher than these instrument errors. This indicates that to see any sort of improvement in time-variable gravity field recovery from quantum technologies, the aliasing problem must be overcome first.

In this study, we propose a way of mitigating temporal aliasing effects by the space-wise approach. This approach consists of first estimating the very long wavelengths by some global technique (e.g., a least-squares adjustment) and then using this estimation to reduce filtered gravity gradients. A modification considering the short-term variations in the time-variable signal is here introduced into the filtering procedure. Later, the computed residuals are processed by a local collocation gridding procedure with the aim of improving the solution, especially for the shorter wavelengths. The signal covariance function estimation required for the gridding is here modified to account for the time variable signal.

The data analysis based on the newly modified mathematical model is applied for the monthly time-variable gravity field retrieval by performing simulations over half a year time span. This is done along with the static gravity field estimation with the aim of evaluating the possible overall improvement coming from the use of quantum gradiometers.

How to cite: Koç, Ö., Reguzzoni, M., Rossi, L., and Migliaccio, F.: Mitigating Temporal Aliasing Effects by the Space-Wise Approach for Quantum Gravimetry Missions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12597, https://doi.org/10.5194/egusphere-egu23-12597, 2023.

The next generation of gravimetric satellite missions will likely  utilize a single laser-based instrument to track distance variations between the satellites in a pair. These variations are used to derive the monthly average of Earth’s gravity field. Mission studies and technology developments are ongoing at NASA/USA, DLR/Germany and at the European Space Agency (ESA) in order to advance the successful technology demonstrator aboard GRACE-FO, the Laser Ranging Instrument (LRI), to a primary instrument with appropriate redundancy. The new instruments should of course incorporate learned lessons from the development as well as in-orbit operation of the instrument on GRACE-FO.

The new generation of instruments is expected to have similar noise requirements as in GRACE-FO, since laser ranging observations are usually not limiting the monthly gravity field maps. Design changes in the future LRI are carefully assessed in order to ensure that the actual in-flight precision can reach the same level as in the LRI aboard GRACE-FO, which has shown at high frequencies a noise of 200 pm/√Hz, i.e. is able to resolve changes in the 200 km distance as small as single atoms over short time scales. Efforts focus in particular on an improved knowledge of the LRI scale factor, i.e. the absolute laser frequency, because the current approach of correlating KBR and LRI range can not be employed in future missions.

In this presentation we address the LRI technology and some of the trade-offs that have been performed in the design of future instruments in the context of the above studies. Moreover, we discuss the limiting performance aspects for tone errors and noise and summarize the learned lessons and their potential relevance for future missions.

How to cite: Müller, V., Misfeldt, M., Müller, L., Weberpals, M., Voss, K., Nicklaus, K., and Heinzel, G.: Towards Laser Ranging in Future Gravimetric Missions, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12725, https://doi.org/10.5194/egusphere-egu23-12725, 2023.

We report on the progress of our novel low-frequency optomechanical accelerometer. This device is designed to be compact and portable, comprised of a monolithically fabricated mechanical resonator and a compact heterodyne laser interferometer. The resonator is made from fused-silica, which is a low-loss material that provides very low mechanical losses near room temperature. The oscillating test mass is read-out with the highly sensitive heterodyne interferometer. With a measured Q of 4.77x10⁵, an mQ-product above 1200 kg, a fundamental mechanical resonance of 4.7 Hz, we can estimated an acceleration noise floor near 1x10^-11 m s^-2/√Hz, which makes this device a good potential candidate for future applications in gravimetry, geodesy, geophysics, and hydrology.

A prototype packaging has been developed to reduce losses caused by typical mechanical mounts. We have conducted comparison measurements with commercial low-frequency systems to an excellent agreement. Recent measurements taken with the resonator mounted in this packaging atop a vibration isolation platform have indicated that our system is seismically limited above 1 mHz. Noise floors in the order of 82 pico-g/√Hz at 0.4 Hz has been demonstrated in our laboratory.

We will present recent updates on this optomechanical accelerometer, including up to date measurements of the resonator and interferometer sensitivity, as well as that of the combined system.

How to cite: Guzman, F., Hines, A., Nelson, A., Guo, X., Valdes, G., and Sanjuan, J.: Optomechanical accelerometers for geodesy, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-16853, https://doi.org/10.5194/egusphere-egu23-16853, 2023.

Over the past decades, gravimeters based on different working principles have been developed, such as superconducting gravimeters, spring gravimeters or interferometric gravimeters. Their ability to measure local changes in gravitational acceleration with a very high level of sensitivity makes these instruments widely used in fundamental physics, inertial navigation and geophysics. Recently, quantum gravimeters based on cold atom interferometry have demonstrated some of the best resolution and stability. The atomic quantum gravimeter (AQG) from iXblue is a drift-free absolute gravimeter with a sensitivity of 750 nm/s^2 at 1 sec and a long-term stability that reaches 10 nm/s^2, currently standing as a top-class industry-standard instrument [1]. However, due to its cyclic operation principle, the sensor is subject to dead times and concentrates on low-frequency variations (DC – 1 Hz). In addition, ground vibrations often overshoot the atom interferometer dynamic range. These issues have been demonstrated to be overcome by combining the quantum gravimeter with a classical accelerometer that senses ground accelerations and decouples the atom interferometer from them, so creating a hybrid quantum-classical sensor [2]. We present the hybridization of an Atomic Quantum Gravimeter with a custom-made optical accelerometer. The accelerometer has been specifically designed to optimally reject ground vibrations in the sensitivity range of the atom interferometer in real time. It consists of a force-feedback interferometric inertial sensor with a bandwidth from 10 s to 100 Hz and sub-picometer resolution. The accelerometer mechanics features fused-silica flexures, allowing to reach a 2.8 Hz natural frequency and a mQ-product of 1100 kg in a compact, 10x10x10 cm3, design. The hybridization of the quantum gravimeter with the optical accelerometer is expected to push down the noise floor of both sensors, ultimately hitting the quantum projection noise of the Absolute Quantum Gravimeter, being 350 nm/s2 at 1 sec. This improvement would therefore open new perspectives for applications of the quantum gravimeter, such as Newtonian-Noise estimation or seismic isolation.

[1] Ménoret et al, Gravity measurements below 10^-9g with a transportable absolute quantum gravimeter, Scientific Reports 8, 12300 (2018)

[2] Merlet et al, Operating an atom interferometer beyond its linear range, Mtrologia 46, 87 (2009)

[3] Lautier et al, Hybridizing matter-wave and classical accelerometers, Applied Physics Letters 105, 144102 (2014)

How to cite: Amorosi, A., Teloi, M., Amez-Droz, L., Faure, L., Ménoret, V., Rosenbusch, P., Thibaut, B., and Collette, C.: High-resolution hybrid atomic quantum gravimeter with real-time vibration compensation, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12432, https://doi.org/10.5194/egusphere-egu23-12432, 2023.

We report on the recent progress on exail’s Differential Quantum Gravimeter (DQG). Developed by exail quantum sensors (formerly known as muquans). The DQG  measures the acceleration due to gravity and the vertical gravity gradient simultaneously. It is an industry-grade demonstrator that has been operational for three years now and has achieved state-of-the-art sensitivity mainly limited by Quantum Projection Noise down to a noise floor at about 40E/sqrt(tau) and a long-term stability better than 1E [1]. For gravity measurements the performances are on par or better than exail’s AQG with a sensitivity of 600nm/s²/sqrt(tau) and a stability down to 5nm/s². Measuring the acceleration of the Earth gravity g and the gravity gradient simultaneously and at the same location promises enhanced information on the distribution of underground masses, especially at shallow depths [2].

In addition to survey measurements, we report on the DQG evaluation at the the LNE-Trappes characterized gravimetry laboratory near Paris [3]. A comparison to the gravity reference value has shown good agreement. The vertical gravity gradient measurement also compared favorably to the determinations obtained using a spring relative gravimeter both in terms of performance and in terms of ease-of-use.

Finally, we present on-going instrumental developments that will be key to the design of more compact instruments. Such instruments will be the basis for the Horizon Europe project FIQUgS which aims at realizing field compatible commercial gravimeters as well as data processing tools.

[1] C. Janvier, et al., “A compact differential gravimeter at the quantum projection noise limit”, Phys. Rev. A 105, 022801 (2022)

[2] G. Pajot, O. de Viron, M. M. Diament, M. F. Lequentrec-Lalancette, V. Mikhailov, Geo-Physics 73, 123 (2008).

[3] S. Merlet, et al., “Micro-gravity investigations for the LNE watt balance project” Metrologia vol 45 265 (2008)

How to cite: Janvier, C., Merlet, S., Rosenbusch, P., Ménoret, V., Landragin, A., Pereira dos Santos, F., and Desruelle, B.: Operational evaluation of an industrial differential quantum gravimeter, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-5171, https://doi.org/10.5194/egusphere-egu23-5171, 2023.

The transportable Quantum Gravimeter QG-1 is based on the principle of atom interferometry with collimated Bose-Einstein condensates (BEC) to determine the absolute value of the local gravitational acceleration g, aiming for an unprecedented level of accuracy < 3 nm s⁻². The QG-1 uses an atom-chip to produce well-defined magnetic fields, allowing high controllability of the atomic cloud and creating a BEC. After release from the magnetic trap into free fall, using well-controlled laser pulses the BEC is split, each part accumulating phase on its trajectory during free fall, and thereafter recombined, leading to self-interference. From the phase difference of the two parts of the BEC, the local gravitational acceleration g can be determined. Environmental vibrations contribute to the accumulating phase during free fall, leading to a disturbing phase shift of the interfering BEC. By measuring the high-frequency environmental noise with a classical accelerometer, this additional phase shift can be infered and corrected for in the determination of g.
In this contribution tide-resolving results of the latest measurement campaign with implemented classical sensors to correct for high-frequency vibrations with an accelerometer and drifts with a tiltmeter will be presented, rendering an important milestone for the development of our QG-1.
We acknowledge financial funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project-ID 434617780 - SFB 1464 TerraQ and under Germany’s Excellence Strategy - EXC 2123 QuantumFrontiers, Project-ID 390837967.

How to cite: Nuñez von Voigt, P., Heine, N., Herr, W., Schubert, C., Timmen, L., Müller, J., and Rasel, E. M.: Atom interferometry in the transportable Quantum Gravimeter QG-1, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-14404, https://doi.org/10.5194/egusphere-egu23-14404, 2023.

This work is concerned with applying machine learning to Bayesian gravity inversion. While various Bayesian frameworks have been explored for this application, these methods are not ideal due to the associated long computation time and can become intractable for a high-dimensional parameter space. For many applications, machine learning can offer a faster approach to obtaining posterior approximations, while not sacrificing accuracy. Normalising flows, which are based on the simple principles of the change of variables formula, recently have become a focus of development for a wide variety of applications. They are a popular alternative to other generative Bayesian frameworks due to their relative ease to train and their simple principles and architecture, making them more transparent and trustworthy for researchers. This work explores how this type of architecture can be applied to the common inverse problem in gravimetry and how it can improve on traditional methods. As a first application, results are shown for the inverse modelling of cuboid underground objects from a variety of gravimetry survey configurations. These simple shapes are not defined by a small number of parameters, rather the model is kept as a 3-dimensional density map defined by a grid of single-density voxels. This decision results in a more difficult problem with a high dimensional posterior space, however, it allows the approach to be more flexible and be directly applicable to the modelling of irregular bodies. Finally, it is discussed how the method performs compared to other traditional and Bayesian inversion methods.

How to cite: Rakoczi, H., Hammond, G., Messenger, C., and Prasad, A.: Normalising Flows for Bayesian Gravity Inversion, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4856, https://doi.org/10.5194/egusphere-egu23-4856, 2023.

The sustainable exploitation of a geothermal reservoir is usually assessed through continuous field monitoring and structural exploration of the hydrothermal reservoir. However, accurate subsurface mass and fluid displacement as well as energy transfer model of the hydrothermal reservoir is most of the time not resolved enough both in space and time. Since 2017, both at Krafla and Theistareykir powerplants (northern Iceland), we use several multi-parameter stations each equipped with a gravity meter (superconducting or spring relative meter), a broad band seismometer, a GNSS receiver and other meteorological and hydrological sensors. With this set-up, we aim to model mass and stress transfer through the combination of absolute and micro gravity measurements, continuous signals measured at the multi-parameter stations and seismic measurements.

We present results from the 2022 micro gravity and absolute gravity campaigns conducted at Theistareykir geothermal field. Through inversion and interpretation of such results, as well as the analysis of the continuous measurements, and injection and production data, we aim to assess the anthropogenic contribution in the mass and energy transfer models of the investigated area.  Furthermore, we show the first continuous measurements and accurate Earth tide model for the Krafla area. The final goal of this study is to verify the conditions of sustainable exploitation of the reservoirs, and establish reservoir parameters, such as permeability, that regulate the response of the geothermal system to changes in production and injection rates.

How to cite: Giuliante, B., Jousset, P., Krawczyk, C., Hinderer, J., Riccardi, U., Toledo, T., Forster, F., and Mortensen, A.: Modelling mass balance and stress transfer at Krafla and Theistareykir geothermal systems, Iceland, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-8358, https://doi.org/10.5194/egusphere-egu23-8358, 2023.

The measurement of gravity acceleration and of its variations are commonly used by geophysicists in many Earth sciences applications. It is quite well known that gravity at the surface of the Earth is influenced by the masses surrounding the instrument, so its measurement can be exploited to characterize subsurface mass density distribution and to investigate many phenomena related to the Earth lithosphere. Gravity measurements also contribute to the exploration of underground resources (mining, hydrology, oil & gas) as well as to civil engineering activities with the detection of voids and cavities. Quantum gravity sensors have already demonstrated interesting competitive advantages with respect to classical gravimeters since they can measure the field with a higher accuracy and they allow to perform absolute measurements. In the framework of FIQUgS project, funded by the European commission in 2022, a new generation of quantum gravity sensors (QGs) is under development to overcome the barriers limiting the first-generation sensors operational usage (e.g. the transportability and robustness not suitable for outdoor operations). Within the project, a new Absolute Quantum Gravimeter (AQGs) and a Differential Quantum Gravimeter (DQGs) are foreseen to allow not only on field absolute gravity measurements but also measures of the vertical derivative.

In the context of the FIQUgS project a wide review of potential use cases for quantum gravity sensors has been performed. Applications, which benefits from the advantages of the next generation QGs, have been identified, within different market sectors. Different scenarios have been considered and by means of specific synthetic simulations the capabilities of this technology have been assessed.

The potential applications for QGs investigated can be divided in two macro-sectors: the first one includes all the static applications that aim at retrieving the density distribution within a certain area to distinguish any kind of target (e.g. geological models for mining exploration, voids and cavities detection, archeological applications…). The second sector includes dynamic, or the so-called time variable applications which are instead focused on analyzing the temporal variability of potential field signals linked to mass changes (e.g. monitoring of CCS, hydrology variations etc.). For each of the identified scenarios a simulation has been set, which means to build a synthetic model of the study area and analyze its effect in terms of gravity supposing different hypothesis and background information.

The results of this analysis will be here presented showing potentialities of quantum sensors and advantages of this next generation of instruments for geophysics applications.

How to cite: Capponi, M., Sampietro, D., Jacob, T., and Janvier, C.: Gravity applications enabled by quantum sensors. Perspectives for the FIQUgS project., EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-12533, https://doi.org/10.5194/egusphere-egu23-12533, 2023.

We present results of repeated absolute gravity and GPS measurements, carried out at Mt. Etna volcano between 2009 and 2018. Absolute gravity measurements are rarely performed along arrays of stations on active volcanoes and, through our unprecedented dataset, we highlight the possibilities of this method to track underground mass changes over long time-scales.

Analysis of the residual absolute gravity data and ground deformation reveals a cycle of gravity increase and uplift during 2009 to 2011, followed by gravity decrease and subsidence during 2011 to 2014.

Data inversion points to a common mass and pressure source, lying beneath the summit area of the volcano, at depth of ~5 km b.s.l. The bulk volume change inferred by the inversion of the deformation data can account for only a small portion of the mass change needed to explain the correspondent gravity variations. We propose that the observed relationship between gravity and vertical deformation was mostly due to the compressibility of the magma in the inferred reservoir, which, in turn, was enhanced by the presence of exsolved gas.

Overall, the gravity and deformation data we present reveal a cycle of magma recharge (2009 – 2011) and discharge (2011 – 2014) to/from the inferred storage zone. During the recharge phase only degassing occurred from the summit craters of Mt. Etna. During the following phase of discharge, the magma lost from the reservoir at ~5 km b.s.l. fed the exceptional phase of volcanic activity during 2011 to 2014, when tens of lava fountaining episodes took place.

How to cite: Greco, F., Bonforte, A., and Carbone, D.: A long-term charge/discharge cycle at Mt. Etna volcano revealed through absolute gravity and GPS measurements, EGU General Assembly 2023, Vienna, Austria, 23–28 Apr 2023, EGU23-4459, https://doi.org/10.5194/egusphere-egu23-4459, 2023.