A review of high-performance MEMS sensors for resource exploration and geophysical applications

MEMS sensors have the advantages of small volume,lightweight,and low cost,therefore,have been widely used in the fields of consumer electronics,industry,health,defence,and aerospace.With their ever-improving performance,MEMS sensors have also started to be used in resource exploration and geophysical applications.However,the requirements of high-precision MEMS sensors for geophysical applications have not been specified in detail.Therefore,this paper systematically analyzes the requirements of high-performance MEMS sensors for prospecting and geophysical applications,including seismic surveillance,Earth tide,volcanic activity monitoring for natural disasters;seismic,gravity,and magnetic resource prospecting;drilling process monitoring and local gravity measurement for gravity aided navigation.Focusing on the above applications,this paper summarizes the state-of-the-art of research on high-performance MEMS sensors for resource exploration and geophysical applications.Several off-the-shelf MEMS sensors have been used for earthquake monitoring,seismic exploration and drilling process monitoring,and a range of MEMS research prototype sensors have successfully been employed for Earth tides measurement and are promising to be used for gravity exploration.MEMS magnetometers should have a lower noise floor to meet the demand for magnetic exploration.MEMS gravity gradiometers are still under early development and will not be deployable in short-term.Highperformance MEMS sensors hold the advantages of low-cost,high integration,and capability of working in extreme environments;therefore,they are likely to gradually replace some conventional geophysical instruments in some application areas.

Numerical simulations of the wavefront distortion of inter-spacecraft laser beams caused by solar wind and magnetospheric plasmas

Plasma turbulence may lead to additional wavefront distortion of inter-spacecraft laser beams during the operation of spaceborne gravitational wave(GW)observatories,e.g.Tian Qin.By making use of the Space Weather Modelling Framework(SWMF)model and realistic orbit data for the Tian Qin constellation,the characteristic parameters of the plasma turbulence present at the Tian Qin orbit are obtained.As a first step,this work is based on the assumptions that the cold plasma approximation is valid and that the effects of the electromagnetic field induced by charge separation within the Debye length on the laser's wavefront can be ignored.An atmospheric turbulence-laser interaction model is then applied to analyze the effects of the plasma turbulence on the inter-spacecraft laser's wavefront.The preliminary results show that the wavefront distortion caused by the plasma turbulence is 10^-9 rad,which is significantly less than the designated error budget,i.e.10^-6 rad,and thus will not affect the laser interferometry.

Demonstration of a Sub-Sampling Phase Lock Loop Based Microwave Source for Reducing Dick Effect in Atomic Clocks

We demonstrate a simple scheme of 6.835 GHz microwave source based on the sub-sampling phase lock loop(PLL). A dielectric resonant oscillator of 6.8 GHz is directly phase locked to an ultra-low phase noise 100 MHz oven controlled crystal oscillator(OCXO) utilizing the sub-sampling PLL. Then the 6.8 GHz is mixed with 35 MHz from an direct digital synthesizer(DDS) which is also referenced to the 100 MHZ OCXO to generate the final6.835 GHz signal. Benefiting from the sub-sampling PLL, the processes of frequency multiplication, which are usually necessary in the development of a microwave source, are greatly simplified. The architecture of the microwave source is pretty simple. Correspondingly, its power consumption and cost are low. The absolute phase noises of the 6.835 GHz output signal are-47 d Bc/Hz,-77 dBc/Hz,-104 dBc/Hz and-121 dBc/Hz at1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. The frequency stability limited by the phase noise through the Dick effect is theoretically estimated to be better than 5.0 × 10^-14τ^1/2 when it is used as the local oscillator of the Rb atomic clocks. This low phase noise microwave source can also be used in other experiments of precision measurement physics.

A 532 nm molecular iodine optical frequency standard based on modulation transfer spectroscopy

We report construction of an iodine-stabilized laser frequency standard at 532 nm based on modulation transfer spectroscopy(MTS)technology with good reproducibility.A frequency stability of 2.5×10^(-14)at 1 s averaging time is achieved,and the frequency reproducibility has a relative uncertainty of 3.5×10^(-13),demonstrating the great stability of our setup.The systematic uncertainty of the iodine-stabilized laser frequency standard is evaluated,especially the contribution of the residual amplitude modulation(RAM).The contribution of the RAM in MTS cannot be evaluated directly.To solve this problem,we theoretically deduce the MTS signal with RAM under large modulation depth,and prove that the non-symmetric shape of the MTS signal is directly related to the MTS effect.The non-symmetric shape factor can be calibrated with a frequency comb,and in real experiments,this value can be obtained by least-squares fitting of the MTS signal,from which we can infer the RAMinduced frequency shift.The full frequency uncertainty is evaluated to be 5.3 kHz(corresponding to a relative frequency uncertainty of 9.4×10^(-12)).The corrected transition frequency has a difference from the BIPM-recommended value of 2 kHz,which is within 1σ uncertainty,proving the validity of our evaluation.

Testing the Universality of Free Fall by Comparing the Atoms in Different Hyperfine States with Bragg Diffraction

We perform a precision atom interferometry experiment to test the universality of free fall.Our experiment employs the Bragg atom interferometer with 87Rb atoms either in hyperfine state|F=1,mF=0>or|F=2,mF=0>,and the wave packets in these two states are diffracted by one pair of Bragg beams alternatively,which is helpful for suppressing common-mode systematic errors.We obtain an Eotvos ratioη1-2=(0.9±2.7)×10^-10,and set a new record on the precision with improvement of nearly 5 times.This measurement also provides constraint on the difference of the diagonal terms of the mass-energy operator.

Influence of the Earth's rotation on measurement of gravitational constant G with the time-of-swing method

In the measurement of the Newtonian gravitational constant G with the time-of-swing method,the influence of the Earth's rotation has been roughly estimated before,which is far beyond the current experimental precision.Here,we present a more complete theoretical modeling and assessment process.To figure out this effect,we use the relativistic Lagrangian expression to derive the motion equations of the torsion pendulum.With the correlation method and typical parameters,we estimate that the influence of the Earth's rotation on G measurement is far less than 1 ppm,which may need to be considered in the future high-accuracy experiments of determining the gravitational constant G.

Critical collapse of massless scalar fields in asymptotically anti-de Sitter spacetime

We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime.Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field.Through our numerical results,we obtain a formula that determines critical amplitude in terms of cosmological constantΛ:A^(*)∝(0.01360σ/v_(0)+0.001751)Λ,whereσdenotes the initial width of the scalar field and is the initial position of the scalar field.Notably,we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.

New results on the dynamics of critical collapse

We study the dynamics of the critical collapse of a spherically symmetric scalar field.Approximate analytic expressions for the metric functions and matter field in the large-radius region are obtained.In the central region,owing to the boundary conditions,the equation of motion for the scalar field is reduced to the flat-spacetime form.

Observations and modeling of flat subduction and its geological effects

Flat subduction refers to low-angle(<10°) or sub-horizontal subduction of oceanic slabs. Flat subduction is only recognized in ~10% of present-day subduction zones, but its impact on the behavior of the overriding plate is particularly strong.For example, flat subduction zones are typically associated with stronger earthquakes. The deformation caused by typical flat subduction will transfer from the trench to the overriding continental interior and form a broad magma belt. The formation mechanism of flat subduction has been linked to the relative buoyancy of subducted oceanic plateaus, overthrusting of the overriding plate, hydrodynamic suction, and trench retreat. However, these mechanisms remain debated. This paper systematically analyzes and summarizes previous studies on flat subduction, and outlines the possible geological effects of flat subduction, such as intracontinental orogeny and magmatism. Using examples from numerical modeling, we discuss the possible formation mechanisms. The most important factors that control the formation of flat subduction are associated with overthrusting of the overriding plate and the arrival of an oceanic plateau at the subduction zone. In addition, trench retreat is necessary to enable flat subduction. Hydrodynamic suction contributes to the reduction of the slab dip angle, but is insufficient to form flat subduction. Future numerical modeling of flat subduction should carry out three-dimensional high-resolution thermo-mechanical simulation, considering the influence of crustal eclogitization(negative buoyancy) and mantle serpentinization(positive buoyancy) of oceanic lithosphere, in combination with geological and geophysical data.

Movable precision gravimeters based on cold atom interferometry

High precision atom interferometers have shown attractive prospects in laboratory for testing fundamental physics and inertial sensing.Efforts on applying this innovative technology to field applications are also being made intensively.As the manipulation of cold atoms and related matching technologies mature,inertial sensors based on atom interferometry can be adapted to various indoor or mobile platforms.A series of experiments have been conducted and high performance has been achieved.In this paper,we will introduce the principles,the key technologies,and the applications of atom interferometers,and mainly review the recent progress of movable atom gravimeters.

Ultraprecision intersatellite laser interferometry

Precision measurement tools are compulsory to reduce measurement errors or machining errors in the processes of calibration and manufacturing.The laser interferometer is one of the most important measurement tools invented in the 20th century.Today,it is commonly used in ultraprecision machining and manufacturing,ultraprecision positioning control,and many noncontact optical sensing technologies.So far,the state-of-the-art laser interferometers are the ground-based gravitational-wave detectors,e.g.the Laser Interferometer Gravitational-wave Observatory(LIGO).The LIGO has reached the measurement quantum limit,and some quantum technologies with squeezed light are currently being tested in order to further decompress the noise level.In this paper,we focus on the laser interferometry developed for space-based gravitational-wave detection.The basic working principle and the current status of the key technologies of intersatellite laser interferometry are introduced and discussed in detail.The launch and operation of these large-scale,gravitational-wave detectors based on space-based laser interferometry is proposed for the 2030s.

Quasinormal oscillations and late-time tail of massless scalar perturbations of a magnetized black hole in Rastall gravity

In this study,we investigate the quasinormal mode and late-time tail of charged massless scalar perturbations of a black hole in generalized Rastall gravity.The black hole metric in question is spherically symmetric,accompanied by a power-Maxwell field surrounded by a quintessence fluid.We show that the massless scalar field,when dressed up with the magnetic field,acquires an effective mass,which significantly affects the properties of the resultant quasinormal oscillations and late-time tails.Specifically,the quasinormal frequencies become distorted and might even be unstable for particular spacetime configurations.Additionally,the exponent of the usual power-law tail is modified according to the modification in the structure of the branch cut of the retarded Green s function.In particular,as the effective mass is generated dynamically owing to the presence of the magnetic field,we may consider a process through which the field is gradually removed from the spacetime configuration.In this context,while the quasinormal oscillations converge to the case of massless perturbations,we argue that the properties of resultant late-time tails do not fall back to their massless counterpart.The relevant characteristics are investigated using numerical and analytic approaches.

Onset of chaotic gravitational lensing in non-Kerr rotating black holes with quadrupole mass moment

In the electromagnetic channel,chaotic gravitational lensing is a peculiar phenomenon in strong gravita-tional lensing.In this study,we analyze the properties and emergence of chaotic gravitational lensing in the Manko-Novikov black hole spacetime.Aiming to better understand the underlying physics,we elaborate on the boundaries of the accessible region through analyses of the contours of the effective potentials.The latter is associated with the two roots of a quadratic equation.In particular,we explore its interplay with an ergoregion,which leads to specific features of the effective potentials,such as the emergence of a cuspy edge and the formation of a pocket,which serve as static constraints on the geodesics.Additionally,we investigate the properties of the radial and angular accelerations at the turning points in photon trajectories.The accelerations are further examined and may provide kinematic constraints on the geodesics,as argued herein.It is concluded that the onset of the chaotic lensing is significantly related to both con-straints;as a result,an arbitrary slight deviation in the incident photon is significantly amplified during evolution through an extensive period,demonstrating the complexity in the highly nonlinear deterministic gravitational system.

Design of freeform geometries in a MEMS accelerometer with a mechanical motion preamplifier based on a genetic algorithm

This paper describes a novel,semiautomated design methodology based on a genetic algorithm(GA)using freeform geometries for microelectromechanical systems(MEMS)devices.The proposed method can design MEMS devices comprising freeform geometries and optimize such MEMS devices to provide high sensitivity,large bandwidth,and large fabrication tolerances.The proposed method does not require much computation time or memory.The use of freeform geometries allows more degrees of freedom in the design process,improving the diversity and performance of MEMS devices.A MEMS accelerometer comprising a mechanical motion amplifier is presented to demonstrate the effectiveness of the design approach.Experimental results show an improvement in the product of sensitivity and bandwidth by 100%and a sensitivity improvement by 141%compared to the case of a device designed with conventional orthogonal shapes.Furthermore,excellent immunities to fabrication tolerance and parameter mismatch are achieved.

Design of a large-range rotary microgripper with freeform geometries using a genetic algorithm

This paper describes a novel electrostatically actuated microgripper with freeform geometries designed by a genetic algorithm.This new semiautomated design methodology is capable of designing near-optimal MEMS devices that are robust to fabrication tolerances.The use of freeform geometries designed by a genetic algorithm significantly improves the performance of the microgripper.An experiment shows that the designed microgripper has a large displacement(91.5μm)with a low actuation voltage(47.5 V),which agrees well with the theory.The microgripper has a large actuation displacement and can handle micro-objects with a size from 10 to 100μm.A grasping experiment on human hair with a diameter of 77μm was performed to prove the functionality of the gripper.The result confirmed the superior performance of the new design methodology enabling freeform geometries.This design method can also be extended to the design of many other MEMS devices.

Mode-localized accelerometer in the nonlinear Duffing regime with 75 ng bias instability and 95 ng/√Hz noise floor

Mode-localized sensors have attracted attention because of their high parametric sensitivity and first-order common-mode rejection to temperature drift.The high-fidelity detection of resonator amplitude is critical to determining the resolution of mode-localized sensors where the measured amplitude ratio in a system of coupled resonators represents the output metric.Operation at specific bifurcation points in a nonlinear regime can potentially improve the amplitude bias stability;however,the amplitude ratio scale factor to the input measurand in a nonlinear regime has not been fully investigated.This paper theoretically and experimentally elucidates the operation of mode-localized sensors with respect to stiffness perturbations(or an external acceleration field)in a nonlinear Duffing regime.The operation of a mode-localized accelerometer is optimized with the benefit of the insights gained from theoretical analysis with operation in the nonlinear regime close to the top critical bifurcation point.The phase portraits of the amplitudes of the two resonators under different drive forces are recorded to support the experimentally observed improvements for velocity random walk.Employing temperature control to suppress the phase and amplitude variations induced by the temperature drift,1/f noise at the operation frequency is significantly reduced.A prototype accelerometer device demonstrates a noise floor of 95 ng/√Hz and a bias instability of 75 ng,establishing a new benchmark for accelerometers employing vibration mode localization as a sensing paradigm.A mode-localized accelerometer is first employed to record microseismic noise in a university laboratory environment.

Magnetic-field-sensitive multi-wave interference

We report an experimental study of magnetic-field-sensitive multi-wave interference,realized in a three-wave RF-atom system.In the F=1 hyperfine level of the ^(87)Rb 5^(2)S_(1/2) ground state,Ramsey fringes were observed via the spin-selective Raman detection.A decrease in the fringe contrast was observed with increasing free evolution time.The maximum evolution time for observable fringe contrasts was investigated at different atom temperatures,under free-falling and trapped conditions.As the main interest of the Ramsey method,the improvement in magnetic field resolution is observed with an increase of evolution time T up to 3 ms and with the measurement resolution reaching 0.85 nT.This study paves the way for precision magnetic field measurements based on cold atoms.

Parameter estimation for Einstein-dilaton-Gauss-Bonnet gravity with ringdown signals

Future space-based gravitational-wave detectors will detect gravitational waves with high sensitivity in the millihertz frequency band,providing more opportunities to test theories of gravity than ground-based detectors.The study of quasinormal modes(QNMs)and their application in gravity theory testing have been an important aspect in the field of gravitational physics.In this study,we investigate the capability of future space-based gravitational wave detectors,such as LISA,TaiJi,and TianQin,to constrain the dimensionless deviating parameter for Einsteindilaton-Gauss-Bonnet(EdGB)gravity with ringdown signals from the merger of binary black holes.The ringdown signal is modeled by the two strongest QNMs in EdGB gravity.Considering time-delay interferometry,we calculate the signal-to-noise ratio of different space-based detectors for ringdown signals to analyze their capabilities.The Fisher information matrix is employed to analyze the accuracy of parameter estimation,with particular focus on the dimensionless deviating parameter for EdGB gravity.The impact of the parameters of gravitational wave sources on the estimation accuracy of the dimensionless deviating parameter is also studied.We find that the constraint ability of EdGB gravity is limited because the uncertainty of the dimensionless deviating parameter increases with a decrease in the dimensionless deviating parameter.LISA and TaiJi offer more advantages in constraining the dimensionless deviating parameter to a more accurate level for massive black holes,whereas TianQin is more suited to less massive black holes.The Bayesian inference method is used to perform parameter estimation on simulated data,which verifies the reliability of the conclusion.

Energy in critical collapse

We study the energy issue in critical collapse.It is found that in critical collapse,the contribution from the material energy is greater than that from the gravitational energy.The quantity m/r plays an important role in identifying the formation of an apparent horizon in gravitational collapse,where m is the Misner-Sharp mass and r is the areal radius.We observe that in critical collapse,the maximum value of m/r fluctuates between 2/15 and 4/15.This denotes a large gap between critical collapse and black hole formation for which the criterion is m/r=1/2.

A high-sensitivity MEMS gravimeter with a largedynamic range

Precise measurement of variations in the local gravitational acceleration is valuable for natural hazard forecasting,prospecting,and geophysical studies.Common issues of the present gravimetry technologies include their high cost,high mass,and large volume,which can potentially be solved by micro-electromechanical-system(MEMS)technology.However,the reported MEMS gravimeter does not have a high sensitivity and a large dynamic range comparable with those of the present commercial gravimeters,lowering its practicability and ruling out worldwide deployment.In this paper,we introduce a more practical MEMS gravimeter that has a higher sensitivity of 8μGal/√Hz and a larger dynamic range of 8000 mGal by using an advanced suspension design and a customized optical displacement transducer.The proposed MEMS gravimeter has performed the co-site earth tides measurement with a commercial superconducting gravimeter GWR iGrav with the results showing a correlation coefficient of 0.91.