GB2464151A - Measuring gravity and magnetic gradients by detecting the displacement of a tensioned ribbon using an optical interferometer - Google Patents

Abstract

An apparatus 1 for measuring quasi-static gravity gradients and/or magnetic field gradients comprises a flexible elongate ribbon 3 held under tension at both ends 5, 7, a sensing means 10 to detect the transverse displacement of the ribbon from an undisturbed position S due to the gravitational gradient or magnetic field gradient and output means 35 coupled to said sensing means to generate an output signal which is a function of the tensor of the gravitational gradient or magnetic field gradient. The sensing means comprises a coherent light source 11 (e.g. laser) to produce a coherent light beam 13, a beam directing means 15 to produce a sensing beam 19 from the coherent light beam and to direct the sensing beam onto the ribbon at a first sensing position 23 from a transverse direction, and detecting means 33 arranged to detect the interferometric superposition of the sensing beam reflected from the surface of the ribbon and another beam 21 and to generate said displacement signal.

Description

-_4*.

Gradiometer for Measuring Gravitational and Magnetic Field Gradients with Improved Sensor The invention relates to an apparatus for directly measuring components of the gravitational gradient tensor or the magnetic field gradient tensor, depending on the configuration of the apparatus, particularly the off-diagonal components of the tensors, and to a method of measuring said tensor components.

Gravitational gradiometry is the measurement of the gravitational gradient field of differential accelerations between two infinitesimally close spatial points.

The gravitational gradient field is described by a second rank tensor, T: = -a2,Vc, y, z) (1) wherein i, j (x, y, z) and the scalar V is the gravitational potential of a local reference frame of orthogonal Cartesian coordinates (x, y, z). Taking the z axis as pointing vertically into the ground, the components of the tensor at some point in the local reference frame (x, y, z), calculated by determining the spatial rate of change along directions x, y and z of the spatial rate of change of the gravitational potential in directions x, y and z, represent the rate of change of acceleration due to gravity along that direction. For example, the component T represents the rate of change along the y direction of acceleration due to gravity along the direction z towards the ground, and is typically measured in units of EOtvOs Units (1 EOtvös = 1 EU =i09 _2) The tensor consists of nine components, only five of which are totally independent due to their geometrical symmetry (i.e. T = T1, where i!=j) and due to * L the validity of the Laplace equation (i.e T + T + = 0) for gravitational potential fields outside of the extent of gravitational field sources.

Similarly, magnetic gradiometry is the measurement of the components of

the magnetic field gradient tensor B:

B=aB1/oj (2) again, wherein i,j (x, y, z), and B, corresponds to the spatial rate of change of the components of the magnetic field B of a local reference frame of orthogonal Cartesian coordinates and is measured in Tm (more typically nTm).

Providing apparatus that enables accurate and absolute measurements of the various components of the gravity gradient tensor T and apparatus that enables accurate and absolute measurements of the various components of the magnetic field gradient tensor B is very important in the fields of oil, gas and mining of various other natural resources. Gravitational gradiometry particularly enables the mapping of variations in the density of subsurface rocks and deposits to assist in the targeting of prospecting, and in increasing the effectiveness of drilling for oil and gas and mining. Gravitational gradiometry finds further application in defence and space industries for navigation and reconnaissance (e.g. void detection), geological prospecting, sub-sea/underwater navigation and exploration, terrestrial and marine archaeology, medicine and space exploration (for example, obtaining density maps of asteroids and other solar system orbital bodies). Magnetic gradiometry also finds application in many, if not all of the aforementioned fields.

For many gravity gradiometry applications, it is the T2 component (i.e. the second order derivative of gravitational potential in the vertical direction) that many gradiometers aim to measure, whether by direct measurement, or by measuring at least some of the other tensor components and recalculating T2 from their dependent relationship, or both. However, in their paper "On combined gravity gradient components modelling for applied geophysics", Journal of Geophysics and Engineering, 2008, Vol 5, pp 348-356, Veryaskin and McRae show that by measuring and using the two off-diagonal gravity gradient tensor components T2 and T, it is possible to obtain more information about anomalous subsurface density contrasts than by measuring and using the vertical gravity gradient component To retrieve this subsurface density information, a gradioineter arrangement is required that is capable of simultaneously producing real-time data sets of direct measurements of both the T, and Tj tensor components.

A method of absolute measurement of gravity gradient tensor components was invented first by Baron Lordnd von Eötvös as early as 1890, utilising a torsion balance with proof masses hung at different heights from a horizontal beam suspended by a fine filament. The gravity gradients give rise to differential forces being applied to the masses which result in a torque being exerted on the beam, and thus to angular deflection of the masses which can be detected with an appropriate sensor. A sensitivity of about 1 EU can be reached but measurement requires several hours at a single position due to the necessity to recalculate the gravity gradient components from at least five independent measurements of an angular deflection each with a different azimuth angle.

Practical devices, which have been built in accordance with this basic method of Eötvös, are large in size, bulky and have low environmental noise immunity, thus requiring specially prepared conditions for measurements. This excludes any possibility of using them on a moving carrier or for many practical applications where there are weight or space constraints, such as in the confined environment of a borehole, and in airborne drones, space launcher payloads, satellites, and extraterrestrial rovers.

Another method for absolute measurement of gravity gradient tensor components which enhances the above method was invented by Forward in the 1960s (see US patents 3,722, 284 (Forward eta!) and 3,769, 840 (Hansen)). The method comprises mounting both a dumbbell oscillator and a displacement sensor on a platform which is in uniform horizontal rotation with some frequency f about the axis of the torsional filament. The dumbbell then moves in forced oscillation with double the rotational frequency, whilst many of the error sources and noise sources are modulated at the rotation frequency or not modulated (particularly 1/f noise). The forced oscillation amplitude is at a maximum when the rotation frequency satisfies the resonance condition 2 O, where W is the angular resonant frequency, and the oscillator quality factor Q tends to infinity. Unlike the non-rotating method, this method enables one to determine rapidly the quantities T, -T and T, by separating the quadrature components of the response using synchronous detection with a reference signal of frequency 2.

The same principles can be directly used, as proposed by Metzger (see US patent 3,564, 921), if one replaces the dumbbell oscillator with two or more single accelerometers properly oriented on such a moving platform. There are no new features of principle in this solution to compare with the previous one except that the outputs of the pairs of accelerometers require additional balancing.

Devices have been built according to this method, but they have met more problems than advantages, principally because of the need to maintain precisely uniform rotation and the small displacement measurement with respect to the rotating frame of reference. The devices have reached a maximum working accuracy of about a few tens of Eötvös for a one second measuring interval, and they are extremely sensitive to environmental vibrational noise due to their relatively low resonant frequencies. The technological problems arising in this case are so difficult to overcome that the existing developed designs of rotating gravity gradiometers show a measurement accuracy which is much lower than the limiting theoretical estimates.

Devices which are capable of directly measuring magnetic gradients have only recently been developed. Before this, two spaced magnetometers could be used to provide an indirect measurement by measuring the magnetic field strength at these two points and dividing the difference in their readings by the spacing to give an approximation of the magnetic field gradient. Sensitive Superconducting * 0 Quantum Interference Device (SQUID) magnetometers could be used to provide measurements of small magnetic field gradients, but the accuracy and practical usefulness of these devices is limited.

In WO-A-96/10759 a method and apparatus for the measurement of two off-diagonal components of the gravity gradient tensor is described. According to this document, the second fundamental mode (S-mode) of a stationary flexible string with fixed ends is coupled to an off-diagonal gravity gradient of the gravitational field, whilst its first fundamental mode (C-mode) is coupled to an effective (averaged with a weight function along the string's length) transverse absolute gravitational acceleration of the gravitational field. In other words, a string with fixed ends is bent into its S-mode by a gravity gradient only, provided that it does not experience any angular movements. Therefore, by measuring absolutely the mechanical displacement of such a string which corresponds to the S-mode it is possible to measure absolutely an off-diagonal component (e.g. T2 or T2, for a string aligned along the z axis) of the gravity gradient tensor. While this document teaches the use of a one-dimensional string', any generic element having a width and depth much smaller than its length, for example, a flat ribbon, is suitable.

WO-A-00/68 702 discloses the use of a similar tensioned string device to measure two off diagonal components of the magnetic field tensor. In this arrangement, an alternating current is passed through the string and a force is exerted on the string due to it being in a magnetic field. The amplitude of displacement of the oscillating string in its S-mode is due to the gradient of the magnetic field and apparatus is provided to detect this amplitude and thus absolutely measure the local value of the off diagonal component of the magnetic field gradient tensor (e.g. B, or B,,, for a string aligned along the z axis).

In this design for a gradiometer having a current-carrying string, or ribbon, of length I aligned along the z axis and having a uniform mass distribution per unit length along its extent, the displacement, y(z,t), of the string from its undisturbed position (i.e. the straight line joining its fixed points at both ends), for example in the y-direction of the local coordinate frame as a function of the z-position, z, of a unit element of the string, and of time, t, can be described by the following force balancing equation for a vibrating string. (N.B. A similar equation and following analysis is applicable to the orthogonal direction transverse to the string and to any number of other directions). Lu 2

---y(z,t)+ h-y(z,t)--at + J(t)B (0, t) -I(t)By: (0, t)z + thermal noise (3) The components on the right hand side of the equation represent the forces acting on the string (including gravitational and magnetic forces) in the y direction, and the components on the left hand side of the equation represent the restoring string forces in the y direction.

The equation has the boundary conditions corresponding to the fixed ends of the string, i.e. y(O,t) -y(l,t) = 0. In this equation denotes the string's mass per unit length, h is the friction coefficient per unit length, the parameters Y, A and Ll/l are the string's Young modulus, the area of its cross section and the strings strain respectively. The quantity g(0,i) is the absolute value of the y-component of the gravitational acceleration and 7,(0,t) the corresponding gravity gradient tensor component along the string, both taken at the centre of the local coordinate frame chosen (i.e. z = 0). The quantity 1(t) is the current flowing through the string. It is well known that a conductor carrying a current 1(t) in a non-uniform magnetic vector field of flux density B(x, y, z) is subject to force F 1(r) {n x B(x,y, z)}, where n is the unit vector in the direction of current flow, in this case the z direction. The quantities B(0, t) and B(O, t) therefore represent the absolute values of the x-component of the magnetic field and the corresponding magnetic gradient tensor component along the string, both taken at the centre of the local coordinate frame chosen.

Since the string is subject to Brownian fluctuations, the corresponding thermal noise driving source is included on the right side of equation (3).

Of the gravitational force components of the equation (3), -j g,, (0, t) represents the force in the y direction on the unit element of the string due to the acceleration due to gravity, and - T (0, t)z represents the force in the y direction on the unit element of the string due to the gradient change along the z direction in the acceleration due to gravity.

Of the magnetic force components of the equation (3), I(t)B(0,t) represents the force in they direction on the unit element of the string due to the magnetic field component in the x direction, and -I(t)B. (0, t)z represents the force in the y direction on the unit element of the string due to the magnetic field gradient tensor.

Applying Fourier analysis to the complex shape of the string caused by its interaction with the gravitational and magnetic field, the function y(z, t), can be described, in the range z = 0 to z = 1, by an infinite sum of sinusoidal functions of period 21, with appropriate coefficients c(n,t). Thus a solution of force balance vibration equation (3), which satisfies the boundary conditions shown above, can be represented by the following sum (4) wherein each term in n corresponds to one of the string's natural vibrational modes.

infIniiv 717'Z "I cy(fl,t)S1fl Z (4) fl4 l By substituting equation (4) into equation (3) and by multiplying its left-hand and right-hand sides by sin(tn'z/l), and then by integrating both sides over z from 0 to 1, one can obtain the following differential equation (4) for c(n, t).

dt2CY (n, t) + Cy (n, r) + (n, t) [(-1)fl -(0, t) �1 I(t)B (0, r)] + (] )fl (0, t) + i I(t)B (0, t) + thermal noise (4) where the quantities fy (5) 1 p1 -10 -represent the string's natural frequencies; r and p are the relaxation time and the volume mass density of the string respectively.

When n takes an even value (i.e. for those terms c(n, t) of the infinite sum in equation (3) corresponding to anti-symmetric vibrational modes of the string having a node at z=l/2, the midpoint of the string), the force component of equation (4) involving g(0, t) and B/O, t) is equal to zero and the force component being a function of the gravitational gradient tensor component T2 and magnetic field gradient tensor component B2(O, t) remains. Thus, for anti-symmetric modes of the string (i.e. n even), c, is dependent only on and B(O, 1) (and thermal noise).

In practice this means that the amplitude, of the anti-symmetric sinusoidal components of the displacement of the string in the y-direction, y(z,t), is dependent only on the magnitude of the gravity gradient tensor component T and the magnetic

field gradient tensor component B(O, t)

The string has an effective mechanical bandwidth of oscillation limiting its displacement response to oscillations below a few kHz (even for extremely stiff strings). The force on the string due to the magnetic field gradient is dependent on the current carried in the string. Therefore, the string can be made to respond to magnetic currents by pumping the string with an alternating current having a frequency within the string's mechanical bandwidth. Pumping the string with an alternating current well outside the bandwidth of the string will not produce any sensitivity to magnetic field gradients because oscillations at such frequencies are damped.

The mid point of the string, r=l/2, is the position of a node in all anti-symmetric vibrational modes of the string. If sensors are positioned symmetrically in the longitudinal direction with respect to this point, it will be possible to identify displacements of the string corresponding to the string's natural anti-symmetric vibrational modes while discounting displacements corresponding to the string's symmetric vibrational modes.

It is particularly advantageous if displacement sensors are positioned at z-l/4 and z=3114, positions corresponding to the antinodes of the first anti-symmetric vibrational mode of the string, n=2, At these points the displacement of the string corresponding to the n2 mode is at a maximum and thus the sensing signal will also be at a maximum, giving optimum sensitivity.

In WO 96/10759, two rectangular type pick-up coils in the form of a Superconducting Quantum Interference Device (SQUID) are arranged to detect the transverse displacement in a superconducting Niobium string held under tension at its ends inside a superconducting casing, the whole apparatus being cooled to 4.2K or less in a cryogenic liquid helium vessel. Solenoids arranged symmetrically at either end of the string are driven by an alternating signal having frequency 1) to induce an AC supercurrent in the string also having frequency. The superconducting casing excludes the external magnetic field from the casing such -12 -that no magnetic field forces act on the string and the displacement of the string from its straight line configuration is in response to the gravitational field only. The two coils of the SQUID device are positioned proximate to the string and are located at symmetrical longitudinal positions one on either side of the mid-point of the string and are arranged in a circuit as two arms of a superconducting magnetic flux transformer. The AC supercurrent carried by the string induces a current in each coil of the SQUID device proportional to the displacement of the string at that point from its undisturbed position. If the positions and responses of the two coils are arranged such that the two arms of the magnetic flux transformer are perfectly balanced either side of the mid-point of the string, the symmetrical modes of the string (i.e. n odd) do not produce any signal current in the flux transfonrner. For the anti-symmetric modes, the displacement response of the string is dominated by the n = 2 mode and all higher modes can be ignored (or factored in to error sources); then it follows that the output voltage of the SQUID is an AC signal having frequency and an amplitude that is proportional to the displacement of the string in the first anti-symmetric mode only (i.e. n = 2), and hence, to the off-diagonal gravitational gradient component (in the example given above, T(0, 1)). The amplitude of this SQUID output signal is obtained by synchronous detection of the signal using the alternating signal driving the solenoids as a reference. A force feedback circuit is also provided which takes as an input the voltage output of the SQUID and induces in the string a feedback current formed from this voltage output to increase the sensitivity of the device to the gravitational gradient component. For a gradiometer of this design having typical practical parameters, the theoretical minimum gravity gradient detectable is calculated as being 0.02 EU. The string-I.., -L.) -based gravitational gradiometer device is less sensitive to vibrational noise and lends itself to deployment on a mobile platform where measurements can be taken to retrieve high resolution data of local differences in gravity gradient. However, deployment is problematic in that the linear and angular accelerations of the mobile platform affect the deformation of the string and the output of the device.

In WO-A-OO/68702, a similarly arranged apparatus is provided to detect an ambient magnetic field gradient, this time deployed in a liquid nitrogen bath at 77K, but not having a superconducting casing, so as to permit the ambient magnetic field to act on the current carrying string. Two pick up coils are arranged symmetrically about the mid-point of the string and are connected in anti-phase so as to cancel out signal components related to symmetrical modes of string oscillation. The string is pumped with an AC sinusoidal current signal having a frequency within the mechanical resonance of the string such that the magnetic field forces acting on the current carrying string cause the string to resonate. The pumping current has a frequency of twice the natural (first order) resonant frequency of the string, corresponding to the frequency of the first anti-symmetric mode. This forced oscillation selects the response of the string and gives the string a high sensitivity to magnetic field gradient forces. The displacement contribution due to the quasi-static gravitational gradient tensor component does not vary over time with 1(t), and can be distinguished from the contribution due to the magnetic field gradient. SQUID devices can be used to give the requisite theoretical sensitivity. Alternatively, high sensitivity can be achieved with a double lock-in detection scheme by pumping the string with an additional carrier-frequency alternating current above the mechanical -14 -bandwidth of the string as a carrier for the displacement signal. The displacement signal is then detected by the two pick-up coils in a resonant circuit tuned to the carrier frequency and is demodulated to recover the displacement. In either case, the cryogenic bath reduces the environmental thermal noise and the thermal noise in the pick up coils.

In WO 03/277 15 the string based gradiometer design is developed further by providing a gravity gradiometer in which the string is in the form of a uniform metal strip or ribbon and is constrained at its mid-point, with, for example, a rigid knife-edge mounted to the casing and touching the ribbon but not exerting any force thereon. This knife-edge restricts any movement of the ribbon at that point and adds another boundary condition with the effect that deformation of the ribbon into all symmetric modes (i.e. n = odd) is prevented while deformation into all anti-symmetric modes (i.e. n = even) is permitted. This use of a ribbon arrangement in place of a string is such that the ribbon is more constrained in its movement, making the output of the device less dependent on linear accelerations exerted on the device and more manageable. This makes the device more suitable for operation on mobile platforms. The device operates in a liquid nitrogen cryogenic bath at 77K which reduces the effects of thermal noise and increases mechanical stability.

Similarly to the arrangement described in the magnetic gradiometer, in place of a SQUID device, two pick-up coils are provided symmetrically about a mid-point of the ribbon arranged as two arms of a resonant bridge circuit tuned to the frequency of an alternating carrier signal supplied to the ribbon as an alternating current. The frequency of the AC carrier current pumped to the ribbon is above the mechanical -15-bandwidth of the tensioned ribbon such that the ribbon's displacement response due to interaction forces with the ambient magnetic field is damped and the detected signal is dependent on the gravitational gradient only. The two coils are located at positions directly adjacent the antinodes of the first anti-symmetric mode of the ribbon (i.e. at z 114 and z= 3//4, where 1 is the length of the ribbon) which correspond to the maximum displacement and increases the sensitivity of the response. A voltage signal is induced in the bridge circuit having the same frequency as the carrier signal and having an amplitude that is a measure of the average displacement of the ribbon over a region situated around the /14 and 3/14 locations. By synchronously detecting the voltage amplitude of the induced signal with reference to the carrier signal, the amplitude of the local off diagonal gravity gradient component can be retrieved. The response of the ribbon is modulated with a square wave by indirectly changing its stiffness between a high value and a low value using a square wave signal to switch a negative feedback circuit arranged to apply a current signal proportional to the output of the bridge circuit but in anti-phase or quadrature therewith. In the high stiffness or tensioned state the response of the detector to the gravity gradients is low, and in low stiffness or relaxed state the response of the detector to the gravity gradients is high. This modulated output is retrieved using a lock-in amplifier. Three sets of four single axis gradiometer modules are provided in an umbrella' arrangement to remove the effect of angular accelerations on the output of the combined device, which is capable of providing absolute and direct measurement of all gravitational gradient tensor components.

In these known string based gravitational and magnetic gradiometers, thermal noise and RF interference in the pick-up coils and sensitive detector electronics significantly inhibits the sensitivity of the devices and limits the resolution with which they can detect signals and renders them unviable for a number of desired practical uses. Further, the signal induced in the pick-up coils gives rise to an electromotive force pointing in the opposite direction to the induced current, which itself establishes a magnetic field which exerts a force on the current carrying string and interferes with the sensitivity of the gradiometer. Other electrostatic force effects from these sensors also perturb the string.

The sensitive electronics provided for generating the current signals, and for amplifying and detecting the displacement signal are bulky, expensive and draw a large amount of power and therefore require a sizeable power source. Also, the high frequency RF currents required to modulate the sensor signals and facilitate detection are difficult to drive down long lengths of cable. This results in the gradiometer device having a large packaging to accommodate these components, and requires short cable lengths which both inhibit remote deployment of the device.

The arrangement of pick-up coils and detection electronics is such that the device has a small dynamic range of sensitivity which limits the versatility and practical usefulness of the device.

Further, the operational requirement of these known gradiometers at cryogenic temperatures requires them to be provided in large cryogenic vessels, which inhibits their assembly and maintenance, prevents the practical provision of arrangements of multiple gradiometers, and limits their ability to be effectively deployed, particularly in restricted environments, such as a borehole. -17-

It is an object of the present invention to provide a magnetic field or gravitational gradiometer in which the detection of the displacement of the string due to the gradient signal has a high sensitivity, and in which the operation of the apparatus facilitates its assembly, maintenance and practical and versatile deployment.

Viewed from one aspect the present invention provides apparatus for the measurement of quasi-static gravity gradients and/or magnetic field gradients comprising: a flexible elongate ribbon held under tension at both ends; sensing means arranged to detect the transverse displacement of the ribbon from an undisturbed position due to the gravitational gradient or magnetic field gradient acting on said ribbon and to generate a signal representing the displacement; and output means coupled to said sensing means and responsive to said displacement signal to generate an output signal which is a function of the tensor of the gravitational gradient or magnetic field gradient; wherein the sensing means comprises: a coherent light source arranged to produce a coherent light beam; beam directing means arranged to produce from the coherent light beam a sensing beam and to direct the sensing beam onto the ribbon at a first sensing position from a transverse direction; and detecting means arranged to detect the interferometric superposition of the sensing beam reflected from the surface of the ribbon and another beam derived from the coherent light beam and to generate said displacement signal.

According to this aspect of the invention, the provision of a sensing beam of coherent light which is reflected from the surface of the ribbon and interfered with another light beam derived from the coherent light beam gives a strong signal in the form of an interference pattern containing information on the displacement of the ribbon, which can be easily detected with an optoelectronic sensor and used to generate a signal representing the displacement of the ribbon. The optoelectronic sensing system exerts negligible force on the ribbon, even when a current signal is applied to measure the magnetic field, thus giving a very accurate and error free measurement. The use of an interferometric detection arrangement achieved by the invention enables high sensitivity detection of the position of the ribbon, from which a high resolution image of the magnetic field or gravitational gradient field can be built up (depending on whichever field component the apparatus is arranged to detect).

The sensing means which can be provided for the production and detection of a coherent light signal is generally relatively stable and immune to thermal noise at non-cryogenic temperatures. Thus the gradiometer does not need to be housed in a cryogenic vessel. Further, a reduced number of components are required for the detection of the ribbon's position, which can be small in size and draw less power in total. Finally, no high frequency RF current modulation signal is required to be supplied to the sensing means. This enables the gradiometer to be housed in a small package and facilitates its practical deployment in restricted environments and at remote locations.

Further, the dynamic range of interferometric detection provided by the gradiometer of the invention enables the gradiometer to be deployed to be sensitive -19-to gradient signals in a number of orientations in which the amplitude of the tensor components differ by many orders of magnitude.

The sensing beam need not be directed onto the surface of the ribbon from a direction orthogonal to the axis of the ribbon but may be incident at an oblique angle to the orthogonal, provided the arrangement is such that the optical path length of the sensing beam varies with the displacement of the ribbon and that the detecting means is arranged to detect the reflected sensing beam.

The beam directing means preferably comprises a beam splitter arranged to interferometrically combine the reflected sensing beam with said other beam for detection by the detecting means. In this arrangement, the sensing means is provided in the form of a Michelson interferometer in which two beams from the same source are recombined by a beam splitter to give an interference signal enabling the sensing means to be provided in a simple arrangement.

The beam splitting means is preferably arranged to produce said other beam from the coherent light beam, the beam directing means is arranged to direct said other beam onto the ribbon at a second sensing position from a transverse direction such that said other beam acts as a second sensing beam, wherein the first and second sensing positions of the sensing beams are located symmetrically on opposite sides of the mid-point between the ends of the ribbon, and wherein the beam splitting means interferometrically recombines the two reflected sensing beams for detection by the detecting means. In this arrangement, the two arms of the Michelson interferorneter each provide a sensing beam that is used to detect the position of the -20 -ribbon. By arranging the sensing positions of the two arms symmetrically on opposite sides of the mid-point of the ribbon, the displacement of the ribbon due to the symmetric modes of vibration can be screened out by the detector. This provides a sensing means which is naturally sensitive only to detecting the displacement of the ribbon due to the gravity gradient or the magnetic field gradient.

The first and second sensing positions of the sensing beams are more preferably both located at a distance of a quarter of the length of the ribbon from the mid-point of the ribbon. In this arrangement, the detected displacement signal is dominated by the displacement in the second fundamental mode (S-mode) of the ribbon's vibration and detects the maximum displacement of the ribbon, giving optimum sensitivity of the device.

Preferably, reflective means are arranged along the optical path of each sensing beam to reflect the optical path of each sensing beam back onto the surface of the ribbon and increase the optical path length of each sensing beam. In this arrangement, the reflections of the sensing beams between the reflective means and the ribbon surface fold and lengthen the optical path, increasing the scale of the optical path difference between the two arms of the interferometric detector due to the displacement of the ribbon, and thus increasing the sensitivity of the sensing means and the accuracy of the gradiometer device.

The apparatus preferably further comprises sensing beam positioning means arranged to automatically adjust the axial location along the ribbon of the first and second sensing positions of the sensing beams to a target position for each sensing beam. This automatic adjustment of the arms of the interferometric sensor such that the sensing positions are correct (i.e. at their predetermined target positions, being symmetrically arranged on opposite sides of the mid-point of the ribbon) balances the sensor by screening out the symmetrical oscillation modes and ensures the correctness of the output displacement signal. This automatic correction can be performed on a semi-regular basis, such as being activated during a sensor head maintenance, or if the gradiometer is intended to be operational for a long time the correction can be performed effectively in real time by periodic detection and adjustment of the sensing positions by servo manipulation of the beam directing means and control by a Digital Signal Processor (DSP) unit.

The apparatus preferably further comprises movement preventing means arranged to prevent transverse movement of the ribbon away from its rest position at the mid-point between the ends of the ribbon. The apparatus also preferably further comprises means for positioning the movement preventing means arranged to automatically adjust the position of the movement preventing means to prevent transverse movement of the ribbon away from its rest position at the mid-point between the ends of the ribbon. In this arrangement, the movement preventing means effectively acts as a filter by applying an extra boundary condition of the mid-point of the ribbon being at rest such that it prevents movement of the ribbon in its symmetrical modes (most importantly its C' mode), while it permits movement in the anti-symmetric modes (most notably the S' mode). This causes the movement of the ribbon to be sensitive only to the gravitational gradient and/or magnetic field gradient. The means for positioning the movement preventing means maintains the -22 -accuracy of the output of the gradiometer device and prevents systematic errors from creeping in. The means for automatic positioning of the movement preventing means can be arranged to operate at intervals on a semi-regular basis, for example, during maintenance, as described above, and can be arranged to operate effectively in real time by periodic detection and correction of the position of the movement preventing means.

In an alternative preferred arrangement of the sensing means to the foregoing arrangement in which two sensing beams are provided, the beam directing means preferably further comprises a reference surface, and wherein said beam splitting means is preferably arranged to produce said other beam from said coherent light beam, and said reference surface is preferably arranged to reflect said other beam to act as a reference beam, such that the reflected sensing beam is combined with said reference beam for detection by the detecting means. In this alternative arrangement only a single sensing beam is provided and the interferometric combination by the sensing means effectively measurably compares the optical path length of this sensing beam, which is dependent on the displacement of the ribbon, with the constant optical path length of the reference beam reflected from the reference surface. Thus the displacement signal output from the sensing means in this alternative preferred arrangement is a function of the absolute position (measured as a displacement from a rest position) of the ribbon at the sensing position of the sensing beam. By using a sensing means according to this alternative preferred arrangement the actual displacement of the ribbon can be characterised, which will be a function of all Fourier modes of vibration.

-23 -The sensing means preferably comprises at least two independent sensing units each comprising a said coherent light source, a said beam directing means and a said detecting means, each said sensing unit being arranged to detect the displacement of the ribbon at a different sensing position along the length of the ribbon, said displacement signal generated by the sensing means being a combination of the detected displacements of each said sensing unit. More preferably, the sensing means comprises more than two said sensing units such that the profile of the displacement of the ribbon in the S mode of oscillation is oversampled along its length. In this arrangement, by using two or more such sensing units arranged along the ribbon, with each unit detecting the actual displacement of the ribbon from its rest position at different sensing positions, the actual displacement profile of the ribbon can be built up by combining the output displacement signals of each of the sensing units. By providing more than two such sensing units, the displacement signal must contain information on the displacement profile of the ribbon at data points more frequent than twice the spatial frequency of the first fundamental S mode of the ribbon. Thus, according to Nyquist theory, the ribbon profile is oversampled for the 5' mode. As a result of this information density, a Fourier decomposition of the ribbon profile can accurately determine the amplitude of the S mode displacement (or of any other higher mode displacement having a spatial frequency of at least the Nyquist sampling rate of the distribution of sensing units). Thus in this alternative preferred arrangement, the ribbon displacement profile can be more fully characterised by the sensing means and the -24 -data can be processed to better calculate the components of the gravitational gradient tensor and/or the magnetic gradient tensor.

Preferably, the output signal is used to determine at least one of the off-diagonal gravity gradient tensor components. According to this arrangement, the gradiometer is arranged to detect gravitational gradients and in particular the off-diagonal components and T of the tensor thereof, whereby it is possible to obtain more information about anomalous subsurface density contrasts than by measuring and using the vertical gravity gradient component The apparatus preferably further comprises filtering means arranged to prevent the reflected sensing beam from re-entering the coherent light source. Such a filtering means includes at least one or all of a second polarising beam splitter, a polariser. and a Faraday rotator, and can be provided in an arrangement of an optical feedback isolator. Such an arrangement prevents the constructively interfered light from re-entering the laser arid disrupting to the output coherent beam, affecting its phase, frequency andlor amplitude by optical feedback which would otherwise inhibit the accuracy of the output displacement signal.

The apparatus preferably further comprises modulation means arranged to modulate the phase of the coherent light beam and thus any beam derived therefrom by a modulation signal. Preferably, the displacement signal is detected by synchronous detection with a lock-in amplifier with reference to the modulation signal. According to this arrangement the component of the displacement signal of -25 -the sensing means that is due to the interferometric detection of the sensing beam reflected from the surface will also be modulated, whereas the component of the displacement signal due to other noise sources, for example in the detecting means, will not be modulated. Therefore, the demodulated displacement signal retrieved after synchronous detection does not contain any non-modulated components of the signal generated by the detection means and thus has a larger signal to noise ratio than a non-modulated, non-synchronously detected arrangement.

Viewed from another aspect, the invention provides a method of measuring quasi-static gravity gradients and/or magnetic field gradients comprising: holding a flexible elongate ribbon under tension at both ends; directing a sensing beam produced from a coherent light beam output from a coherent light source onto the ribbon from a transverse direction at a sensing position on the ribbon; detecting the interferometric superposition of the sensing beam reflected from the surface of the ribbon and another beam derived from the coherent light beam and generating from said detection a signal representing the transverse displacement of the ribbon from an undisturbed position due to the gravitational gradientor magnetic field gradient acting on said ribbon; and generating, responsive to said displacement signal, an output signal which is a function of the tensor of the gravitational gradient or

magnetic field gradient.

According to the method and apparatus of the invention, the sensitivity of the gradiometer device may be two orders of magnitude greater than a gradiometer having a capacitive pick-up sensor arrangement. The theoretical increase in sensitivity is 800 times. The output of the gradiometer is also much more stable and has a greater dynamic range, making the device more versatile in deployment.

Certain preferred embodiments of the invention will now be described by way of example only, and with reference to the accompanying drawings, in which: Figure 1 is a schematic of a gradiometer according to a first embodiment of the present invention; Figure 2 is a schematic of a gradiometer according to a second embodiment of the present invention; Figure 3 is a schematic of a gradiometer according to a third embodiment of the present invention, the gradiometer having a sensing means including a plurality of sensing units deployed adjacent the ribbon of the gradiometer; and Figure 4 is a schematic of a detailed view of a sensing unit of the gradiorneter shown in Figure 3.

In the embodiments described herein the gradiometer is arranged to detect gravitational gradients. However, from the following description it will be understood that the arrangement of the device can be adapted such that it can be

used to detect magnetic field gradients.

The sensing element of the first embodiment of a gradiometer device 1 according to the invention shown in Figure 1 is provided by a long ribbon 3 having a width and a depth much smaller than its length.

The ribbon 3 has a length, L, of the order of tens of centimetres and has a width, W, that is greater than its depth, D, such that the ribbon 3 resembles a length -27 -of tape (i.e. L>> W > D). This ribbon shape means that the displacement of the ribbon 3 is constrained to the direction orthogonal to the plane of the ribbon's extent (i.e. the direction orthogonal to the ribbon's major length and width directions) and the gradiometer is thus only sensitive to forces causing the ribbon 3 to be displaced in this direction (i.e. forces acting on the ribbon in the depth direction). The ribbon is of a phosphor bronze material formed by machining a metal sheet to the appropriate dimensions.

The ribbon 3 is held under tension between two fixed points 5, 7 at its longitudinal ends by clamps (not shown). Between these two fixed points 5, 7 the ribbon 3 is free to move such that it can be displaced away from the straight line S joining the two points by any external force acting on the ribbon 3, such as a force due to acceleration due to absolute gravity experienced by the ribbon 3, a differential gravitational gradient across the ribbon 3, and, if the ribbon 3 is carrying a current, magnetic field forces acting on the ribbon 3 including the magnetic field gradient, as well as any residual electrostatic forces.

The displacement of the ribbon 3 can be described by the force balance equation (3) set out above which has solutions in the form of the sum of the modes of vibration of the ribbon 3 that make up the components of the decomposed infinite Fourier sum set out above in equation (4).

Sensing means 10 is provided to detect the transverse displacement of the ribbon 3 from an undisturbed position S due to the gravitational gradient acting on the ribbon and to generate a signal representing the displacement. The sensing means 10 is provided generally in the form of a Michelson interferometer.

-28 -The sensing means has as a coherent light source 11 a compact solid state Nd:YAG laser which is pumped by a laser diode. The Nd:YAG laser produces an essentially monochromatic coherent light beam 13 having a wavelength of lj.tm which is projected onto beam directing means 15.

The beam directing means 15 has a beam splitter cube 17 (i.e. a 50-50 beam splitter) which splits the coherent light beam in two, producing a first sensing beam 19 and another beam 21. The first sensing beam 19 is directed onto the surface of the ribbon 3 from a direction transverse to the ribbon's length and in the direction in which the ribbon 3 is sensitive to displacements due to external forces acting on the ribbOn. The beam directing means 15 is arranged such that the first sensing beam 19 is incident on the ribbon 3 at a first sensing position 23 along the length of the ribbon 3. The other beam 21 is used, in this embodiment, as a second sensing beam reflected onto the ribbon 3 by a planar reflector 27 from the same direction as the first sensing beam 19, the beam directing means 15 being arranged such that the second sensing beam 25 is incident on the ribbon 3 at a second sensing position 29 along the length of the ribbon.

After reflection from the surface of the ribbon 3, the return path of the first sensing beam 19 and the second sensing beam 25 generally follows the path of their incidence back to the beam splitter cube 17 where the first and second sensing beams 19, 25 are recombined to produce a combined beam 31. The combined beam 31 is an interferometric superposition of first and second sensing beams 19, 25 and produces an interference pattern of fringes across the beam on any surface that it illuminates. The intensity of this interference pattern at any point is dependent on -29 -the difference in the optical path length between the two arms of the Michelson interferometer, i.e. the first sensing beam 19 and the second sensing beam 25.

A detection means 33 has a photodiode detector having an effective detecting area of a few square millimetres that is arranged in the path of the combined beam 31 to detect the intensity of the beam at a point in the interference pattern. The detection means 33 provides as its output a signal which is dependent on the intensity of the interference pattern produced on its detecting surface by the combined beam 31.

The intensity detected by the detection means 33 is therefore dependent on the optical path difference between the first and second sensing beams 19, 25.

Therefore variations in the distance travelled to the ribbon surface can be detected by the detecting means 33 and the displacement of the ribbon can be retrieved. This dependence is utilised to make the sensing means 10 directly sensitive to the gravity gradient by arranging the beam directing means 15 such that first and second sensing positions 23, 29 are located symmetrically about the mid-point M of the ribbon 3. In this arrangement the detection means 33 detects in the combined beam 3 1 the combination of the reflected sensing beams, 19, 25 in anti-phase. Some anti-symmetric modes of oscillation, for example, the S-mode, cause the path length for sensing beam 19 to increase while the path length for sensing beam 25 decreases (and vice versa) resulting in a optical path length difference that is detectable by monitoring the interference pattern of the two beams. In contrast, in the symmetric modes of oscillation, for example the C mode, cause both the upper and lower halves of the ribbon move in the same direction by the same amount and thus no optical path length differepce between the two balanced arms of the interferometer -3 -results. The detected beam intensity is therefore insensitive to displacement of the ribbon in symmetric modes of oscillation and is inherently directly dependent only on the amplitude of the ribbon's displacement in its anti-symmetrical modes of oscillation.

The first and second sensing positions 23, 29 are located in particular at the L/4 and 3L/4 positions along the ribbon 3, respectively (i.e. both a quarter distance from the mid-point lvi of the ribbon 3). This arrangement increases the sensitivity of the sensing means 10 to the displacement of the ribbon 3 in the first anti-symmetric or S' mode of oscillation.

Thus the signal output from the detection means 33 is sensitive only to the displacement of the ribbon due to the gravitational gradient acting on the ribbon.

This displacement signal is fed to output means 35 which is arranged to amplify and process the displacement signal to produce an output signal from the gradiometer which is a function of the gravitational gradient tensor which can be analysed to retrieve information, for example, on subsurface density anomalies.

The gravitational gradient tensor component detected by the gradiorneter device 1 depends on the orientation of deployment of the gradiometer. It is preferable that the gradiometer is deployed to detect the off-diagonal components of the tensor. However, the dynamic range of sensitivity provided by the sensing means 10 of the invention allows the operational orientation of the gradiometer device I to be easily adjusted.

Figure 2 shows a gradiometer device 40 according to a second embodiment of the invention. This gradiometer device 40 is similar to the gradiometer device 1 -3 -of the first embodiment shown in Figure 1, and is arranged to operate in the same way, except for the following additional features.

To prevent constructively interfered light from re-entering the coherent light source 11 and disrupting to the output coherent beam 13, filtering means 37 is provided, arranged in the beam path to prevent reflected beams from re-entering the coherent light source 11. Such a filtering means 37 is provided as an optical diode or an optical feedback isolator which includes a second polarising beam splitter, a polariser and a Faraday rotator to filter out any light incident on the filtering means 37 from the return path of the Michelson interferometer.

Modulating means 39 is provided in the form of an electro-optic modulator 41 which is driven with an input modulation voltage signal generated by a modulation signal generator 43. The modulation signal generator 43 outputs a sinusoidal voltage signal having a frequency of 2 MHz. The electro-optic modulator 41 modulates phase of the coherent light beam 13 with this 2 MHz sinusoidal signal.

The electro-optic modulator 41 generates small side-bands on either side of the frequency of the output coherent laser beam 13 that beat with the carrier frequency of the coherent laser beam 13. On their return paths, this difference or beating signal of each of the first and second sensing beams 19, 25 is encoded with information about the length of each arm of the interferometer and the optical path difference is recovered at the detection means 33 by optical heterodyne detection together with the modulation signal provided by the modulation signal generator 43.

The displacement signal, thus recovered, is then processed in the output means 35 to produce an output signal from the gradiometer device 40 which is a function of the -3 -tensor of the gravitational gradient T. All non-modulated noise sources are excluded from the recovered output signal and the signal-to-noise ratio is increased.

Stationary mirrors 45 are provided in the optical path of both the first and the second sensing beams 19, 25 to increase the magnitude of the change of the optical path difference between the two arms of the Michelson interferometer by causing multiple reflections of the first and the second sensing beams 19, 25 between the surface of the ribbon 3 and the mirrors 45. This increases the sensitivity of the sensing means 10, and thus the output of the gradiometer 1, to the displacement of the ribbon 3 due to gradient forces acting on the ribbon 3.

Movement preventing means 47 is provided as a knife-edge' device mounted at the mid-point M of the ribbon 3 to touch the ribbon 3 but not exert any force thereon. This movement preventing means 47 restricts any transverse movement of the ribbon 3 away from its rest position at the mid-point M and reduces the deformation of the ribbon 3 into symmetric modes of oscillation (however, a W-mode of oscillation remains, which is the linear sum of all remaining symmetrical mode displacements) while permitting the deformation of the ribbon 3 into all anti-symmetric modes. This improves further the sensitivity of the gradiometer device I to the detection of gravity and magnetic field gradients by excluding the symmetric modes of oscillation of the ribbon 3.

The position of the movement preventing means 47 can be adjusted automatically by the positioning means 49 provided to correct the position of the knife-edge to be at the target mid-point M location on the ribbon 3. Similarly positioning means 51 are provided to automatically adjust the position of the beam splitter cube 17 and the planar reflector 27 such that the beam directing means 15

--

directs the first and second sensing beams 19, 25 to be incident on the surface of the ribbon 3 at the first and second target locations, i.e. at L14 and 3L/4, respectively.

The positioning means 49, 5 1 is provided as a servo-controlled position detection and feedback adjustment mechanism to correct the position of the movement preventing means 47, the beam splitter cube 17 and the planar reflector 27 which cart be operated periodically, for example, on servicing the device, or in effectively real-time. These positioning mechanisms ensure that the two sides of the ribbon 3 are correctly mechanically balanced and that the sensitivity of the sensing means 10 is optimised.

Figure 3 shows a gradiometer device 101 according to a third'embodiment of the invention in which the sensing means 110 is provided with a number of individual identical sensing units I IOa, 1 lOb, ... 1 lOh arranged adjacent ribbon 103, each sensing unit llOa-1 lOh being connected to output means 135.

Figure 4 shows a detailed view of a single sensing unit llOi positioned adjacent a section of ribbon 103. Each sensing unit 1101 of sensing means 110 includes an arrangement of apparatus in the form of a Michelson interferometer but which differs from the interferometric arrangement of sensing means 10 of the first and second embodiments in that only one arm of the interferometer of each sensing unit llOi provides a sensing beam 119 reflected from the surface of the ribbon 103 from a sensing position 123i of that sensing unit 1101.

The sensing beam 119 is produced by a beam splitting means 117 of the beam directing means 115, which splits the coherent light beam 113, produced from the coherent light source ill, in two. The beam splitting means 117 is arranged -34 -such that the sensing beam 119 is incident on the ribbon surface at sensing position 123i.

In this embodiment, the other beam 121 produced by the beam splitting means 117 is reflected from the surface of a stationary planar reflector 127 arranged to direct the reflected beam 121 back to the beam splitting means 117 to provide as a standard reference arm of the interferometer a reflected static reference beam 121 having a constant optical path length. At the beam splitting means 117, the reflected sensing beam 119 is interferometrically combined with the reflected reference beam 121 to produce a combined beam 131. The interference pattern produced by the combined beam 13 1 on illuminating the detecting surface of the detecting means 133 varies only as the optical path length of the sensing beam 119 arm of the interferometer varies. This variation of the interference pattern, and thus the intensity detected by the detecting means 133 and the amplitude of the signal produced thereby, depends only on the position of the ribbon in its axis of displacement. Thus the signal produced by the detecting means 133 of each sensing unit 11 Oi is representative of the displacement of the ribbon away from its undisturbed rest' position. By monitoring the change in the displacement signal using the output means 135 and calibrating the sensing unit 1101 in an appropriate manner, the displacement of the ribbon 103 away from its undisturbed position at the sensing position 123i can be retrieved.

In each sensing unit 1101, each coherent light source 111 is provided by a laser diode and each detecting means 133 is provided by a photodiode. Also, the optics components 117, 127 are provided as compact optics components. These electro-optic and optics components are very small in size and are provided mounted

-

together on a silicon chip (not shown) which provides a single sensor unit 11 Oi as a miniature package.

In Figure 3 it can be seen that eight such chip packages are arranged adjacent the ribbon 103 to provide a sensing means 110 having eight sensing units llOa-llOb each providing to the output means 135 a displacement signal for the ribbon in eight sensing positions 123a-123h arranged in equally spaced locations along the ribbon's length. The output means processes each of these displacement signals to build up a picture of the ribbon's displacement and characterise its displacement profile up to the accuracy permitted by the spatial sampling rate of the ribbon 103 as governed by Nyquist-Shannon sampling theorem. From this characterisation, the output means calculates the amplitude of the ribbon's displacement in the Fourier modes of oscillation of the ribbon by performing a Fourier decomposition of the ribbon profile. The output means 135 then uses the calculated amplitude of the displacement in the S' mode to in turn calculate the gravitational gradient tensor component T, and the amplitude of the displacement in the C' mode to in turn calculate the gravitational acceleration component gx. In this arrangement with eight equally spaced sensing units 1 1 Oa-11 Oh and with the known positional boundary conditions for the endpoint of the ribbon, Nyquist sampling theory dictates that the amplitude of the displacement of the ribbon 103 can generally be accurately calculated up to the fourth (i.e. n = 4) fundamental mode of oscillation.

By miniaturising the sensing means components, more than two sensing units 1 lOi can be deployed along the length of the ribbon 103 to characterise the displacement profile of the ribbon 103. The greater the number of sensing units 11 Oi deployed to sample the displacement of the ribbon 103 at different locations -j -along its length, the greater the detail in which the ribbon's displacement profile can be characterised. That is, the amplitude of the ribbons oscillation in the different Fourier modes can be calculated up to the mode having half the spatial sampling frequency of the arrangement of sensing units 1101. The higher the sampling rate, the more accurately the amplitude of the ribbon's modes of oscillation can be calculated. By providing two sensing units 1101 positioned equally spaced along the length of the ribbon such that they are symmetrically positioned about the mid-point (similar to the arrangement described in the first and second embodiments), the amplitude of the ribbon's displacement in the S' mode can be calculated. However, by providing more than two sensing units 1101 positioned equally spaced along the length of the ribbon 103, the S' mode of oscillation of the ribbon 103 is over-sampled, and thus the amplitude of oscillation in the S' mode can be calculated more accurately, as well as higher modes of oscillation. The gradiometer having this over-sampled arrangement gives a more accurate measurement of the gravity gradient acting on the ribbon 103. Further, its full characterisation of the eigenmodes of the ribbon's displacement enables the gradiometer of this embodiment to also output a measurement of the components of the absolute acceleration due to gravity, gx,;,z(i.e. that which causes displacement in the symmetrical modes of oscillation), in addition to the off-diagonal components of the gravitational gradient tensor T. This makes the gradiometer more versatile. The miniature packages are cheap, to construct, relatively insensitive to environmental noise, and require only minimal power, making the gradiometer easy to deploy.

Alternatively, the coherent light for each sensing unit 11 Oa-II Oh could be provided by a single coherent light source. Also, all of the sensing units 1 lOa-l lOh -37-could be provided together on a single chip or could be provided mounted to any rigid surface located adjacent the ribbon 103.

it will be understood that the sensor units and sensing means of the third embodiment of the invention can be adapted to include the features described herein in relation to the second embodiment which are additional to those described in the first embodiment.

In the embodiments described herein the ribbon is a one-dimensional sensing element, having a width larger than its depth and a tape like form. Alternatively, the ribbon may have a width and a depth of similar dimensions such that the ribbon resembles a string having a circular or square cross-section and can be displaced in both directions orthogonal to its length such that the gradiometer has two axes of sensitivity which can be measured if two sensing means are orthogonally arranged.

In the embodiments described herein a laser diode or a diode-pumped Nd:YAO laser is provided as a coherent light source. Alternatively, other types of laser can be used such as other solid state, dye or gas lasers which produce a temporally coherent light beam. Deployment of the coherent light beam by optical fibre may alternatively be employed. Lasers operating in Continuous Wave mode are preferred for the gradiometer device, though pulsed laser operation may be -----possible.

In the embodiments described herein the gradiometer is arranged to detect gravitational gradients. In order to adapt the gradiometer to detect magnetic gradients the ribbon 3, 103 is connected as part of a current signal generating circuit (not shown) and an alternating current signal having a frequency within the mechanical resonance of the ribbon 3, 103 is passed down the ribbon 3, 103 such -38 -that the magnetic field forces cause the ribbon to resonate. The pumping current has a frequency of twice the natural (first order) resonant frequency of the ribbon 3, 103, corresponding to the frequency of the first anti-symmetric or S' mode. The contribution to the displacement amplitude of the ribbon 3, 103 in the S' mode due to gravitational gradient does not vary with time and can be separated out from the detected displacement signal, for example by a double lock-in detection arrangement.

Alternatively the apparatus of any of the embodiments described above can be adapted to act as an absolute gravimeter' and detect the local components of acceleration due to gravity. That is, the gravimeter' apparatus is arranged to detect the amplitude of the displacement of the ribbon in its symmetric modes of oscillation. If the ribbon is not constrained at its mid-point, it is then free to oscillate in any of its symmetric modes. However, for this gravimeter' operation, constraining the ribbon at its mid-point with a knife edge is preferred because, for a ribbon thus constrained, the gravimeter signal can be detected by sensing the displacement of the ribbon in its W' mode. The W' mode is the linear sum of all residual symmetric mode displacements of the constrained string, the amplitude of which is directly dependent on the force acting on the ribbon resulting from the acceleration due to gravity g and/or from the absolute magnetic field B (i.e. the non-gradiometric forces). The arrangements of the first and second embodiments described above can be adapted to be directly sensitive to the displacement of the ribbon in its symmetric modes and insensitive to the anti-symmetric modes by arranging the two arms of the interferometer such that the first and second sensing positions 23, 29 are on opposite surfaces of the ribbon. Thus the output means can -.3 -be adapted to provide an output signal which is a function of this force acting on the ribbon.

As mentioned above in relation to the third embodiment, where there are a number of sensing units 11 Oi provided along the length of the ribbon such that its displacement is oversampled', the amplitude of displacement for symmetric modes of oscillation of the ribbon can be detected and the gravimetric' force components can be retrieved.

Claims (16)

1. Claims: I. Apparatus for the measurement of quasi-static gravity gradients and/ormagnetic field gradients comprising:a flexible elongate ribbon held under tension at both ends; sensing means arranged to detect the transverse displacement of the ribbon from an undisturbed position due to the gravitational gradient or magnetic field gradient acting on said ribbon and to generate a signal representing the displacement; and output means coupled to said sensing means and responsive to said displacement signal to generate an output signal which is a function of the tensor of the gravitational gradient or magnetic field gradient; wherein the sensing means comprises: a coherent light source arranged to produce a coherent light beam; beam directing means arranged to produce from the coherent light beam a sensing beam and to direct the sensing beam onto the ribbon at a first sensing position from a transverse direction; and detecting means arranged to detect the interferometric superposition of the sensing beam reflected from the surface of the ribbon and another beam derived from the coherent light beam and to generate said displacement signal.
2. 2. Apparatus as claimed in claim 1, wherein the beam directing means comprises a beam splitter arranged to interferometrically combine the reflected sensing beam with said other beam for detection by the detecting means.

   -41 -
3. 3. Apparatus as claimed in claim 2, wherein the beam splitting means is arranged to produce said other beam from the coherent light beam, the beam directing means is arranged to direct said other beam onto the ribbon at a second sensing position from a transverse direction such that said other beam acts as a second sensing beam, wherein the first and second sensing positions of the sensing beams are located symmetrically on opposite sides of mid-point between the ends of the ribbon, and wherein the beam splitting means interferometrically recombines the two reflected sensing beams for detection by the detecting means.
4. 4. Apparatus as claimed in claim 3, wherein the first and second sensing positions of the sensing beams are both located at a distance of a quarter of the length of the ribbon from the mid-point of the ribbon.
5. 5. Apparatus as claimed in claim 3 or 4 further comprising reflective means arranged along the optical path of each sensing beam to reflect the optical path of each sensing beam back onto the surface of the ribbon and increase the optical path length of each sensing beam.
6. 6. Apparatus as claimed in any preceding claim further comprising sensing beam positioning means arranged to automatically adjust the axial location along the ribbon of the first and second sensing positions of the sensing beams to a target position for each sensing beam.

   -42 -
7. 7. Apparatus as claimed in any preceding claim further comprising movement preventing means arranged to prevent transverse movement of the ribbon away from its rest position at the mid-point between the ends of the ribbon.
8. 8. Apparatus as claimed in claim 7 further comprising means for positioning the movement preventing means arranged to automatically adjust the position of the movement preventing means to prevent transverse movement of the ribbon away from its rest position at the mid-point between the ends of the ribbon.
9. 9. Apparatus as claimed in claim 2, wherein the beam directing means further comprises a reference surface, and wherein said beam splitting means is arranged to produce said other beam from said coherent light beam, said reference surface being arranged to reflect said other beam to act as a reference beam, such that the reflected sensing beam is combined with said reference beam for detection by the detecting means.
10. 10. Apparatus as claimed in claim 9, wherein the sensing means comprises at least two independent sensing units each comprising a said coherent light source, a said beam directing means and a said detecting means, each said sensing unit being arranged to detect the displacement of the ribbon at a different sensing position along the length of the ribbon, said displacement signal of the sensing means being a combination of the detected displacements of each said sensing unit.

    -43 -
11. 11. Apparatus as claimed in claim 10, wherein the sensing means comprises more than two said sensing units such that the profile of the displacement of the ribbon in the S mode of oscillation is oversampled along its length.
12. 12. Apparatus as claimed in any preceding claim, wherein the output signal is used to determine at least one of the off-diagonal gravity gradient tensor components.
13. 13. Apparatus as claimed in any preceding claim, further comprising filtering means arranged to prevent the reflected sensing beam from re-entering the coherent light source.
14. 14. Apparatus as claimed in any preceding claim, further comprising phase modulation means arranged to modulate the phase of the coherent light beam and thus any beam derived therefrom by a modulation signal.
15. 15. Apparatus as claimed in claim 14, wherein the displacement signal is detected by synchronous detection with a lock-in amplifier with reference to the modulation signal.
16. 16. A method of measuring quasi-static gravity gradients aridlor magnetic field gradients comprising: holding a flexible elongate ribbon under tension at both ends; directing a sensing beam produced from a coherent light beam output from a coherent light source onto the ribbon from a transverse direction at a sensing position on the ribbon; detecting the interferometric superposition of the sensing beam reflected from the surface of the ribbon and another beam derived from the coherent light beam and generating from said detection a signal representing the transverse displacement of the ribbon from an undisturbed position due to the gravitational gradient or magnetic field gradient acting on said ribbon; and generating, responsive to said displacement signal, an output signal which is a function of the tensor of the gravitational gradient or magnetic field gradient.