During the summer of 1968 a gravity survey was conducted over the Fox* Glacier, Yukon Territory, ... more During the summer of 1968 a gravity survey was conducted over the Fox* Glacier, Yukon Territory, for the purpose of finding ice depths. Choice of the Fox Glacier was as a result of its predicted surge, and the survey was part of a long-term analysis of the physical condition of the glacier. Although seismic sounding was attempted, the thinness of the glacier prevented successful results. Analysis of the gravity measurements indicated 88m as the maximum depth; comparison with depths from three drilled holes showed that the gravity results were not seriously in error. A small near-surface temperature program was completed and the results identify the Fox as a sub-polar glacier. This is not an officially accepted name.
I review some features of the Global Geodynamics Project during its initial phase of operation 19... more I review some features of the Global Geodynamics Project during its initial phase of operation 1997-2003. These fall into three categories: (1) instrumental-the development of the superconducting gravimeters during this time; (2) organizational-how the various SG groups have come together to improve their installations and provide their data; and (3) scientific-what have been some of the notable observational achievements of the project. This overview is then followed by a brief description of some of the new tasks for GGP Phase 2 (2003)(2004)(2005)(2006)(2007).
Scaling arguments have been used to justify the subseismic approximation (SSA) for analysing long... more Scaling arguments have been used to justify the subseismic approximation (SSA) for analysing long-period oscillations of the Earth's liquid core. This approximation neglects the contribution of flow pressure to elastic compression relative to that of transport along the equilibrium pressure gradient. Here we present numerical tests of the SSA for a suite of 90 core undertones (gravity modes) in non-rotating Earth models with uniformly stable liquid cores. These tests confirm that the error incurred by invoking the SSA in the interior of the liquid core is at most 0(1 per cent), for an oscillation of-6 hr period, and decreases with increasing period. On the other hand, the SSA is grossly violated at the core boundaries, and its adoption at the boundaries is likely to lead to serious errors in computations of the surface gravity signal associated with the oscillations. This failure of the SSA also prevents the construction of a variational principle for the subseismic wave equation in a non-neutral core with elastic boundaries.
... 337 AM Forte and RL Woodward 11. ... He himself also looked forward to this stay in Paris wit... more ... 337 AM Forte and RL Woodward 11. ... He himself also looked forward to this stay in Paris with his wife Lanny, a French teacher. We are all gathered here in this beautiful place, in the name of SEDI, after our previous meetings in Mizusawa, Sante Fe and Blanes. ...
has devoted considerable space to point out that ' . . . the normal mode eigenspectrum of a rotat... more has devoted considerable space to point out that ' . . . the normal mode eigenspectrum of a rotating Earth is not controlled by a single coefficient in the equation of motion' and therefore ' . . . as a result, the numerical results of Crossley's calculation cannot be usefully interpreted in terms of the normal-mode eigenspectrum of the rotating Earth'. Yet he concludes by stating ' . . . these criticisms do not reflect upon the validity of the normal-mode eigensolutions presents'. Indeed one cannot disagree with Smith's discussion of the sign of transverse inertia as an insufficient criterion for diagnosing the existence of real eigenvalues of the equations of motion in a rotating fluid core. On the other hand nowhere does he prove that a positive value of the coefficient of inertia is not a necessary condition for the existence of such eigenvalues. To support the idea that transverse inertia plays a role in determining the eigenspectrum of the rotating Earth, I wish to emphasize two points already mentioned in ' Core Undertones with Rotation '.
There has been some recent controversy over the precise nature of the conditions to be imposed at... more There has been some recent controversy over the precise nature of the conditions to be imposed at the core-mantle boundary when the Earth suffers a static deformation. We here define static deformation by requiring the fluid core to be in hydrostatic equilibrium both before and after the deformation, and then show how to determine the fluid response in terms of the gravitational potential and normal stress, without reference to particle displacement. The core-mantle boundary is modelled by a thin transition layer between the solid and the fluid in which the rigidity drops to zero. A careful examination of the jump conditions across the transition layer leads to the conclusion that the variables Yl, Y2 and Y6 as defined in the solid are all discontinuous.
Until recently superconducting gravimeters (SGs) have been used principally in tidal studies (per... more Until recently superconducting gravimeters (SGs) have been used principally in tidal studies (periods 6^24 hr) due to their high sensitivity and low drift rates. This paper considers the performance of these instruments as long-period seismometers, particularly in the normal mode band (periods 1^54 min). To judge their suitability in providing useful information to seismology, it is important to determine their noise characteristics compared to other established instruments such as spring gravimeters. We compare several continuously recording instruments: the SGs in Esashi (Japan), Wuhan (China), Strasbourg (France) and Cantley (Canada) and the spring gravimeter ET-19 and seismometer STS-1 at the Black Forest Observatory (BFO, Germany). We also include non-permanent instruments, the SG102 at BFO as well as the ET-18 in MetsÌhovi (Finland). The ¢ve quietest days out of the available records are stacked to obtain the power spectral density of the noise in the frequency band 0.05^20 mHz (50 s to 6 hr). Our reference is the New Low Noise Model designed for seismometers. Only at the BFO site were there several instruments that could be compared; even so, in order to obtain the best individual data for each instrument the records selected were not simultaneous. The noise characteristics of the di¡erent instrument^site combinations are compared, leading to conclusions about site selection, instrument modi¢cations and the recent potential of SGs to contribute to seismic normal mode studies. We refer to our previous work on the seismic noise magnitude, a summary statistic derived from the power spectral density which has been used to rank the performance of instrument^site combinations.
The known surface of Mercury is unique among the photographed portions of the terrestrial planets... more The known surface of Mercury is unique among the photographed portions of the terrestrial planets in that there are no obvious tensional features, but instead some compressional wrinkling. If, as has been variously proposed, the Earth has undergone expansion due to a secular decrease in the gravitational constant G, then presumably so will all astronomical bodies. Using two alternative geophysical models for the interior of Mercury, the estimated expansion due to a decrease in G is probably in conflict with present observation. This constraint on the size of the change in G may be significant for planetary evolution.
We present an analysis of more than two years of data from the superconducting gravimeter CO24 at... more We present an analysis of more than two years of data from the superconducting gravimeter CO24 at the National Oceanic and Atmospheric Administration's Table Mountain Geodetic Observatory (TMGO) near Boulder, Colorado. The gravity data, sampled at intervals of 5 s, were cleaned for gaps, disturbances and o¡sets and then decimated to 1 hr, and an ETERNA analysis was done to determine the tidal gravimetric factors and phases, during which the atmospheric pressure loading and the period and damping of the free core nutation were obtained. We ¢nd T~418+14 days and 1152`Q`2848. A short-period analysis of the ¢ve quietest days in the seismic-mode band (200^600 s) shows the combined instrument/site noise to be one of the lowest of all the superconducting gravimeters analysed to date. For the long periods, a local tide, including various ocean loading models, is subtracted from the data and the residual gravity shows very good correlation with IERS polar motion. Instrument drift is well ¢tted by a positive exponential function with a value of about 5 ]gal yr {1 at the end of the record. Analysis of the pressure using a complex frequency-dependent admittance shows some improvement in noise over using a simple scalar admittance function. In the Slichter mode and core mode bands, there are no signi¢cant peaks to be noted; more de¢nitive evidence of signals from the Earth's core will require stacking using the Global Geodynamics Project network. TMGO is an extremely stable site with excellent noise characteristics.
Fox Gl acier", Yuko n T erri to ry, has a histo ry of surging a nd is a t present in a qui escent... more Fox Gl acier", Yuko n T erri to ry, has a histo ry of surging a nd is a t present in a qui escent period . In 1968 a gravity survey was carried out over th e glacier, in o rd er to fi nd ice depths. The result s indi cate the gl acier is thin with a m aximum d epth of 88 m. R EsuME. iVlesures gravimetriques sllr L e " Fox GL acier" , r ukoll T erritory, Ca nad a. Le " Fox Glacier", d ans le Yuko n T erritory, a subi d es crues d a ns le passe et est actue ll em ent d a ns une period e ca lme. En 1968 u ne prospect io n g ravime trique a e te m enee a bien sur le gl acier pour trouver la pro fond eur d e la glace. Les result al s indique nt que le gl a cier est min ce avec un e profo nd eur max imum d e 88 m . ZUSA MM EN FASSUNG . Schweremessllngen atU dem "Fox Glacier" , Yukon T erritory , K a nada . VOln "Fox G lacier",
The superconducting gravimeter (SG) uses magnetic levitation as a stable gravity spring and is th... more The superconducting gravimeter (SG) uses magnetic levitation as a stable gravity spring and is the default relative instrument for observatory gravity. SGs have high precision (~ 0.01 μGal), exceptional calibration stability (~ 0.01%), low drift (few μGal per year), and record at periods from 1 s to years. The newest iGrav SG is transportable in a small SUV, requires no liquid helium, has integrated electronics, and is easy to set up. We review instrument design, reduction and data processing, and many applications: seismic modes; tides and nutations; large- and small-scale atmospheric, oceanic, and hydrologic loading; volcanology; coseismic signals; and time-variable gravity exploration.
During the summer of 1968 a gravity survey was conducted over the Fox* Glacier, Yukon Territory, ... more During the summer of 1968 a gravity survey was conducted over the Fox* Glacier, Yukon Territory, for the purpose of finding ice depths. Choice of the Fox Glacier was as a result of its predicted surge, and the survey was part of a long-term analysis of the physical condition of the glacier. Although seismic sounding was attempted, the thinness of the glacier prevented successful results. Analysis of the gravity measurements indicated 88m as the maximum depth; comparison with depths from three drilled holes showed that the gravity results were not seriously in error. A small near-surface temperature program was completed and the results identify the Fox as a sub-polar glacier. This is not an officially accepted name.
I review some features of the Global Geodynamics Project during its initial phase of operation 19... more I review some features of the Global Geodynamics Project during its initial phase of operation 1997-2003. These fall into three categories: (1) instrumental-the development of the superconducting gravimeters during this time; (2) organizational-how the various SG groups have come together to improve their installations and provide their data; and (3) scientific-what have been some of the notable observational achievements of the project. This overview is then followed by a brief description of some of the new tasks for GGP Phase 2 (2003)(2004)(2005)(2006)(2007).
Scaling arguments have been used to justify the subseismic approximation (SSA) for analysing long... more Scaling arguments have been used to justify the subseismic approximation (SSA) for analysing long-period oscillations of the Earth's liquid core. This approximation neglects the contribution of flow pressure to elastic compression relative to that of transport along the equilibrium pressure gradient. Here we present numerical tests of the SSA for a suite of 90 core undertones (gravity modes) in non-rotating Earth models with uniformly stable liquid cores. These tests confirm that the error incurred by invoking the SSA in the interior of the liquid core is at most 0(1 per cent), for an oscillation of-6 hr period, and decreases with increasing period. On the other hand, the SSA is grossly violated at the core boundaries, and its adoption at the boundaries is likely to lead to serious errors in computations of the surface gravity signal associated with the oscillations. This failure of the SSA also prevents the construction of a variational principle for the subseismic wave equation in a non-neutral core with elastic boundaries.
... 337 AM Forte and RL Woodward 11. ... He himself also looked forward to this stay in Paris wit... more ... 337 AM Forte and RL Woodward 11. ... He himself also looked forward to this stay in Paris with his wife Lanny, a French teacher. We are all gathered here in this beautiful place, in the name of SEDI, after our previous meetings in Mizusawa, Sante Fe and Blanes. ...
has devoted considerable space to point out that ' . . . the normal mode eigenspectrum of a rotat... more has devoted considerable space to point out that ' . . . the normal mode eigenspectrum of a rotating Earth is not controlled by a single coefficient in the equation of motion' and therefore ' . . . as a result, the numerical results of Crossley's calculation cannot be usefully interpreted in terms of the normal-mode eigenspectrum of the rotating Earth'. Yet he concludes by stating ' . . . these criticisms do not reflect upon the validity of the normal-mode eigensolutions presents'. Indeed one cannot disagree with Smith's discussion of the sign of transverse inertia as an insufficient criterion for diagnosing the existence of real eigenvalues of the equations of motion in a rotating fluid core. On the other hand nowhere does he prove that a positive value of the coefficient of inertia is not a necessary condition for the existence of such eigenvalues. To support the idea that transverse inertia plays a role in determining the eigenspectrum of the rotating Earth, I wish to emphasize two points already mentioned in ' Core Undertones with Rotation '.
There has been some recent controversy over the precise nature of the conditions to be imposed at... more There has been some recent controversy over the precise nature of the conditions to be imposed at the core-mantle boundary when the Earth suffers a static deformation. We here define static deformation by requiring the fluid core to be in hydrostatic equilibrium both before and after the deformation, and then show how to determine the fluid response in terms of the gravitational potential and normal stress, without reference to particle displacement. The core-mantle boundary is modelled by a thin transition layer between the solid and the fluid in which the rigidity drops to zero. A careful examination of the jump conditions across the transition layer leads to the conclusion that the variables Yl, Y2 and Y6 as defined in the solid are all discontinuous.
Until recently superconducting gravimeters (SGs) have been used principally in tidal studies (per... more Until recently superconducting gravimeters (SGs) have been used principally in tidal studies (periods 6^24 hr) due to their high sensitivity and low drift rates. This paper considers the performance of these instruments as long-period seismometers, particularly in the normal mode band (periods 1^54 min). To judge their suitability in providing useful information to seismology, it is important to determine their noise characteristics compared to other established instruments such as spring gravimeters. We compare several continuously recording instruments: the SGs in Esashi (Japan), Wuhan (China), Strasbourg (France) and Cantley (Canada) and the spring gravimeter ET-19 and seismometer STS-1 at the Black Forest Observatory (BFO, Germany). We also include non-permanent instruments, the SG102 at BFO as well as the ET-18 in MetsÌhovi (Finland). The ¢ve quietest days out of the available records are stacked to obtain the power spectral density of the noise in the frequency band 0.05^20 mHz (50 s to 6 hr). Our reference is the New Low Noise Model designed for seismometers. Only at the BFO site were there several instruments that could be compared; even so, in order to obtain the best individual data for each instrument the records selected were not simultaneous. The noise characteristics of the di¡erent instrument^site combinations are compared, leading to conclusions about site selection, instrument modi¢cations and the recent potential of SGs to contribute to seismic normal mode studies. We refer to our previous work on the seismic noise magnitude, a summary statistic derived from the power spectral density which has been used to rank the performance of instrument^site combinations.
The known surface of Mercury is unique among the photographed portions of the terrestrial planets... more The known surface of Mercury is unique among the photographed portions of the terrestrial planets in that there are no obvious tensional features, but instead some compressional wrinkling. If, as has been variously proposed, the Earth has undergone expansion due to a secular decrease in the gravitational constant G, then presumably so will all astronomical bodies. Using two alternative geophysical models for the interior of Mercury, the estimated expansion due to a decrease in G is probably in conflict with present observation. This constraint on the size of the change in G may be significant for planetary evolution.
We present an analysis of more than two years of data from the superconducting gravimeter CO24 at... more We present an analysis of more than two years of data from the superconducting gravimeter CO24 at the National Oceanic and Atmospheric Administration's Table Mountain Geodetic Observatory (TMGO) near Boulder, Colorado. The gravity data, sampled at intervals of 5 s, were cleaned for gaps, disturbances and o¡sets and then decimated to 1 hr, and an ETERNA analysis was done to determine the tidal gravimetric factors and phases, during which the atmospheric pressure loading and the period and damping of the free core nutation were obtained. We ¢nd T~418+14 days and 1152`Q`2848. A short-period analysis of the ¢ve quietest days in the seismic-mode band (200^600 s) shows the combined instrument/site noise to be one of the lowest of all the superconducting gravimeters analysed to date. For the long periods, a local tide, including various ocean loading models, is subtracted from the data and the residual gravity shows very good correlation with IERS polar motion. Instrument drift is well ¢tted by a positive exponential function with a value of about 5 ]gal yr {1 at the end of the record. Analysis of the pressure using a complex frequency-dependent admittance shows some improvement in noise over using a simple scalar admittance function. In the Slichter mode and core mode bands, there are no signi¢cant peaks to be noted; more de¢nitive evidence of signals from the Earth's core will require stacking using the Global Geodynamics Project network. TMGO is an extremely stable site with excellent noise characteristics.
Fox Gl acier", Yuko n T erri to ry, has a histo ry of surging a nd is a t present in a qui escent... more Fox Gl acier", Yuko n T erri to ry, has a histo ry of surging a nd is a t present in a qui escent period . In 1968 a gravity survey was carried out over th e glacier, in o rd er to fi nd ice depths. The result s indi cate the gl acier is thin with a m aximum d epth of 88 m. R EsuME. iVlesures gravimetriques sllr L e " Fox GL acier" , r ukoll T erritory, Ca nad a. Le " Fox Glacier", d ans le Yuko n T erritory, a subi d es crues d a ns le passe et est actue ll em ent d a ns une period e ca lme. En 1968 u ne prospect io n g ravime trique a e te m enee a bien sur le gl acier pour trouver la pro fond eur d e la glace. Les result al s indique nt que le gl a cier est min ce avec un e profo nd eur max imum d e 88 m . ZUSA MM EN FASSUNG . Schweremessllngen atU dem "Fox Glacier" , Yukon T erritory , K a nada . VOln "Fox G lacier",
The superconducting gravimeter (SG) uses magnetic levitation as a stable gravity spring and is th... more The superconducting gravimeter (SG) uses magnetic levitation as a stable gravity spring and is the default relative instrument for observatory gravity. SGs have high precision (~ 0.01 μGal), exceptional calibration stability (~ 0.01%), low drift (few μGal per year), and record at periods from 1 s to years. The newest iGrav SG is transportable in a small SUV, requires no liquid helium, has integrated electronics, and is easy to set up. We review instrument design, reduction and data processing, and many applications: seismic modes; tides and nutations; large- and small-scale atmospheric, oceanic, and hydrologic loading; volcanology; coseismic signals; and time-variable gravity exploration.
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Papers by David Crossley