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843:
1746:. The gravity gradient (components of the gravity field) is measured using a spinning wheel with accelerometers also called as the gravity gradiometer. The instrument is positioned in different orientations to measure the respective component of the gravitational field. The values of gravitational gradient tensors are calculated and analyzed. The analysis includes observing the contribution of each object under consideration. A maximum likelihood procedure is followed and
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808:, we can determine the frequencies and the time associated with that signal. By representing any signal as the linear combination of the wavelet functions, we can localize the signals in both time and frequency domain. Hence wavelet transforms are important in geophysical applications where spatial and temporal frequency localisation is important.
34:
and analysis of the electric and
Magnetic fields is very crucial. As the Electromagnetic and gravitational waves are multi-dimensional signals, all the 1-D transformation techniques can be extended for the analysis of these signals as well. Hence this article also discusses multi-dimensional signal processing techniques.
1038:
825:
Simply put, space-time signal filtering problem can be thought as localizing the speed and direction of a particular signal. The design of filters for space-time signals follows a similar approach as that of 1D signals. The filters for 1-D signals are designed in such a way that if the requirement of
235:
Jim
Zimmerman co-developed the rf superconducting quantum interference device (SQUID) during his tenure at Ford research lab. However, events leading to the invention of the SQUID were in fact, serendipitous. John Lambe, during his experiments on nuclear magnetic resonance noticed that the electrical
218:
With the help of these meters, either the gravity values at different locations are measured or the values of Earth's magnetic field are measured. Then these measured values are corrected for various corrections and an anomaly map is prepared. By analyzing these anomaly maps one can get an idea about
273:
The motion of any mass is affected by the gravitational field. The motion of planets is affected by the Sun's enormous gravitational field. Likewise, a heavier object will influence the motion of other objects of smaller mass in its vicinity. However, this change in the motion is very small compared
33:
data for spatial studies. Detection and analysis of the geophysical signals forms the core of
Geophysical signal processing. The magnetic and gravitational fields emanating from the Earth's interior hold essential information concerning seismic activities and the internal structure. Hence, detection
1758:
Various sensors located on the surface of Earth spaced equidistantly receive the seismic waves. The seismic waves travel through the various layers of earth and undergo changes in their properties - amplitude change, time of arrival, phase shift. By analyzing these properties of the signals, we can
850:
This approach is applied for filtering space-time signals. It is designed to isolate signals travelling in a particular direction. One of the simplest filters is weighted delay and sum beamformer. The output is the average of the linear combination of delayed signals. In other words, the beamformer
791:
A variety of window functions can be used for analysis. Wavelet functions are used for both time and frequency localisation. For example, one of the windows used in calculating the
Fourier coefficients is the Gaussian window which is optimally concentrated in time and frequency. This optimal nature
332:
Traditional sampling of 1D time varying signals is performed by measuring the amplitude of the signal under consideration in discrete intervals of time. Similarly sampling of space-time signals (signals which are functions of 4 variables – 3D space and time), is performed by measuring the amplitude
328:
As the name suggests, the gravitational and electromagnetic waves in the analog domain are detected, sampled and stored for further analysis. The signals can be sampled in both time and frequency domains. The signal component is measured at both intervals of time and space. Ex, time-domain sampling
296:
are nano fabricated materials with a separation of a quarter wavelength of light. When a beam of atoms pass through a diffraction grating, due to the inherent wave nature of atoms, they split and form interference fringes on the screen. An atom interferometer is very sensitive to the changes in the
264:
Gravitational wave sensors can detect even a minute change in the gravitational fields due to the influence of heavier bodies. Large seismic waves can interfere with the gravitational waves and may cause shifts in the atoms. Hence, the magnitude of seismic waves can be detected by a relative shift
73:
detect fluctuations in the gravitational and magnetic field. The data collected from a geophysical survey is analysed to draw meaningful conclusions out of that. Analysing the spectral density and the time-frequency localisation of any signal is important in applications such as oil exploration and
1531:
816:
Geophysical signals are continuously varying functions of space and time. The wavelet transform techniques offer a way to decompose the signals as a linear combination of shifted and scaled version of basis functions. The amount of "shift" and "scale" can be modified to localize the signal in time
255:
wires and niobium ribbons to form two
Josephson junctions connected in parallel. The ribbons act as the interruptions to the superconducting current flowing through the wires. The junctions are very sensitive to the magnetic fields and hence are very useful in measuring fields of the order of 10T.
1167:
The spectral estimates can be obtained by finding the square of the magnitude of the
Fourier transform also called as Periodogram. The spectral estimates obtained from the periodogram have a large variance in amplitude for consecutive periodogram samples or in wavenumber. This problem is resolved
227:
Magnetometers are used to measure the magnetic fields, magnetic anomalies in the earth. The sensitivity of magnetometers depends upon the requirement. For example, the variations in the geomagnetic fields can be to the order of several aT where 1aT = 10T . In such cases, specialized magnetometers
305:
This section addresses the methods and mathematical techniques behind signal recognition and signal analysis. It considers the time domain and frequency domain analysis of signals. This section also discusses various transforms and their usefulness in the analysis of multi-dimensional waves.
1339:
1699:
675:
1721:
The method being discussed here assumes that the mass distribution of the underground objects of interest is already known and hence the problem of estimating their location boils down to parametric localisation. Say underground objects with center of masses
1537:
4. The periodogram under consideration can be modified by multiplying it with a window function. Smoothing window will help us smoothen the estimate. Wider the main lobe of the smoothing spectrum, smoother it becomes at the cost of frequency resolution.
1345:
2.Welch's method suggested to divide the measurements using data window functions, calculate a periodogram, average them to get a spectral estimate and calculate the power spectrum using Fast
Fourier Transform. This increased the computational speed.
319:
The first step in any signal processing approach is analog to digital conversion. The geophysical signals in the analog domain has to be converted to digital domain for further processing. Most of the filters are available in 1D as well as 2D.
859:
This section deals with the estimation of the power spectral density of the multi-dimensional signals. The spectral density function can be defined as a multidimensional
Fourier transform of the autocorrelation function of the random signal.
786:
830:
with appropriate passband and stop band frequencies in determined. Similarly, in the case of multi-dimensional systems, the wavenumber-frequency response of filters is designed in such a way that it is unity in the designed region of
37:
Geophysical surveys may use a great variety of sensing instruments, and data may be collected from above or below the Earth's surface or from aerial, orbital, or marine platforms. Geophysical surveys have many applications in
866:
1352:
471:
354:
came up with the
Fourier representation to estimate the heat distribution of a body. The same approach can be followed to analyse the multi-dimensional signals such as gravitational waves and electromagnetic waves.
498:) is a 4-dimensional space-time signal which can be imagined as travelling plane waves. For such plane waves, the plane of propagation is perpendicular to the direction of propagation of the considered wave.
1177:
1775:. Data inside the 3-d dataset is projected to the 2-d space (display screen) using various techniques. Different data encoding schemes exist for various applications such as MRI, Seismic applications.
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1162:
532:
851:
output is formed by averaging weighted and delayed versions of receiver signals. The delay is chosen such that the passband of beamformer is directed to a specific direction in the space.
523:) at a particular time instant. Analysing the Fourier coefficients of this signal gives us information about the frequency components of the signal at a particular time instant.
1171:
1.Bartlett suggested a method that averages the spectral estimates to calculate the power spectrum. Average of spectral estimates over a time interval gives a better estimate.
297:
positions of atoms. As heavier objects shifts the position of the atoms nearby, displacement of the atoms can be measured by detecting a shift in the interference fringes.
66:
204:
This section deals with the principles behind measurement of geophysical waves. The magnetic and gravitational fields are important components of geophysical signals.
686:
329:
refers to measuring a signal component at several instances of time. Similarly, spatial-sampling refers to measuring the signal at different locations in space.
2200:
J.D. Welch (1967). "The use of fast
Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms".
350:
The Fourier expansion of a time domain signal is the representation of the signal as a sum of its frequency components, specifically sum of sines and cosines.
215:
is used. There are two types of magnetometers, one that measures only vertical component of the magnetic field and the other measures total magnetic field.
1033:{\displaystyle P\left(K_{x},w\right)=\int _{-\infty }^{\infty }\int _{-\infty }^{\infty }\varphi _{ss}\left(x,t\right)\ e^{-j\left(wt-k'x\right)}\,dx\,dt}
333:
of the signals at different time instances and different locations in the space. For example, the Earth's gravitational data is measured with the help of
156:
and marine control source electromagnetic (mCSEM) or EM seabed logging. This type of survey is carried out mainly to study the existence of groundwater.
1526:{\displaystyle P_{W}\left(w\right)={\frac {1}{\mathrm {det} \,N}}\sum _{l}|\sum _{n}\ g\left(n\right)\ x\left(n+MI\right)\ e^{-j\left(w'n\right)}|^{2}}
1771:
is an important tool to analyse the scalar fields. Volume rendering simplifies representation of 3D space. Every point in a 3D space is called a
1706:
211:. This meter measures the variation in the gravity due to the subsurface formations and deposits. To measure the changes in magnetic field the
2091:
Halpeny, O. S.; Childers, Donald G. (1975-06-01). "Composite wavefront decomposition via multidimensional digital filtering of array data".
364:
2261:
229:
1334:{\displaystyle P_{B}\left(w\right)={\frac {1}{\mathrm {det} \,N}}\sum _{l}|\sum _{n}\ x\left(n+MI\right)\ e^{-j\left(w'n\right)}|^{2}}
2175:
Bartlett, M. S.,"An introduction to stochastic processes, with special reference to methods and applications, CUP Archive, 1978,
251:. Jim Zimmerman pioneered the development of SQUID by proposing a new approach to making the Josephson junctions. He made use of
1989:
101:. This type of survey is carried out to discover the detailed structure of the rock formations beneath the surface of the Earth.
82:
There are many methods and types of instruments used in geophysical surveys. Technologies used for geophysical surveys include:
1694:{\displaystyle P_{M}\left(w\right)={\frac {1}{detN}}|\sum _{n}\ g\left(n\right)\ x\left(n\right)\ e^{-j\left(w'n\right)}|^{2}}
1925:
507:
The motivation for development of the Wavelet transform was the Short-time Fourier transform. The signal to be analysed, say
2806:
2158:
Dan E. Dudgeon, Russell M. Mersereau, “Multidimensional Digital Signal Processing”, Prentice-Hall Signal Processing Series,
2132:
Dan E. Dudgeon, Russell M. Mersereau, “Multidimensional Digital Signal Processing”, Prentice-Hall Signal Processing Series,
1046:
670:{\displaystyle \{x(t)\}(\tau ,\omega )\equiv X(\tau ,\omega )=\int _{-\infty }^{\infty }x(t)w(t-\tau )e^{-j\omega t}\,dt}
175:
2513:
1801:
145:
219:
the structure of rock formations in that area. For this purpose one need to use various analog or digital filters.
124:. This type of survey is carried out to discover the structure of rock formations beneath the surface of the Earth.
20:
247:
SQUIDs have the capability to detect magnetic fields of extremely low magnitude. This is due to the virtue of the
2254:
2180:
2163:
2137:
334:
1908:
Chiba, J.; Obata, Tsunehiro (1992-10-01). "Gravitational field sensor for prediction of big seismic waves".
274:
to the motion of heavenly bodies. Hence, special instruments are required to measure such a minute change.
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2479:
2768:
2325:
2247:
2021:
Daubechies, I. (1990-09-01). "The wavelet transform, time-frequency localization and signal analysis".
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167:
2335:
104:
1910:
Proceedings 1992 International Carnahan Conference on Security Technology: Crime Countermeasures
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826:
the filter is to extract frequency components in a particular non-zero range of frequencies, a
47:
1978:
E.H. Metzger, "Development Experience of Gravity Gradiometer System", IEEE Plans Meeting, 1982
2847:
2506:
2289:
2284:
153:
90:
781:{\displaystyle X(a,b)={\frac {1}{\sqrt {a}}}\int \limits _{\ }\Psi ({\frac {t-b}{a}})x(t)dt}
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using techniques that constitute the classical estimation theory. They are as follows:
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1996:
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or gradiometer by placing it in different locations at different instances of time.
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1951:"Gravity Detector Applies Outside-the-Box Thinking to Show What's Inside the Box"
113:
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2725:
2605:
2373:
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2064:
Daubechies, I (1996). "Where do wavelets come from? A personal point of view".
241:
188:
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can be explained by considering the time scaling and time shifting parameters
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58:. Geophysical surveys are used in industry as well as for academic research.
1950:
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1995:(Report). Defense Technical Information Center. AD0433611. Archived from
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The instrument used to measure the change in gravitational field is the
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2811:
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1830:
244:. However, Lambe was not able to fully recognize the utility of SQUID.
208:
117:
86:
62:
30:
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1885:
1794:
Looking into the earth : an introduction to geological geophysics
2903:
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2077:
2042:
466:{\displaystyle S(K,\omega )=\iint s(x,t)e^{-j(\omega t-k'x)}\,dx\,dt}
277:
127:
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846:
Spatial distribution of phased arrays to filter geophysical signals
1990:
The representation of seismic waves in frequency-wave number space
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2735:
2522:
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252:
240:
varied due to a change in the magnetic field of the order of few
39:
237:
1750:(CRB) is computed to assess the quality of location estimate.
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2239:
1772:
16:
Systematic collection of geophysical data for spatial studies
1818:
Electromagnetic seabed logging, A new tool for geoscientists
2418:
358:
The 4D Fourier representation of such signals is given by
171:
2491:
1705:
For further details on spectral estimation, please refer
222:
260:
Seismic wave measurement using gravitational wave sensor
345:
269:
Measurement of seismic waves using atom interferometer
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869:
689:
535:
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301:
Existing approaches in geophysical signal recognition
1835:
USGS Groundwater Information: Hydrogeophysics Branch
1157:{\displaystyle \varphi _{ss}\left(x,t\right)=s\left}
839:) a.k.a. wavenumber – frequency and zero elsewhere.
800:
respectively. By choosing the appropriate values of
1734:) are located under the surface and at positions p
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1525:
1333:
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1032:
780:
669:
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2202:IEEE Transactions on Audio and Electroacoustics
2090:
1754:Array processing for seismographic applications
323:
199:
1865:IEEE Transactions on Applied Superconductivity
1707:Spectral Analysis of Multi-dimensional signals
854:
77:
2507:
2255:
1974:
1972:
551:
536:
178:(also known as magnetic resonance sounding).
1791:
1762:
1717:Estimating positions of underground objects
281:Describes the atom interferometer principle
230:superconducting quantum interference device
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2500:
2262:
2248:
2199:
2154:
2152:
2150:
2148:
2146:
2063:
2020:
1907:
812:Time frequency localisation using wavelets
2093:IEEE Transactions on Circuits and Systems
1987:
1969:
1884:
1796:. Cambridge: Cambridge University Press.
1397:
1222:
1023:
1016:
660:
456:
449:
19:For its archaeological applications, see
1957:. Lawrence Livermore National Laboratory
841:
276:
2143:
2023:IEEE Transactions on Information Theory
1792:Mussett, A. E.; Khan, M. Aftab (2000).
1759:model the activities inside the Earth.
526:The STFT is mathematically written as:
515:) is multiplied with a window function
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2128:
2126:
2124:
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2084:
223:Measurement of Earth's magnetic fields
172:transient/time-domain electromagnetics
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1858:
1854:
1852:
680:The Wavelet transform is defined as
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502:
340:
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2119:
1831:"Magnetic Resonance Sounding (MRS)"
346:Multi-dimensional Fourier transform
13:
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480:represents temporal frequency and
176:surface nuclear magnetic resonance
14:
2992:
1988:Kelly Jr., E. J. (6 March 1964).
1837:. United States Geological Survey
181:Borehole geophysics, also called
146:electrical resistivity tomography
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2941:
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2560:
2473:
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2449:
61:The sensing instruments such as
29:is the systematic collection of
21:Geophysical survey (archaeology)
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2169:
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1955:Science & Technology Review
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2014:
1981:
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48:mineral and energy exploration
1:
1861:"Jim Zimmerman and the SQUID"
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484:represents spatial frequency.
324:Analog to digital conversion
265:in the gravitational waves.
200:Geophysical signal detection
7:
2585:Geological history of Earth
2521:
2409:Precession of the equinoxes
855:Classical estimation theory
314:
78:Types of geophysical survey
10:
2997:
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2326:Geophysical fluid dynamics
1859:Kautz, R.L. (2001-03-01).
18:
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2599:Composition and structure
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2570:
2552:Index of geology articles
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2443:
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335:gravitational wave sensor
288:work on the principle of
189:Remote sensing techniques
67:gravitational wave sensor
2222:10.1109/TAU.1967.1161901
2189:10.1109/ATC.2010.5672752
2113:10.1109/TCS.1975.1084081
1918:10.1109/CCST.1992.253730
1763:Visualization of 3D data
168:ground penetrating radar
2336:Near-surface geophysics
2066:Proceedings of the IEEE
160:Electromagnetic methods
105:Seismoelectrical method
2384:Earth's magnetic field
1695:
1527:
1335:
1158:
1034:
847:
782:
671:
467:
282:
2848:Environmental geology
2456:Geophysics portal
2379:Earth's energy budget
1701:Modified periodogram
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1528:
1336:
1159:
1035:
845:
783:
672:
468:
280:
154:spontaneous potential
142:Electrical techniques
91:reflection seismology
2807:Planetary geophysics
2002:on November 17, 2015
1912:. pp. 218–224.
1820:. Ed. Springer, 2017
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1353:
1178:
1047:
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687:
533:
365:
294:diffraction gratings
286:Atom interferometers
150:induced polarization
132:aeromagnetic surveys
2909:Petroleum geologist
2873:Forensic geophysics
2843:Engineering geology
2590:Timeline of geology
2542:Glossary of geology
2428:Related disciplines
2394:Geothermal gradient
2214:1967ITAE...15...70W
2140:,pp. 291-294, 1983.
2105:1975ITCS...22..552H
2035:1990ITIT...36..961D
1877:2001ITAS...11.1026K
937:
919:
610:
128:Magnetic techniques
122:gravity gradiometry
2981:Geophysical survey
2935:Geology portal
2863:Geologic modelling
2802:Geophysical survey
2754:Geodetic astronomy
2680:Structural geology
2641:Historical geology
2572:History of geology
2547:History of geology
2537:Outline of geology
2311:Geophysical survey
2166:,pp. 315-338, 1983
1816:Stéphane Sainson,
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249:Josephson junction
232:(SQUID) are used.
114:gravity techniques
99:seismic tomography
95:seismic refraction
27:Geophysical survey
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2853:Planetary geology
2769:Planetary geodesy
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2404:Mantle convection
1927:978-0-7803-0568-7
1886:10.1109/77.919524
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503:Wavelet transform
341:Spectrum analysis
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2838:Economic geology
2764:Gravity of Earth
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740:
731:
728:
722:
716:
712:
676:
674:
673:
668:
659:
658:
609:
604:
472:
470:
469:
464:
448:
447:
440:
164:magnetotellurics
2996:
2995:
2991:
2990:
2989:
2987:
2986:
2985:
2971:
2970:
2969:
2964:
2927:
2918:
2892:
2888:Mineral physics
2821:
2783:
2730:
2704:
2690:Plate tectonics
2668:
2664:Palaeogeography
2635:
2611:Crystallography
2594:
2566:
2565:
2556:
2525:
2520:
2490:
2485:
2448:
2439:
2423:
2374:Coriolis effect
2369:Chandler wobble
2361:
2355:
2331:Mineral physics
2294:
2273:
2268:
2238:
2237:
2198:
2194:
2174:
2170:
2157:
2144:
2131:
2120:
2089:
2085:
2062:
2058:
2029:(5): 961–1005.
2019:
2015:
2005:
2003:
1999:
1992:
1986:
1982:
1977:
1970:
1960:
1958:
1947:
1943:
1928:
1906:
1902:
1857:
1850:
1840:
1838:
1829:
1828:
1824:
1815:
1811:
1804:
1790:
1786:
1781:
1765:
1756:
1745:
1741:
1737:
1733:
1729:
1725:
1719:
1714:
1685:
1680:
1679:
1661:
1660:
1656:
1649:
1645:
1631:
1614:
1602:
1593:
1577:
1572:
1558:
1552:
1548:
1546:
1543:
1542:
1517:
1512:
1511:
1493:
1492:
1488:
1481:
1477:
1456:
1452:
1435:
1423:
1414:
1408:
1386:
1385:
1380:
1366:
1360:
1356:
1354:
1351:
1350:
1325:
1320:
1319:
1301:
1300:
1296:
1289:
1285:
1264:
1260:
1248:
1239:
1233:
1211:
1210:
1205:
1191:
1185:
1181:
1179:
1176:
1175:
1122:
1118:
1097:
1093:
1092:
1088:
1067:
1063:
1054:
1050:
1048:
1045:
1044:
998:
988:
984:
977:
973:
955:
951:
942:
938:
932:
924:
914:
906:
882:
878:
877:
873:
868:
865:
864:
857:
828:bandpass filter
823:
817:and frequency.
741:
739:
727:
711:
688:
685:
684:
645:
641:
605:
597:
534:
531:
530:
505:
433:
414:
410:
366:
363:
362:
348:
343:
326:
317:
312:
303:
271:
262:
225:
202:
87:Seismic methods
80:
24:
17:
12:
11:
5:
2994:
2984:
2983:
2966:
2965:
2963:
2962:
2950:
2938:
2923:
2920:
2919:
2917:
2916:
2911:
2906:
2900:
2898:
2894:
2893:
2891:
2890:
2885:
2883:Mining geology
2880:
2875:
2870:
2865:
2860:
2855:
2850:
2845:
2840:
2835:
2829:
2827:
2823:
2822:
2820:
2819:
2817:Tectonophysics
2814:
2809:
2804:
2799:
2793:
2791:
2785:
2784:
2782:
2781:
2779:Geopositioning
2776:
2774:Remote sensing
2771:
2766:
2761:
2756:
2751:
2746:
2740:
2738:
2732:
2731:
2729:
2728:
2726:Marine geology
2723:
2718:
2712:
2710:
2706:
2705:
2703:
2702:
2697:
2692:
2687:
2682:
2676:
2674:
2670:
2669:
2667:
2666:
2661:
2656:
2651:
2645:
2643:
2637:
2636:
2634:
2633:
2628:
2623:
2618:
2613:
2608:
2606:Cosmochemistry
2602:
2600:
2596:
2595:
2593:
2592:
2587:
2582:
2576:
2574:
2568:
2567:
2559:
2557:
2555:
2554:
2549:
2544:
2539:
2533:
2531:
2527:
2526:
2519:
2518:
2511:
2504:
2496:
2487:
2486:
2484:
2483:
2471:
2459:
2444:
2441:
2440:
2438:
2437:
2431:
2429:
2425:
2424:
2422:
2421:
2416:
2411:
2406:
2401:
2396:
2391:
2386:
2381:
2376:
2371:
2365:
2363:
2357:
2356:
2354:
2353:
2351:Tectonophysics
2348:
2343:
2341:Paleomagnetism
2338:
2333:
2328:
2323:
2321:Geomathematics
2318:
2313:
2308:
2302:
2300:
2296:
2295:
2293:
2292:
2287:
2281:
2279:
2275:
2274:
2267:
2266:
2259:
2252:
2244:
2236:
2235:
2192:
2168:
2142:
2118:
2099:(6): 552–563.
2083:
2072:(4): 510–513.
2056:
2013:
1980:
1968:
1941:
1926:
1900:
1848:
1822:
1809:
1802:
1783:
1782:
1780:
1777:
1767:The method of
1764:
1761:
1755:
1752:
1743:
1739:
1735:
1731:
1727:
1723:
1718:
1715:
1713:
1710:
1703:
1702:
1688:
1683:
1675:
1671:
1667:
1664:
1659:
1655:
1652:
1648:
1640:
1637:
1634:
1630:
1623:
1620:
1617:
1613:
1605:
1601:
1596:
1589:
1586:
1583:
1580:
1576:
1571:
1567:
1564:
1561:
1555:
1551:
1535:
1534:
1520:
1515:
1507:
1503:
1499:
1496:
1491:
1487:
1484:
1480:
1472:
1468:
1465:
1462:
1459:
1455:
1451:
1444:
1441:
1438:
1434:
1426:
1422:
1417:
1411:
1407:
1400:
1395:
1392:
1389:
1384:
1379:
1375:
1372:
1369:
1363:
1359:
1343:
1342:
1328:
1323:
1315:
1311:
1307:
1304:
1299:
1295:
1292:
1288:
1280:
1276:
1273:
1270:
1267:
1263:
1259:
1251:
1247:
1242:
1236:
1232:
1225:
1220:
1217:
1214:
1209:
1204:
1200:
1197:
1194:
1188:
1184:
1165:
1164:
1152:
1147:
1143:
1140:
1137:
1134:
1131:
1128:
1125:
1121:
1117:
1114:
1110:
1106:
1103:
1100:
1096:
1091:
1087:
1084:
1080:
1076:
1073:
1070:
1066:
1060:
1057:
1053:
1041:
1040:
1029:
1026:
1022:
1019:
1012:
1008:
1004:
1001:
997:
994:
991:
987:
983:
980:
976:
968:
964:
961:
958:
954:
948:
945:
941:
935:
930:
927:
923:
917:
912:
909:
905:
901:
897:
893:
890:
885:
881:
876:
872:
856:
853:
822:
819:
789:
788:
777:
774:
771:
768:
765:
762:
759:
754:
750:
747:
744:
738:
735:
726:
719:
715:
710:
707:
704:
701:
698:
695:
692:
678:
677:
666:
663:
657:
654:
651:
648:
644:
640:
637:
634:
631:
628:
625:
622:
619:
616:
613:
608:
603:
600:
596:
592:
589:
586:
583:
580:
577:
574:
571:
568:
565:
562:
559:
556:
553:
550:
547:
544:
541:
538:
504:
501:
500:
499:
485:
474:
473:
462:
459:
455:
452:
446:
443:
439:
436:
432:
429:
426:
423:
420:
417:
413:
409:
406:
403:
400:
397:
394:
391:
388:
385:
382:
379:
376:
373:
370:
352:Joseph Fourier
347:
344:
342:
339:
325:
322:
316:
313:
311:
308:
302:
299:
270:
267:
261:
258:
236:properties of
224:
221:
201:
198:
197:
196:
186:
179:
157:
139:
125:
107:
102:
79:
76:
74:seismography.
15:
9:
6:
4:
3:
2:
2993:
2982:
2979:
2978:
2976:
2961:
2960:
2951:
2949:
2948:
2939:
2937:
2936:
2931:
2925:
2924:
2921:
2915:
2914:Volcanologist
2912:
2910:
2907:
2905:
2902:
2901:
2899:
2895:
2889:
2886:
2884:
2881:
2879:
2876:
2874:
2871:
2869:
2866:
2864:
2861:
2859:
2856:
2854:
2851:
2849:
2846:
2844:
2841:
2839:
2836:
2834:
2831:
2830:
2828:
2824:
2818:
2815:
2813:
2810:
2808:
2805:
2803:
2800:
2798:
2795:
2794:
2792:
2790:
2786:
2780:
2777:
2775:
2772:
2770:
2767:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2749:Earth's orbit
2747:
2745:
2742:
2741:
2739:
2737:
2733:
2727:
2724:
2722:
2719:
2717:
2714:
2713:
2711:
2707:
2701:
2698:
2696:
2695:Geomorphology
2693:
2691:
2688:
2686:
2683:
2681:
2678:
2677:
2675:
2673:Dynamic Earth
2671:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2646:
2644:
2642:
2638:
2632:
2631:Sedimentology
2629:
2627:
2624:
2622:
2619:
2617:
2614:
2612:
2609:
2607:
2604:
2603:
2601:
2597:
2591:
2588:
2586:
2583:
2581:
2580:Geochronology
2578:
2577:
2575:
2573:
2569:
2563:
2553:
2550:
2548:
2545:
2543:
2540:
2538:
2535:
2534:
2532:
2528:
2524:
2517:
2512:
2510:
2505:
2503:
2498:
2497:
2494:
2482:
2481:
2472:
2470:
2469:
2460:
2458:
2457:
2452:
2446:
2445:
2442:
2436:
2433:
2432:
2430:
2426:
2420:
2417:
2415:
2412:
2410:
2407:
2405:
2402:
2400:
2397:
2395:
2392:
2390:
2387:
2385:
2382:
2380:
2377:
2375:
2372:
2370:
2367:
2366:
2364:
2358:
2352:
2349:
2347:
2344:
2342:
2339:
2337:
2334:
2332:
2329:
2327:
2324:
2322:
2319:
2317:
2314:
2312:
2309:
2307:
2304:
2303:
2301:
2297:
2291:
2290:Geophysicists
2288:
2286:
2283:
2282:
2280:
2276:
2272:
2265:
2260:
2258:
2253:
2251:
2246:
2245:
2242:
2231:
2227:
2223:
2219:
2215:
2211:
2207:
2203:
2196:
2190:
2186:
2182:
2178:
2172:
2165:
2161:
2155:
2153:
2151:
2149:
2147:
2139:
2135:
2129:
2127:
2125:
2123:
2114:
2110:
2106:
2102:
2098:
2094:
2087:
2079:
2075:
2071:
2067:
2060:
2052:
2048:
2044:
2040:
2036:
2032:
2028:
2024:
2017:
1998:
1991:
1984:
1975:
1973:
1956:
1952:
1949:Parker, Ann.
1945:
1937:
1933:
1929:
1923:
1919:
1915:
1911:
1904:
1896:
1892:
1887:
1882:
1878:
1874:
1870:
1866:
1862:
1855:
1853:
1836:
1832:
1826:
1819:
1813:
1805:
1803:9780521785747
1799:
1795:
1788:
1784:
1776:
1774:
1770:
1760:
1751:
1749:
1709:
1708:
1686:
1673:
1669:
1665:
1662:
1657:
1653:
1650:
1646:
1638:
1635:
1632:
1628:
1621:
1618:
1615:
1611:
1603:
1599:
1587:
1584:
1581:
1578:
1574:
1569:
1565:
1562:
1559:
1553:
1549:
1541:
1540:
1539:
1533:Welch's case
1518:
1505:
1501:
1497:
1494:
1489:
1485:
1482:
1478:
1470:
1466:
1463:
1460:
1457:
1453:
1449:
1442:
1439:
1436:
1432:
1424:
1420:
1409:
1405:
1398:
1382:
1377:
1373:
1370:
1367:
1361:
1357:
1349:
1348:
1347:
1326:
1313:
1309:
1305:
1302:
1297:
1293:
1290:
1286:
1278:
1274:
1271:
1268:
1265:
1261:
1257:
1249:
1245:
1234:
1230:
1223:
1207:
1202:
1198:
1195:
1192:
1186:
1182:
1174:
1173:
1172:
1169:
1150:
1145:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1119:
1115:
1112:
1108:
1104:
1101:
1098:
1094:
1089:
1085:
1082:
1078:
1074:
1071:
1068:
1064:
1058:
1055:
1051:
1043:
1042:
1027:
1024:
1020:
1017:
1010:
1006:
1002:
999:
995:
992:
989:
985:
981:
978:
974:
966:
962:
959:
956:
952:
946:
943:
939:
925:
921:
907:
903:
899:
895:
891:
888:
883:
879:
874:
870:
863:
862:
861:
852:
844:
840:
838:
834:
829:
818:
814:
813:
809:
807:
803:
799:
795:
775:
772:
766:
760:
752:
748:
745:
742:
724:
717:
713:
708:
702:
699:
696:
690:
683:
682:
681:
664:
661:
655:
652:
649:
646:
642:
635:
632:
629:
623:
617:
611:
598:
594:
590:
584:
581:
578:
572:
569:
563:
560:
557:
545:
539:
529:
528:
527:
524:
522:
518:
514:
510:
497:
493:
489:
486:
483:
479:
476:
475:
460:
457:
453:
450:
441:
437:
434:
430:
427:
424:
418:
415:
411:
404:
401:
398:
392:
389:
386:
380:
377:
374:
368:
361:
360:
359:
356:
353:
338:
336:
330:
321:
307:
298:
295:
291:
287:
279:
275:
266:
257:
254:
250:
245:
243:
239:
233:
231:
220:
216:
214:
210:
205:
194:
193:hyperspectral
190:
187:
184:
180:
177:
173:
169:
165:
161:
158:
155:
151:
147:
143:
140:
137:
136:magnetometers
133:
129:
126:
123:
119:
115:
111:
108:
106:
103:
100:
96:
92:
88:
85:
84:
83:
75:
72:
71:magnetometers
68:
64:
59:
57:
53:
49:
45:
41:
35:
32:
28:
22:
2957:
2945:
2926:
2826:Applications
2801:
2797:Geomagnetism
2721:Hydrogeology
2654:Paleontology
2649:Stratigraphy
2616:Geochemistry
2478:
2466:
2447:
2414:Seismic wave
2316:Geomagnetism
2310:
2208:(2): 70–73.
2205:
2201:
2195:
2171:
2096:
2092:
2086:
2069:
2065:
2059:
2026:
2022:
2016:
2004:. Retrieved
1997:the original
1983:
1959:. Retrieved
1954:
1944:
1909:
1903:
1868:
1864:
1839:. Retrieved
1834:
1825:
1817:
1812:
1793:
1787:
1766:
1757:
1720:
1712:Applications
1704:
1536:
1344:
1170:
1166:
858:
849:
836:
832:
824:
815:
811:
810:
805:
801:
797:
793:
790:
679:
525:
520:
516:
512:
508:
506:
495:
491:
487:
481:
477:
357:
349:
331:
327:
318:
304:
284:
272:
263:
246:
234:
228:such as the
226:
217:
213:magnetometer
206:
203:
191:, including
183:well logging
144:, including
130:, including
116:, including
81:
60:
52:oceanography
36:
26:
25:
2897:Occupations
2878:Meteoritics
2744:Cartography
2700:Volcanology
2685:Geodynamics
2306:Geodynamics
821:Beamforming
310:3D sampling
290:diffraction
56:engineering
44:archaeology
31:geophysical
2858:Geobiology
2833:Biogeology
2812:Seismology
2789:Geophysics
2716:Glaciology
2621:Mineralogy
2346:Seismology
2271:Geophysics
2181:0521215854
2164:0136049591
2138:0136049591
1779:References
209:gravimeter
162:, such as
118:gravimetry
89:, such as
63:gravimeter
2904:Geologist
2759:Geomatics
2626:Petrology
2530:Overviews
2389:Geodynamo
2362:phenomena
2360:Physical
2299:Subfields
1651:−
1600:∑
1483:−
1421:∑
1406:∑
1291:−
1246:∑
1231:∑
1139:−
1136:τ
1127:−
1124:ξ
1116:∗
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