Geophysical survey is the systematic collection of geophysical data for spatial studies. 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 geology, archaeology, mineral and energy exploration, oceanography, and engineering. Geophysical surveys are used in industry as well as for academic research.
The sensing instruments such as gravimeter, gravitational wave sensor and magnetometers 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 seismography.
- 1 Types of geophysical survey
- 2 Existing approaches in geophysical signal recognition
- 3 Applications
- 4 Notes
- 5 References
Types of geophysical survey
There are many methods and types of instrumentation used in geophysical surveys. Technologies used for geophysical surveys include:
- Seismic methods, such as reflection seismology, seismic refraction, and seismic tomography.
- Seismoelectrical method
- Geodesy and gravity techniques, including gravimetry and gravity gradiometry.
- Magnetic techniques, including aeromagnetic surveys and magnetometers.
- Electrical techniques, including electrical resistivity tomography, induced polarization and spontaneous potential.
- Electromagnetic methods, such as magnetotellurics, ground penetrating radar and transient/time-domain electromagnetics, magnetic resonance sounding (MRS).
- Borehole geophysics, also called well logging.
- Remote sensing techniques, including hyperspectral.
Geophysical signal detection
Measurement of Earth’s magnetic fields
Magnetometers are used to measure the magnetic fields, magnetic anomalies in the earth. The sensitivity of magnetometers depends upon the requirement. Ex, the variations in the geomagnetic fields can be to the order of several aT where 1aT = 10^-18T . In such cases, specialized magnetometers such as the superconducting quantum interference device (SQUID) are used.
Jim Zimmerman co-developed the rf SQUID (Superconducting QUantum Interference Device) during his tenure at Ford research lab. However, events leading to the invention of squid were in fact, serendipitous. John Lambe, during his experiments on Nuclear Magnetic Resonance noticed that the electrical properties of Indium varied due to a change in magnetic field of the order of few nT. But, Lambe was not able to fully recognise the utility of SQUID.
SQUIDs have the capability to detect magnetic fields of extremely low magnitude. This is due to the virtue of Josephson junctions. Jim Zimmerman pioneered the development of SQUID by proposing a new approach to making the Josephson junctions. He made use of niobium 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 10^-18T.
Seismic wave measurement using gravitational wave sensor
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 van be detected by a relative shift in the gravitational waves.
Measurement of seismic waves using atom interferometer
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 to the motion of heavenly bodies. Hence, special instruments are required to measure such a minute change.
Atom interferometers work on the principle of diffraction. The diffraction gratings are nano fabricated materials with a separation of a quarter wavelength of light. When a beam of atoms pass through a diffraction grating, due 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 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.
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.
Analog to digital conversion
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 domain. The signal component is measured at both intervals of time and space. Ex, time domain sampling refers to measuring a signal component at several instances of time. Similarly, spatial sampling refers to measuring the signal at different locations in space.
Existing approaches in geophysical signal recognition
Traditional sampling of 1-D 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 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 gravitational wave sensor or gradiometer by placing it in different instances at different instances of time.
Analysis of 3D data
The method of volume rendering 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 voxel. 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.
Multi-dimensional Fourier transform
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. Joseph Fourier 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.
The 4d - Fourier representation of such signals is given by
S(K, ω) = ∫ ∫ s(x,t) exp [-j(ωt- k'x)] dx dt
- ω represents temporal frequency and k represents spatial frequency.
- s(x,t) is a 4-dimensional space time signal which can be imagined as travelling plane waves. The plane of propagation is perpendicular to the direction of propagation of an Electromagnetic wave.
The motivation for development of Wavelet transform was the Short-time fourier transform.The signal to be analysed, say f(t) is multiplied with a window function w 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.
where m,n ∈ Z.
Cmn are the windowed fourier coefficients.
Wavelet transform is defined as
A variety of window functions can be used for analysis. Interestingly, wavelet functions are used for both time and frequency localisation. Ex,one of the windows used in calculating the fourier coefficients Gaussian window isoptimally concentrated in time and frequency. Hence wavelet transforms are important in geophysical applications where spatial and temporal frequency localisation is important.
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 spacetime signals follows a similar approach as that of 1-D signals. The filters for 1-D signals are designed in such a way that if the requirement of the filter is to extract frequency components in a particular non-zero range of frequencies, a bandpass filter 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 (k, ω) a.k.a wavenumber - frequency and zero elsewhere.
This approach is applied for filtering spacetime 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 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.
Estimating positions of underground objects
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. Since the mass distribution of objects of interest is already known, say underground objects with center of masses (CM1, CM2…CMn) are located under the surface and at positions p1, p2...pn. 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 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 Cramér–Rao bound (CRB) is computed to assess the quality of location estimate.
Time frequency localisation using wavelets
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 and frequency.
Array processing for seismographic applications
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 model the activities inside the earth.
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