Hence this article also discusses multi-dimensional signal processing techniques. 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.

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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.

There are many methods and types of instruments used in geophysical surveys. Technologies used for geophysical surveys include: [1].

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This section deals with the principles behind measurement of geophysical waves. The magnetic and gravitational fields are important components of geophysical signals. The instrument used to measure the change in gravitational field is the gravimeter. This meter measures the variation in the gravity due to the subsurface formations and deposits. To measure the changes in magnetic field the magnetometer 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.

Magnetometers are used to measure the magnetic fields, magnetic anomalies in the earth. The sensitivity of magnetometers depends upon the requirement. In such cases, specialized magnetometers such as the superconducting quantum interference device SQUID are used.

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John Lambe, [4] during his experiments on [[nuclear magnetic resonance noticed that the electrical properties of indium varied due to a change in the magnetic field of the order of few nT. SQUIDs have the capability to detect magnetic fields of extremely low magnitude. This is due to the virtue of the Josephson junction. 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. 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 in the gravitational waves. The motion of any mass is affected by the 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.

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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. 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. 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. 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 refers to measuring a signal component at several instances of time.

Similarly, spatial-sampling refers to measuring the signal at different locations in space. 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 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 [7] by placing it in different locations at different instances of time. 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 motivation for development of the Wavelet transform was the Short-time Fourier transform. The signal to be analysed, say f t is multiplied with a window function w t at a particular time instant.

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Analysing the Fourier coefficients of this signal gives us information about the frequency components of the signal at a particular time instant. 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 can be explained by considering the time scaling and time shifting parameters a and b respectively. By choosing the appropriate values of a and b , 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. 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. Simply put, space-time signal filtering problem [11] can be thought as localizing the speed and direction of a particular signal.

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. This approach is applied for filtering space-time signals. One of the simplest filters is weighted delay and sum beamformer.

Ships in 7 to 10 business days. Link Either by signing into your account or linking your membership details before your order is placed. Description Table of Contents Product Details Click on the cover image above to read some pages of this book! Presents recently developed methodological findings of the earth's study, including seismoelectrical and renewed magnetovariational approaches Provides methodological guidelines for Electromagnetic data interpretation in various geological environments Contains a balanced set of lectures covering all aspects of Electromagnetic sounding at global, regional and local levels along with case studies, highlighting the practical importance of electromagnetic data Updates current findings in the field, in particular MT, magnetovariational and seismo-electrical methods and the practice of 3D interpretations Industry Reviews "The articles are well written, and the text is heavily referenced to published material in the field.

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