Geophysical signal analysis is concerned with the detection and a subsequent processing of signals. Any signal which is varying conveys valuable information. Hence to understand the information embedded in such signals, we need to 'detect' and 'extract data' from such quantities. Geophysical signals are of extreme importance to us as they are information bearing signals which carry data related to petroleum deposits beneath the surface and seismic data. Analysis of geophysical signals also offers us a qualitative insight into the possibility of occurrence of a natural calamity such as earthquakes or volcanic eruptions. Gravitational and magnetic fields are detected using extremely sensitive gravitometers and magnetometers respectively. The gravitational field changes are measured using devices such as atom interferometers. A superconducting quantum interference device (SQUID) is an extremely sensitive device which measures minute changes in the magnetic field. After detection, the data from these signals is extracted by performing spectral analysis, filtering and beamforming techniques. These techniques can be used in oil exploration to estimate the position of underground objects, harnessing geothermal energy.
Background The position of underground objects can be determined by measuring the gradient in Earth's gravitational field. It is known that an object with heavier mass “attracts” other objects of a considerably lower value of mass. This force of attraction is explained by understanding the following topics.
Spatial and temporal frequency Temporal frequency is the number of occurrences of an event in unit "time". It is defined relative to time. Frequency of a wave can be X cycles per second. Spatial frequency on the other hand is the characteristic of any entity that periodically varies in space.
Digitizing in time and space domain Digitizing of any signal has two aspects : "digitizing in time domain" and "digitizing in space domain". These concepts pertain to the signals varying in space, time or both.
Time domain digitization is the process of measuring the amplitude of signal in discrete time intervals. Space domain digitization is the process of measuring the amplitude of signal in discrete spatial domain. Ex: Measuring intensity of electromagnetic field at various spatial intervals.
Tensor To explain the concept of a tensor, consider the definition of a vector: “Vector is a quantity having both magnitude and direction. Vectors are tensors with rank 1”. There is only basis vector for a component. Ex: Velocity is represented as Ai + Bj + Ck where i,j,k are unit vectors in the x,y,z directions respectively. We can see that there is a one-one mapping between the basis vector and its component.
Tensor, on the other hand has rank greater than one. Gravitational field is an example for a tensor.
The set of figures on the left represent the various components of the gravitational field. These components fully characterize all the forces acting on a body. These can be represented in a matrix form as follows:
Now that we are familiar with the concepts of gravity and tensors, a qualitative discussion of gravity and its significance in geophysical analysis can be done. A certain mass distribution creates a gravitational force field around it, In other words, the object under consideration has a finite mass ‘M’ and hence bends the space around it. The gravitational field gradient is given by the divergence of the gravitational field.
Existing approaches in geophysical signal recognition and analysis
Estimating the positions of the underground objects by measuring gravitational measurements 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 earth 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 is computed to assess the quality of location estimate.
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 a superconducting quantum interference device (SQUID) are used. Jim Zimmerman co-developed the 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 the 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 10−18 T.
Measurement of seismic waves
Background 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 interferometer
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