List of top Questions asked in GATE Geology and Geophysics

A stacked seismic section shows a single dipping event with a slope of \(0.5\ \text{s/km}\). Stolt migration with a constant velocity of \(2\ \text{km/s}\) is applied to the data. The dip of the event in the migrated section in degrees is __________ (rounded off to one decimal place).

The number of half-lives \((t_{1/2})\) required for a radioactive isotope to decrease to \(2\%\) of its original abundance is _________ (rounded off to two decimal places).

A monochromatic cosine wave with frequency \(0.24\ \text{Hz}\) and wavelength \(16\ \text{km}\) interferes with another monochromatic cosine wave with frequency \(0.3\ \text{Hz}\) and wavelength \(10\ \text{km}\). The group velocity of the resulting wave in km/s is _________ (rounded off to one decimal place).

The figure shows a homogeneous rock layer of thickness \(100\ \text{m}\). A vertical borehole is drilled through the layer and gravity is measured at the top point \(A\) and at the base point \(B\). If the difference in measurements between \(A\) and \(B\) is \(5\ \text{mGal}\), find the density \(\rho\) of the rock layer in g/cc (ignore terrain corrections). \includegraphics[width=0.5\linewidth]{17.png}

A magnetic field (B) of strength 50000 nT induces a magnetization (M) of magnitude 5 A/m in a rock. Given the magnetic permeability of free space \(\mu_0 = 4\pi \times 10^{-7}\,\text{H/m}\), the susceptibility of the rock is __________ (rounded off to three decimal places).

The amplitude of a monochromatic 1000 Hz EM wave reduces by a factor of \(1/e\) after penetrating to a depth of 100 m in a homogeneous medium. Given the magnetic permeability of free space \(\mu_0 = 4\pi \times 10^{-7}\,\text{H/m}\), the electrical conductivity of the medium in S/m is _________ (rounded off to three decimal places).

A plane P-wave is incident at an angle of \(60^\circ\) with respect to the normal to a horizontal reflector. If the incident medium is a homogeneous Poisson solid (\(\nu=0.25\)), the angle of the reflected, mode-converted S-wave with respect to the normal (in degrees) is _______ (rounded off to one decimal place).

A marine seismic survey was performed in a region with a flat, horizontal sea bed at a depth of 100 m from the sea surface. The datum of the stacked seismic section was fixed at the sea surface. If the P-wave velocity in water is \(1600\ \text{m/s}\), the radius of the first Fresnel zone at the sea bed at a frequency of \(50\ \text{Hz}\) corresponding to the stacked seismic section is _________ (rounded off to one decimal place).

Choose the CORRECT statement(s) on the phenomenon of spatial aliasing of seismic data.

The speed of a ship is given as \(V_1\) (km/h) and \(V_2\) (knots). The latitude of observation and the direction of the ship with respect to the North are \(\theta_1\) and \(\theta_2\), respectively. The CORRECT expression(s) for the Eötvös correction in mGal is/are:

If $\vec{B$ is the magnetic field in a region free of currents, then which of the following statements is/are correct? }

Which of the following operations performed in the time-domain with any two causal seismic signals result(s) in the \textbf{subtraction of their corresponding phase spectra in the frequency domain? }

A geophysical forward problem is expressed as \( d = 7m_1^2 m_2 + 6m_2 \), where \( m_1 \) and \( m_2 \) represent the model parameters and \( d \) represents the data. Then, the relationship between data and model parameters is

Assuming that the polar flattening of the Earth \( f = 3.353 \times 10^{-3} \), the difference between the geodetic and geocentric latitudes is maximum at

Which of the following statements related to an equipotential surface is/are CORRECT?

Match the electromagnetic methods in Group–I with their corresponding frequency range in Group–II. Group–I:
P. Very Low Frequency
Q. Radio Magnetotelluric
R. Ground Penetrating Radar
S. Control Source Magnetotelluric
Group–II:
1. 10 MHz – 1 GHz
2. 1 Hz – 20 kHz
3. 100 kHz – 1 MHz
4. 15 kHz – 30 kHz

The magnitude of horizontal and vertical components of the total magnetic field at a particular location are 40500 nT and 36450 nT, respectively. The magnetic inclination at the same location in degrees is ________ (rounded off to one decimal place).

A stress tensor $\sigma$, with elements in MPa, is as given. The maximum value of the principal stress in MPa is \[ \sigma = \begin{bmatrix} 1 & 0 & \sqrt{2}
0 & 1 & 0
\sqrt{2} & 0 & 0 \end{bmatrix} \]

An overdetermined linear inverse problem is expressed as \( Gm = d \), where \( G \) is the data kernel, \( m \) is the vector of model parameters and \( d \) is the vector of observed data. If damping is applied to the inverse problem and the resultant generalized inverse is represented by \( G^{-g} \), the \textbf{model resolution matrix can be expressed as:}