List of top Questions asked in GATE Geology and Geophysics

A thin wire is used to construct all the edges of a cube of 1 m side by bending, cutting, and soldering the wire. If the wire is 12 m long, what is the minimum number of cuts required to construct the wire frame to form the cube?
Rohit goes to a restaurant for lunch at about 1 PM. When he enters the restaurant, he notices that the hour and minute hands on the wall clock are exactly coinciding. After about an hour, when he leaves the restaurant, he notices that the clock hands are again exactly coinciding. How much time (in minutes) did Rohit spend at the restaurant?

A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K). Which one of the following options displays the color codes that are consistent with the color model? 


 

Consider a two-dimensional reflection experiment, where a horizontal boundary between two layers is at a depth of 500 m below the free surface. A source and geophone are placed on the free surface with an offset of 2000 m. The P-wave velocity of the top layer is 3000 m/s. The travel time of a recorded free-surface reflection multiple, which got reflected twice at the free surface, is ________ s.

While doing Bayesian inference, consider estimating the posterior distribution of the model parameter (m), given data (d). Assume that Prior and Likelihood are proportional to Gaussian functions given by \[ {Prior} \propto \exp(-0.5(m - 1)^2) \] \[ {Likelihood} \propto \exp(-0.5(m - 3)^2) \]

The mean of the posterior distribution is (Answer in integer)

Suppose a mountain at location A is in isostatic equilibrium with a column at location B, which is at sea-level, as shown in the figure. The height of the mountain is 4 km and the thickness of the crust at B is 1 km. Given that the densities of crust and mantle are 2700 kg/m\(^3\) and 3300 kg/m\(^3\), respectively, the thickness of the mountain root (r1) is km. (Answer in integer)


 

A primary electromagnetic field (\( H_P \)) is being generated from current \( I_P \) flowing in a coil A with negligible capacitance, such that \( H_P = K I_P \sin \omega t \), where \( \omega \) is the angular frequency, \( K \) is a constant and \( t \) is time. A secondary electromagnetic field is being produced by induction in a conducting coil B. The phase difference between the primary and the secondary electromagnetic fields depends on which of the following factors?

In seismology, Born approximation of the scattered (perturbed) wavefield is given by \[ \delta u(\mathbf{r}, \mathbf{s}; t) \approx \int_V \delta r(\mathbf{x}) \left(u_0(\mathbf{x}, \mathbf{s}; t) _t u_0(\mathbf{r}, \mathbf{x}; t)\right) \, d\mathbf{x}. \] Here, \( _t \) denotes temporal convolution, \( \delta r(\mathbf{x}) \) is the strength of the scatterer at \( \mathbf{x} \) in volume \( V \), \( \delta u(\mathbf{r}, \mathbf{s}; t) \) is the scattered wavefield measured at the receiver \( \mathbf{r} \) from the source \( \mathbf{s} \), \( u_0(\mathbf{x}, \mathbf{s}; t) \) is the downgoing wavefield (to the scatterer at \( \mathbf{x} \) from the source \( \mathbf{s} \)) in the unperturbed medium, \( u_0(\mathbf{r}, \mathbf{x}; t) \) is the upgoing wavefield (to the receiver \( \mathbf{r} \) from the scatterer at \( \mathbf{x} \)) in the unperturbed medium. 
Select the correct statement(s).

A loop of radius \( R \) carries a current \( I \) and produces a magnetic field \( B \). Which of the following statements is/are correct about \( B \)?

For a half space composed of 3 layers with resistivities \( \rho_1 \), \( \rho_2 \) and \( \rho_3 \), as shown in the figure, which of the following statements is/are correct about the variation of apparent resistivity with electrode spacing?


 

Which of the following statements is/are correct regarding the properties of the oceanic lithosphere?
Consider ray tracing in an isotropic elastic Earth, with travel time function \( T(x, y, z) \) in Cartesian coordinates. Select the correct option(s).
What factor(s) determine(s) the magnitude of peak ground acceleration measured at a particular station due to an earthquake?
Given the following electric field in Cartesian coordinates: \[ \mathbf{E} = x^2 y \hat{i} + y^2 z \hat{j} + z^2 x \hat{k}, \] which of the following statements is/are correct?

Consider a ray tomography experiment, where the goal is to estimate the wave velocity of 9 square cells plotted in each of the cases A and B. The ray paths for source-receiver pairs for both these cases are shown in the figure. Select the correct statement.


 

Consider a steady-state heat conduction equation for the Earth’s crust where \( A \) is the heat source and \( k \) is the thermal conductivity. Given the boundary conditions: \( T = 0 \) at the surface and \( Q \) is the heat flux at the surface, Which one of the following options would be the temperature \( T \) at depth \( z \)?

For a horizontal liquid-solid interface as shown, which one of the following ray diagrams with an incident P wave is correct? SH and SV denote shear-horizontal and shear-vertical waves, respectively.


 

A geophysicist is analyzing the elastic-wave radiation to infer the body force equivalent of a seismic source. She has plotted the horizontal component of the displacement field, denoted as \( u(m, t) \), for time \( t \) and location \( m \). The measured field at two locations \( m \) and \( n \) is plotted in the figure. Note that \( S \) and \( P \) waves have negligible amplitudes at locations \( m \) and \( n \), respectively. Assuming a homogeneous medium, select the most probable direction (specified by the angle \( \alpha \)) along which the force \( \vec{F} \) is applied.


 

Select the correct statement regarding surface waves and upper mantle structure.
The components \(u\), \(v\), \(w\) of the displacement field along \(x\), \(y\), \(z\) directions, respectively, are given by: \[ u = - \sin(\omega t - kz) \] \[ v = \sin(\omega t - kz) \] \[ w = 0 \] where \(t\), \(k\), and \(\omega\) are time, wavenumber, and angular frequency, respectively. Assuming \(k\) is real, which one of the following describes the wave?
If seismic signals of periods greater than 10 s are of interest, the minimum sampling frequency should be ________ Hz. (Round off to one decimal place).
What is/are the primary effect(s) of applying upward continuation to magnetic field data?

The following figure shows a region in which rocks in areas A, B and C follow Hooke's law and are subject to the same stress. B exhibits lower strain than both A and C. What can we infer about the nature of B?