Step 1: Understanding the different geophysical methods.
Geophysical methods are used to investigate the Earth's internal structure. Each method has a different resolution and penetration depth.
Step 2: Seismic methods.
Seismic methods provide the highest resolution for exploring deep Earth structures, including those at depths of up to 1000 km. This method uses the propagation of seismic waves (P-waves and S-waves) through the Earth to gather data about its interior.
Step 3: Comparing with other methods.
Magnetic methods measure variations in the Earth's magnetic field and are primarily used for mapping crustal structures, not deep Earth.
Electrical methods measure resistivity, but they do not provide the resolution necessary for studying deep Earth structures.
Gravity methods measure variations in Earth's gravitational field, which can provide some insights into the deep structure, but they have lower resolution compared to seismic methods.
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).
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 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?
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)