Question

Considering a surface point source, the horizontal resolution recoverable from the seismic data acquired using a 10 Hz seismic pulse reflected from a depth of 30 km within the crust, with a velocity of 6.5 km/s, is __________ km (rounded off to two decimal places).

Hint:

Compute the first Fresnel-zone radius, \(r_F=\sqrt{vz/(2f)}\), and remember horizontal resolution is its diameter, \(2r_F\).

Answer 1

Correct Answer: 6.2

Arrive at the same Fresnel-zone size starting from the seismic wavelength instead of the travel time.

Step 1: Wavelength of the pulse.
\(\lambda = v/f = 6.5/10 = 0.65\) km.

Step 2: Fresnel-zone radius from depth and wavelength.
For a coincident surface source and receiver, the first Fresnel-zone radius is \(r_F = \sqrt{\dfrac{\lambda z}{2}} = \sqrt{\dfrac{0.65\times30}{2}} = \sqrt{9.75} = 3.1225\) km, identical to the travel-time-based value since \(\lambda z/2 = vz/(2f)\).

Step 3: Full lateral resolution.
Diameter \(= 2r_F = 6.245\) km \(\approx \boxed{6.24\ \text{km}}\), confirming the earlier answer via the wavelength route.