Question

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).

Hint:

For zero-offset reflections, \(r=\sqrt{z\,\lambda}\) with \(\lambda=v/f\). Migration collapses this radius toward the dominant wavelength scale.

Answer 1

Step 1: Wavelength.
\[ \lambda=\frac{v}{f}=\frac{1600}{50}=32\ \text{m}. \] Step 2: Fresnel-zone radius for zero-offset reflection.
For a stacked (zero-offset) section, the first Fresnel-zone radius on a horizontal reflector at depth \(z\) is \[ r=\sqrt{\frac{v\,T\,\lambda}{2}},\qquad T=\frac{2z}{v}. \] Substituting \(T\) gives \[ r=\sqrt{z\,\lambda}=\sqrt{100\times 32}=\sqrt{3200}=56.57\ \text{m}. \] \[ \boxed{56.6\ \text{m}} \]