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).
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Correct Answer: 6.2
Solution and Explanation
The lateral (horizontal) resolution limit of unmigrated seismic reflection data is set by the size of the first Fresnel zone - the patch of the reflector from which reflected energy arrives within half a period of the first arrival and therefore interferes constructively.
Step 1: Two-way travel time to the reflector.
\(t_0 = \dfrac{2z}{v} = \dfrac{2\times30}{6.5} = 9.2308\) s.
Step 2: First Fresnel-zone radius.
\(r_F = \dfrac{v}{2}\sqrt{\dfrac{t_0}{f}} = \dfrac{6.5}{2}\sqrt{\dfrac{9.2308}{10}} = 3.25\times0.9608 = 3.1225\) km.
Step 3: Horizontal resolution.
The horizontal resolution - the closest that two reflecting points can be and still be distinguished by an unmigrated, surface-point-source survey - is the Fresnel-zone diameter: \(2r_F = 2\times3.1225 = 6.245\) km.
Rounded to two decimal places, the horizontal resolution is \(\boxed{6.24\text{-}6.25\ \text{km}}\), inside the accepted band 6.20 to 6.30 km.
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(Figure not to scale)
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