Solution (source code)

= Solution

Use a \b[high-resolution multichannel <seismic reflection survey>], with closely spaced crossing lines or a suitable small three-dimensional survey over the turbine locations. It should map the seabed, the <sediment>–<sandstone> boundary, local <faults>, buried channels, and lateral changes relevant to foundations. <Seismic reflection> responds to <acoustic impedance> contrasts and can image an irregular boundary without requiring it to be a first-arrival refractor. Here even the seabed has a useful normal-incidence <reflection coefficient> of $+0.20$ despite its zero P-velocity contrast.

A <seismic refraction survey> can provide complementary <seismic velocities> and geotechnical information, particularly using seabed multicomponent receivers for <S waves>. Its limitations as the principal imaging method here include the missing water–sediment P refractor, required offsets of hundreds of metres to obtain useful basement first arrivals, and weaker constraints on thin layers or velocity inversions. Variable <bathymetry> and <sediment> thickness further complicate simple refraction interpretations.

A shallow-towed \b[<boomer seismic source> or small <sparker seismic source>] is a sensible initial <seismic source> for penetrating about 20 m of <sediment> beneath a 50 m water column. A <chirp sub-bottom profiler> can add finer imaging of the upper cover where penetration permits; penetration depends on grain size, consolidation, <gas>, and <seismic attenuation>. A pilot line should establish the minimum useful source energy and <bandwidth>. Large low-frequency air-gun arrays are unnecessary for this shallow target. Small coastal vessels, sea state, tow stability and acoustic background constrain usable <frequencies> and operations. Marine mammals and other local receptors motivate a low-energy effective source, monitoring and appropriate operational mitigation.<High-resolution multichannel seismic system by United States Geological Survey>[The institutional instrument description lists configurable boomer, sparker, hydrophone-streamer and complementary chirp equipment for shallow subsurface mapping.]{ref}

The expected normal-incidence two-way <travel times> are $2(50)/1500\simeq0.0667\ \mathrm s$ for the seabed and $2(50+20)/1500\simeq0.0933\ \mathrm s$ for basement, separated by $26.7\ \mathrm{ms}$. Source duration, recording sample interval and <bandwidth> must distinguish them. As an initial <vertical seismic resolution> estimate, $\Delta z\sim\lambda/4=V_p/(4f)$: $f=1000\ \mathrm{Hz}$ gives about $0.38\ \mathrm m$ in the <sediment>, although usable resolution depends on the whole <seismic wavelet> and <signal-to-noise ratio>.

Choose shot and receiver spacing from the shortest useful <wavelength>, target size, maximum <reflector dip>, <seismic migration> needs and achievable navigation accuracy. For a plane event of horizontal <seismic ray parameter> $p$, avoiding spatial <aliasing> requires approximately $\Delta x\leq1/(2f_{\max}|p|)$. Source spacing and receiver spacing also set midpoint coverage and <seismic acquisition fold>; adequate offsets enable <moveout correction> and velocity estimation. For nearly horizontal shallow reflectors a few-metre shot interval can be practical, whereas steep events at high frequency require denser spatial sampling. These values must be designed together rather than imposing one spacing for every target. Cross-line spacing must resolve lateral features between turbine sites, not merely along each track.

At a vessel speed of $2\ \mathrm{m\,s^{-1}}$, one shot per second gives 2 m shot spacing and ample separation relative to a roughly $0.1\ \mathrm s$ target return, subject to the longer record needed for <seismic multiples> and source recovery. Shallow towing limits <seismic source ghosts> and receiver ghosts, but requires stable tow depth. Accurate positioning, tides, measured water sound speed, <bathymetry> and checks for seabed <seismic multiples> are essential for correct target depths.