A theory for marine source arrays

Abstract

General mathematical expressions for a marine source array’s (1) far‐field pulse spectrum, (2) radiated energy density, and (3) directivity are developed for both a source in an infinite homogeneous medium and a source operating near the ocean surface. These results, intended to assist the analysis and design of marine source arrays, apply to any marine source array when (1) individual elements radiate isotropically, (2) their individual waveforms are specified, and (3) the array geometry is specified. Arbitrary geometry and arbitrary isotropic waveforms are allowed. The theory assumes linear superposition of the individually specified waveforms, and is consistent with the “square law effect” for identical elements. For an array of small elements, expended energy agrees with the array’s radiated energy found using far‐field methods. Also, the energy radiated from an array with large element spacing is equal to the sum of the independently radiated energies. Two closely spaced identical elements radiate four times the energy contained in a single outgoing waveform over all space. The appropriate directivity definition for marine seismic sources is the ratio of the radiated energy density per unit solid angle in a particular direction to the average radiated energy density per unit solid angle. This definition allows directivity to be expressed explicitly in terms of the individual frequency spectra and geometry.

Influence of upscaling on identification of reservoir fluid properties using seismic-scale elastic constants

“…The directional behavior of transducers makes the amplitude with different offsets undesirable variations, and should be compensated prior to any seismic amplitude analysis. Following the work of Duren 28 and Mahmoudian et al . 29 , directivity can be corrected by dividing measured amplitudes by the cosine of the angle between the wave propagation direction and the vertical direction.…”

Acoustically induced cavity cloud generated by air-gun arrays—Comparing video recordings and acoustic data to modeling

“…In marine seismic reflection profiling where the geological structure beneath the seabed is delineated, marine seismic sources such as air-guns, water-guns, and marine vibrators are used (Duren, 1988). The objective of such exploration surveys is usually to find hydrocarbon resources.…”

“…Other applications are academic research and mapping of Earth's subsurface. By far, air-gun arrays have been the most prevalent and efficient marine seismic source (Duren, 1988;Barger and Hamblen, 1980) and still are (Watson et al, 2016). An air-gun generates acoustic pressure waves from expansion and contraction of an air bubble which is formed by releasing high-pressure air (typically 2000 psi) into the surrounding water within a short time (Caldwell and Dragoset, 2000).…”