The physics used inside the GUNDALF airgun modelling engine is evolutionary building on numerous pioneering pieces of theoretical work which have been done in the last 20 years by (in alphabetic order) Bill Dragoset, Martin Landro, Robert Laws, Gregg Parkes, Svein Vaage, Anton Ziolkowski and others as well as important published experimental backup by Mike Hall, Tor Haugland and recent broadband activities. The gun physics as it stands today was originally based on the work described by Laws, Hatton and Haartsen (1990) "Computer modelling of clustered airguns", First Break, 8(9) incrementally improved by Les Hatton to attempt to model the asymmetric "super-foam" region of very close interaction which has hitherto defeated attempts to model it. This "super-foam" physics correctly models the observation that very close interaction causes the bubble to be increasingly severely attenuated as well as the peak itself. This allows Gundalf to auto-sense clustering.
The model has been calibrated on a number of occasions notably using the measurements kindly supplied by Mike Hall then of Horizon taken from cluster experiments at Loch Linnhe in Scotland. Under most environments, it predicts interacting arrays within a few percent and correctly models the phase-locking reported by Laws et. al. (1990). More recently, modifications to the physics to enable GI (generator-injector) guns to be modelled have benefitted from measurements kindly supplied by Ewan Neill of Grant Geophysical.
Excellent data has kindly been made available by numerous people over the years; Alain Regnault then of CGG, (G and sleeve guns), by Mike Saunders then of Bolt, (1500LL, 1900LLX and 8500 APG guns), and Morten Svendsen and Elaina Hurst then of WesternGeco, (2800LLX, 1500LL and 1900LLX in single, 2 and 3 gun clusters at depths from 3-30m).
Phil Fontana then of VeritasDGC kindly made available the first broadband data (0-25kHz) acquired by the IFRC and this has been used to calibrate Gundalf in the acoustic frequency band of particular importance when trying to predict acoustic impact on marine mammals. It is important to note that an airgun bubble is highly anisotropic at these frequencies as can be seen by viewing the videos at this web location. It is very likely that the best that can be done in modelling kHz frequencies is to provide an average radiation level. This is important though as animals may accumulate impact damage through repeated exposure. The original IFRC data hase been considerably supplemented in recent years by broadband data for numerous gun types supplied by WesternGeco / Schlumberger.
The Gundalf model is continually under development and is recalibrated whenever more high quality data becomes available.
Recent developments including modelling support for the new generation Bolt environmental sources e300 and e500 in A, B and C form in 2015-2018 and experimental support for a generic very large airgun with internal code XLA in Gundalf in 2020. This is pending the availability of good quality calibration data for any implementations which may come along.
In 2021, temporally dispersed arrays (also know as "popcorn" arrays) were re-implemented and further modelling development is under way for new generation environmentally conscious sources.
The determination of the reflection coefficient uses two pieces of published work.
The first was done originally by Jovanovich et. al. (1983) Geophysics, v. 48, p. 1468- and Loveridge (1985) D.Phil. thesis, University of Oxford. For more details, see Parkes and Hatton (1986), "The Marine Seismic Source", ISBN 90-277-2228-5, Reidel. This algorithm requires the expected dominant frequency of the signature, (usually around 20Hz. for an airgun) and an estimate of the observed wave height in m. If the wave-height is zero, a reflection coefficient of -1.0 is used independent of the dominant frequency.
The second was done by Hatton (2006) by analysing high-quality shallow data supplied by Morten Svendsen and Elaina Hurst of Westerngeco. This allows Gundalf to calculate the reflection coefficient automatically based on the anelastic break-down of the sea-surface itself. This work is freely available from this web location.
The optimisation algorithm is a variant of an unpublished genetic algorithm due to Les Hatton. This algorithm combines elements of genetic and annealing optimisation algorithms to solve the problem of global optimisation from a discrete inventory.
It is important to realise that there remain limitations.
In the modelling of injector guns, the current status of this in GUNDALF is experimental. The results have only partially been calibrated at this stage and this should be borne in mind.
There is a modern trend towards designing air gun arrays which have very high levels of interaction. Gundalf was modified in December 2003 to converge for all levels of interaction and Gundalf agrees well with the 2 and 3 gun cluster data supplied by WesternGeco in October 2005.
Full calibration results can be found here.