Since the introduction of arrays of sources, geophysicists have sought to optimise their deployment to meet geophysical objectives. Originally, these objectives were quite simple, such as maximising the primary to bubble ratio. The geophysical idea behind this was that the closer the array signature was to a spike, the better the signature would deconvolve in the acquired data.
As acquisition has become more sophisticated, so optimisation needs have evolved correspondingly. An example is the need to image below deep basalt reflectors. Such reflectors tend to hide whatever might be underneath them because they are difficult to penetrate with acoustic energy. As a result, a need has arisen to maximise the low frequencies in airgun arrays to optimise the illumination of any sub-basalt reflectors of interest.
It is important to realise that optimising one property will usually be at the expense of another. Optimising low frequency content will enhance the bubble and greatly reduce the primary to bubble ratio.
Gundalf tackles this problem by allowing multiple constraints and weights to be specified in the Options -> Change Optimisation -> Optimisation parameters menu. The geophysicist can experiment with this but to reduce the learning curve, a number of typical scenarios have been introduced.
These are some of the ways in which you might use Gundalf to optimise your array for a specific goal.
Shallow reservoir imaging
In shallow reservoir imaging, we are normally looking for wide bandwidth. This
is achieved typically in seismic arrays by shallow deployment. Typically, you might try
to maximise primary to bubble ratio concurrently with spectral flatness.
Although related, they are not quite the same thing. Gundalf also allows the user
to specify the desired spectral bandwidth and an initial wide band is recommended.
Sub basalt imaging
Imaging below basalt requires an array to maximise its low frequency content in order
to penetrate optimally. This is generally at the expense of any particular signature
property. With airgun arrays, the best way to achieve this appears to be by deep
deployment, perhaps 20m. or even deeper. You might achieve this by
maximising both the peak and average spectral levels within a low bandwidth. You will also
need to allow a greater maximum depth in the run parameters. An alternative is to use the XLA airgun source
which is considerable richer in very low frequencies than a conventional airgun source.
Optimise inversion potential
It is observed that flat spectra tend to assist attempts at inversion. To optimise this,
try minimising the spectral ripple within a relatively wide bandwidth whilst allowing
volumes within the supplied inventory of guns and also the sub-array depths to vary.
Optimise close reflector images
When viewed in a typical seismic band, an airgun bubble is much more obvious than
in the rather idealised world of source specification. Array specifications might
require a minimum primary to bubble of say 15:1 in a bandwidth of 0-256 Hz. The earth
however is rather less accommodating and in a seismic band of 10-80Hz, the same
signature might have a primary to bubble of only 5:1 or so. Even at this level, predictive
deconvolution tends to work pretty well as can be seen by setting typical Q and
Wiener filtering options in Gundalf. However it is possible if there are very close
reflectors, particularly when a small reflector appears directly under a better
reflector, that the bubble from the good reflector interferes with the small reflector.
Deconvolution may not resolve this satisfactorily, so try
maximising the primary to bubble ratio whilst lengthening the bubble pulse
as much as possible.
Optimally flatten spectrum
This is essentially the same as optimising inversion potential but try
varying the depths of individual guns. This is not easy to implement on many
gun decks in practice, but may well be of interest in some projects.
Reduce low frequency bubble peaks
The goal here is to flatten the low frequency spectral ripples
common to many airgun arrays. The primary ripple is often 10-15dB
and occurs somewhere between 7-15 Hz on most arrays. Try flattening the spectrum
but within this bandwidth.
The goal is very similar to that of optimally flattening the spectrum but it takes place at a lower bandwidth aimed at suppressing the primary ripple and the overall sub-array depth should be varied rather than individual gun depths as this is not a popular option in the field. In practice, this seems to make little difference on the array simulations we have conducted and a significant beneficial reduction in ripple can still be achieved by varying the sub-array depth as a whole.
Minimise impact on echo-locators
Echo-locating marine mammals such as odontoceti typically have peak echo-location
efficiency around 20kHz. To do this, you must minimise the amount
of acoustic energy in the airgun array in the most sensitive band. It should be
recognised that there isn't much energy here anyway with typical airgun arrays,
(typically less than 1%), but this can often be reduced even further by choosing
to minimise the high frequency acoustic energy.
The run parameters control the various constraints on the array, such as total volume limits, depth limits and so on. Gundalf will operate within these constraints in trying to optimise your array. It also recognises the discrete nature of gun deck limits so allows increments to be set for depth change and so on to fit within any practical constraints.
Gundalf also allows the number of trials, mutation steps and inheritance steps to be varied. The latter two may be left alone but increasing the number of trials with any Gundalf optimisation simply gives it a better chance of improving the array. The only penalty is time.
Gundalf uses a hybrid algorithm for optimisation to take account of the mixed discrete / continuous nature of airgun array optimisation. The gun parameters which are varied such as volume and depth are discrete by their nature, (the latter because of deployment limitations). Some optimisation goals such as optimising the primary to bubble ratio, however are continuous. Gundalf approaches this by using a mutation phase which is similar to simulated annealing. This is followed by an inheritance phase which is similar to an n-dimensional game of Tetris, (the snuggling phase), where the solution is rotated in n-dimensional space to see if a more optimal orientation is possible. Interested readers are directed to general texts on optimisation - it is a huge subject.