After obtaining a better understanding on Forest Acoustics and reviewing previous research on the field, I decided to investigate different ways of modelling a virtual forest for my project. This directed me towards Physical Modelling Synthesis and Digital Waveguides, as it has been used twice before for the same purpose.
What is Physical Modelling
Physical Modelling Synthesis makes use of mathematical models to mimic the physical characteristics of an instrument [1]. Digital Waveguide models are physical models made up using delay lines, digital filters and other components which have an effect on the signal chain, targeted towards a realistic virtual representation of a musical instrument [2]. The wave propagation and hence the delay lines can be considered in 1D (string), 2D (membrane) or 3D (space). For the modelling of a virtual forest, a 2D representation would be sufficient with the tree trunks acting as circles on a horizontal plane, but a 3D representation would result into significantly more accurate results due to more realistic scattering and sound attenuation.
Modelling a Virtual Forest
In a 2D system, as sound moves across the membrane, its intensity decreases over time. When the signal reaches a tree trunk, absorption and scattering are taking place due to the medium, texture and shape of the surface. The absorption coefficient will act as a digital filter, diminishing the harmonic spectrum of the signal and attenuating the sound. Scattering can be modelled by applying a different resistance on the two mediums (from air to the tree trunk), which varies depending on the wavelength of the wave. The process is repeated depending on the number of times a sound wave reflects on surfaces before reaching the receiving position. After a certain number of reflections, some sound waves completely lose their energy and disappear.
Conclusion
I discussed with Professor Damien Murphy and Dr Amelia Gully about the use of physical modelling for my own project, and they suggested that I should prioritise other things due to the complexity of the topic. They still directed me towards further literature to approach and understand Digital Waveguide Synthesis. This made me change my project aims and reconsider my project approach, targeted more towards improving already existing models rather than inventing my own.
Figure: Digital Waveguides with different resistances on the delay lines resulting into Signal Scattering, as shown by J. Smith [2].
[1] Välimäki, V., Pakarinen, J., Erkut, C. and Karjalainen, M. (2005). Discrete-time modelling of musical instruments. Reports on Progress in Physics, [online] 69(1), pp.1-78. Available at: https://iopscience.iop.org/article/10.1088/0034-4885/69/1/R01/meta
[2] Smith, J. (2006). A Basic Introduction to Digital Waveguide Synthesis (for the Technically Inclined). [online] Center for Computer Research in Music and Acoustics. Available at: https://ccrma.stanford.edu/~jos/swgt/
George Sarantinos 