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In 2D acoustic and elastodynamic problems the spatial variability of aconstitutive parameter such as the mass density makes it difficult to employboundary integral and domain integral techniques to solve the forward andinverse wave scattering problems. The oft-employed method for avoiding thisproblem is to assume this constitutive parameter (which is chosen herein to bethe mass density) to be spatially-invariant throughout all space. Thereliability of this assumption is evaluated both theoretically and numericallyand it is shown, in the example of a canonical-shaped scattering obstacle, thatthe scattered field can be obtained in the form of a series of powers of themass density contrast (the latter vanishing for constant mass density). Thefirst term of this series is the solution for the scattered field correspondingto the constant density assumption and it is shown that taking into accountonly two more terms in the series enables to correct for practically all theerrors incurred by the constant mass density assumption for a wide range of theother constitutive parameters and frequencies. It is shown how to apply thisresult for obstacles of non-canonical shape.

On the constant constitutive parameter (e.g., mass density) assumption in integral equation approaches to (acoustic) wave scattering