  In 2D acoustic and elastodynamic problems the spatial variability of a
constitutive parameter such as the mass density makes it difficult to employ
boundary integral and domain integral techniques to solve the forward and
inverse wave scattering problems. The oft-employed method for avoiding this
problem is to assume this constitutive parameter (which is chosen herein to be
the mass density) to be spatially-invariant throughout all space. The
reliability of this assumption is evaluated both theoretically and numerically
and it is shown, in the example of a canonical-shaped scattering obstacle, that
the scattered field can be obtained in the form of a series of powers of the
mass density contrast (the latter vanishing for constant mass density). The
first term of this series is the solution for the scattered field corresponding
to the constant density assumption and it is shown that taking into account
only two more terms in the series enables to correct for practically all the
errors incurred by the constant mass density assumption for a wide range of the
other constitutive parameters and frequencies. It is shown how to apply this
result for obstacles of non-canonical shape.
