A linearized frequency domain inversion of receiver transfer functions is investigated as a means for determining crustal structure. The forward problem is solved using a Thomson-Haskell method which includes the effects of attenuating layers. The function to be fit consists of the deconvolved radial component of teleseismic P waves (to remove source effects) which is sensitive mainly to variations in shear velocity and density. Compressional velocity and attenuation are adjusted by assuming a Poisson solid. Complex partial derivatives are computed with respect to the complex shear velocity in each layer using a finite difference approach. Thus, it is possible to simultaneously invert for shear velocity and shear attenuation. Test cases show that for short path lengths, the effects of attenuation are relatively small compared to the effects of velocity contrasts at layer interfaces.
Test cases utilizing synthetic and real data demonstrate the impressive resolving power of the technique for the determination of crustal thickness and the importance of density on the calculated receiver functions. Examination of partial derivatives for the receiver transfer functions with respect to various layer parameters further demonstrates that the effect of density is nearly as important as that due to shear velocity. The test cases also bring out the importance of an accurate trial solution, especially in the presence of noise. Thus, in actual practice it is necessary to combine the inversion with trial and error calculations.