In local earthquake ( LE) tomography for P- and S-wave velocities ( or
Vp/Vs ratios), constraints punishing deviations from a given Vp/Vs ratio
are often used. In a synthetic model test we demonstrate that though
such constraints inhibit unreasonable Vp/Vs ratio variations, they bias
the resulting Vp/Vs ratios. As an alternative approach, structural
constraints based on the cross-product of the model gradients can be
used to constrain the joint P- and S-wave inversion. We show that the
resulting models are as low in artifacts as if a Vp/Vs damping was used,
but the resulting Vp/Vs ratios are less biased, which is important for a
quantitative interpretation of physical properties and processes in the
Earth.