Roughness constraints in surface wave tomography

A set of inversion experiments is described that tests the ability of global surface wave tomography to retrieve long‐wavelength upper mantle velocity structure in the presence of a modest level of rough structure. We use upper‐mantle model M84A, augmented with randomly‐generated lateral structure to smax = 20, to calculate coupled‐mode synthetic seismograms by means of the subspace projection method. The data kernels for path‐integral data observables do not belong to the model space of allowable phase velocity perturbations, suggesting that constraints on model roughness in the inversion should lead to a better agreement with the long‐wavelength part of the ‘true‧ model than do the commonly‐used constraints on model size. Coherence C between the inverted and the input model is enhanced by using roughness constraints. Estimation of perturbation size is more stable using roughness constraints, but is subject to a positive bias, especially for periods T > 200 s. We can achieve, with a data set of 672 R1 and R2 phase delays, C ≥ 0.9 only for s ≤ 6, suggesting ‘leakage‧ bias caused by the breakdown of the pure‐path assumption.