Triplications on traveltime surface for pure and converted wave modes in elastic orthorhombic media

Named by the bowtie shape in traveltime surface, triplications can cause a serious problem in seismic processing such as the data with phases arrive close in time and overlap with each other, which should be properly handled or avoided for tomography and other inversion methods. Compared with transversely isotropic (TI) media, the triplication in orthorhombic (ORT) medium is more complicated and seldom investigated since two S waves behaviour differently and the presence of singularities. In order to analyse the triplication condition for pure and converted waves in ORT media, we define the local curvature defined by the elliptic function. For a given point at the slowness surface, three possible cases are analysed for the existence of the triplications. Tested in the numerical examples, the triplications for all wave modes are examined from the defined function. We show that the triplications for S waves caused by singularities and concave curvature behave differently. For converted PS1 and PS2 waves, the triplications are only induced by singularities. In order to see the impact from different type of triplication on the wave front that can be referred accordingly when handling the seismic data, we illustrate the anomalous behaviour of the traveltime surface in ORT model due to the presence of triplications for different cases.