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S U M M A R YWe jointly invert teleseismic radial-component receiver functions and regional Rayleigh and Love surface-wave group velocities for 1-D shear-wave velocity structure beneath station TBZ located on the northern side of the eastern Pontides. An influence factor is employed to control the relative influence of receiver function and surface-wave dispersion on the resultant velocitydepth profile. Radial-and transverse-component receiver functions at station TBZ exhibit an azimuthal amplitude and polarity pattern consistent with 2-D receiver structure that has a general dip direction towards approximately south. The radial-component receiver functions are least affected by the dipping structures along the strike direction and thereby we prefer teleseismic events sampling along-strike structures to alleviate the deflecting effect of dipping interfaces on the 1-D solution. The 1-D inversion effectively reveals the two-layer nature of the crust which is perturbed by high-and low-velocity layers, and serves as a provisional model for the 2-D forward modelling. Minor-to-moderate changes to the 1-D model, such as changing depth to and velocity contrast across an interface, are needed to achieve the results with the 2-D modelling. Dipping interfaces and seismic anisotropy are included in the 2-D modelling to fit both radial-and transverse-component receiver functions.The upper crust is characterized by a shear velocity of ∼3.5 km s −1 and cut through by a 4 km thick high-velocity (i.e. ∼3.8 km s −1 ) layer. Overlying the upper crust, the sedimentary cover (i.e. the top 5 km) has velocities within the range ∼2.0-3.5 km s −1 . A mid-crustal velocity discontinuity between the upper granitic crust and the lower basaltic crust is identified at ∼16-km depth. This boundary is analogous to the mid-crustal discontinuity found under the Black Sea basin across which the shear velocity jumps from 3.5 to 4.1 km s −1 . A relatively thick (i.e. ∼12 km) low-velocity layer in the lower crust with a velocity reversal from 4.1 to 3.7 km s −1 is needed to better explain reverberations off this depth range. We infer a 2-D Moho discontinuity placed at ∼35-km depth beneath the station. The proposed dip angle for the Moho is rather steep (i.e. ∼25 • ), although coincident with regional gravity studies. The associated Sn velocity (i.e. ∼4.4 km s −1 ) is rather low, indicating disturbed upper-mantle structure beneath the region. Initial amplitudes of transverse-component receiver functions are rather energetic, for which we propose substantial P and S velocity anisotropy (∼12 per cent) for the topmost depths (<5 km).

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S U M M A R YWe used the Green's function method to describe the multiple scattering of surface waves generated by interactions with the complex 3-D earth structures. The basic process involves an integral equation of convolutional type. An efficient multilevel fast multipole method is utilized to accelerate the matrix-vector products that correspond to the integrals on the horizontal plane. This new algorithm is shown to be quite successful when compared to its more traditional complement (e.g. direct integration method, DIM) with particularly the large number of data points. The fast execution is achieved through well-organized truncated multipole expansions, functions grouping and translation operators. In general, the new algorithm has a fruitful logarithmic time complexity as opposed to an uncomfortable exponential time complexity attainable with the traditional algorithms. This algorithm requires the user provide some important parameters to operate. One of them is the truncation number of the infinite series associated with the multipole expansions for which two linear relationships are derived for an automatic determination. The other central parameter is the clustering number that is used to group data points in the data structure. We showed that the clustering number around 5 is mostly an optimum value providing a minimum run time. However, greater clustering numbers (i.e. ∼10) become necessary for an optimum operation when the number of data points gets real large.In order to test the convergence of the current algorithm we compared our numerical results with analytical solutions provided for cylindrical obstacles by other researchers. A halfspace model in which the total wavefield is represented by a finite number of propagating modes describes the reference structure. Not all waves are trapped in this representation since leaking modes and body waves downward radiating into the half-space can exist. The comparisons with the exact solutions revealed that the quality of vertical component amplitudes is reasonably well while some amplitude discrepancies on the horizontal components particularly near and inside the heterogeneities exist. Extra fast half-space velocities complementing the deficiencies on the modal structure greatly help reduce the discrepancies on the horizontal components.

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