Velocity and Attenuation Structure of the Tibetan Lithosphere Under the Hi-CLIMB Array From the Modeling of Pn Attributes

Abstract

Using seismic data from regional earthquakes in Tibet recorded by the Hi-CLIMB experiment, Pn attributes are used to constrain the velocity gradient and attenuation structure of the Tibetan lithosphere under the Hi-CLIMB array. Numerical modeling is performed using the spectral-element method (SEM) for laterally varying upper-mantle velocity and attenuation, and the seismic attributes considered include the Pn travel-time, envelope amplitude, and pulse frequency. The results from the SEM modeling provide two alternative models for the upper-mantle beneath the Hi-CLIMB array in Tibet. The first model is derived from the 3D velocity model of Griffin et al. (Bull Seism Soc Am 101:1938–1947, 2011) with a constant upper-mantle velocity gradient, and laterally varying upper mantle attenuation. The second model has a laterally varying upper-mantle velocity gradient, and constant upper-mantle attenuation. In both cases, the Qiangtang terrane is distinguished from the Lhasa terrane by a change in Moho depth and upper-mantle velocities. The lower upper-mantle velocities, as well as higher Pn attenuation, suggest hotter temperatures beneath the Qiangtang terrane as compared to the Lhasa terrane. Although the fits to the Pn amplitude and pulse frequency data are comparable between the two models, the first model with the constant upper-mantle velocity gradient fits the travel times somewhat better in relation to the data errors.

Appendices

Appendix 1: Specification of the Moment Tensor for 2D SEM Modeling

From Aki and Richards (2002), Eqs. 4.96, 4.97), the ray-theoretical far-field P-wave radiation pattern incorporates the moment tensor using a term $\gamma \,_{p} \,\dot{M}_{p\,q} \,(\,t\, - \,T_{P} \,)\,\gamma_{q}$ where there are implied sums over p and q from 1, 3, γ _p is the unit take-off vector at the source, $\dot{M}_{p\,q} \,(t)\,$ is the time derivative of the moment tensor which for a step source-time function would be the moment tensor elements times a delta function, and T _P is the travel time. If the coordinate system is specified with x ₁ − x ₃ in the plane of incidence of the ray from the source, then the radiation pattern term incorporating the moment tensor for the far-field P-waves can be written in terms of a reduced 2 × 2 moment tensor as $(\,\gamma_{1} \,\,\gamma_{3} \,)\,\left( {\begin{array}{*{20}c} {M_{11} } & {M_{13} } \\ {M_{31} } & {M_{33} } \\ \end{array} } \right)\,\left( {\begin{array}{*{20}c} {\gamma_{1} } \\ {\gamma_{3} } \\ \end{array} } \right)\,\delta \;(\,t\, - \,T_{P} ).$ The elements of this 2 × 2 moment tensor represent the strengths of the couples and dipoles in the plane of incidence of the ray from the source. We first make several 2D azimuthal slices of the 3D moment tensor shown in Fig. 12a along specific azimuths to the receivers and rotate the moment tensor in the azimuthal directions noted by the dashed lines. The dashed circles denote the approximate take-off angles at the source for the Pg and Pn waves from ray tracing using the velocity model from Griffin et al. (2011). The radiation patterns determined from the reduced moment tensor terms given above rotated along the different azimuths are shown in Fig. 12b, and the radiation pattern terms are consistent with the overall focal mechanism pattern given in Fig. 12a.

Fig. 12

a Shows the 3D focal mechanism for a particular double-couple moment tensor source with different azimuth angles given by dashed lines. The regional Pg and Pn take-off angles in Tibet are shown by small circles. b Shows the amplitudes on the focal sphere from the reduced moment tensor for the azimuthal angles given in a as a function of take-off angle derived from the 3D moment tensor. c Shows the SEM envelope amplitudes for the azimuthal angles given in a. Different symbols represent different azimuthal angles

We next compare the calculated P-wave amplitudes for several azimuths using the reduced moment tensor slices derived from the 3D moment tensor and input into the 2D SEM modeling. It was found that to be consistent with the amplitudes for the Pg and Pn arrivals with take-off angles given by the dashed circles given in Fig. 12a, and additional factor of π − az in the azimuth was required for specification in the 2D SEM code and related to how the moment tensor is specified. The Pn and Pg amplitudes computed from the SEM modeling are then shown in Fig. 12c for several azimuths with respect to the 3D focal mechanism in Fig. 12a. For these cases, the SEM amplitudes of the Pg and Pn are consistent with the radiation patterns of the 3D moment tensor.

Appendix 2: Calculation of Seismic Attributes

The amplitude and pulse frequency attributes are obtained following the approach of Matheney and Nowack (1995). The data is first bandpass filtered with a 0.5 to 5 Hz six-pole Butterworth filter to reduce low and high frequency noise. The Hilbert envelope is computed from the analytic signal (Bracewell, 2000). An assessment is first made if the Hilbert envelope sufficiently drops after the first arrival P-wave pulse. If so, a cosine tapered box-car is chosen to window out the first arriving P-wave pulse. If not, then it is assumed that the P-wave pulse is contaminated with later arrivals and the trace is not included for further processing. Once the P-wave pulse is windowed, the peak of the Hilbert envelope is used to measure the pulse amplitude. Following Matheney and Nowack (1995) the instantaneous frequency at the peak amplitude is utilized to estimate the pulse frequency. Damping and weighting are used to stabilize the instantaneous pulse frequencies, although this is less important at the peak of the signal envelope. In addition to the instantaneous pulse frequency estimates, the centroid of the power spectrum weighted by the squared envelope of the windowed pulse is used to estimate the pulse frequency. For noise free data, the averaged instantaneous pulse frequency will approach that of the weighted centroid pulse frequency (Matheney and Nowack, 1995; Nowack and Stacy, 2002), and the consistency of the two values can be used to assess the reliability of the observed pulse frequencies.

An example of a data trace from the Hi-CLIMB array, and a windowed trace and envelope amplitude, are shown in Fig. 13. For the pulse, the amplitude is taken at the peak of the Hilbert envelope. The instantaneous pulse frequency is also obtained at the time where the peak of Hilbert envelope occurs. The centroid pulse frequency is obtained from the weighted centroid of the power spectrum of the windowed seismic pulse. If the envelope does not sufficiently drop after the first arriving pulse of the original data, the trace is not included for further amplitude and frequency analysis (Matheney and Nowack, 1995). Also, if the estimated instantaneous and centroid frequencies are not consistent with each other or with adjacent trace values with distance, then the pulse is assumed to be contaminated with later arrivals and not included for further processing. Both the observed and the calculated data are analyzed using the same processing steps, although only the instantaneous frequency values are shown for the calculated data.

Fig. 13

Example of the windowing of the Pn wave and the extraction of the peak envelope amplitude. The extracted pulse is also used to obtain the instantaneous and centroid pulse frequencies