Azimuthal Variation in the Surface Wave Velocity of the Philippine Sea Plate

Abstract

A study of the azimuthal variation in the surface wave fundamental-mode phase velocity is performed for the Philippine Sea Plate (PSP). This azimuthal variation has been anisotropically inverted for the PSP to determine the isotropic and anisotropic structure of this plate from 0 to 260 km. This azimuthal variation is due to anisotropy in the upper mantle. The crust is found in an isotropic structure, but the lithosphere and asthenosphere exhibit anisotropic structures. For the lithosphere, the main cause of anisotropy is the alignment of anisotropic crystals approximately parallel to the direction of seafloor spreading, and the fast axis of the seismic velocity is in the direction of ~163° of azimuth. For the asthenosphere, the seismic anisotropy can be derived from the lattice-preferred orientation (LPO) in response to the shear strains induced by mantle flow, and the fast axis of the seismic velocity is also the direction of ~163° of azimuth. This result suggests that a mantle flow pattern may occur in the asthenosphere and seems to be approximately parallel to the direction of seafloor spreading observed for the lithosphere. Finally, the changes in the parameter ξ with depth are studied to estimate the depth of the lithosphere–asthenosphere boundary (LAB), observing a clear change in this parameter at 80 km depth.

1. Introduction

The Philippine Sea Plate (PSP) is considered a single plate because it has a very scarce intraplate seismicity. The detailed investigation of the crustal, lithospheric, and asthenospheric properties of this plate was started in previous studies (e.g., [1]) and will be completed with the present study of seismic anisotropy. This investigation is not only scientifically interesting but also necessary to achieve an understanding of the geodynamic and geological processes in this unique region of the western Pacific. The seismic anisotropy provides direct and independent information on geodynamics (e.g., [2,3,4]), and particularly, the azimuthal variation in the surface wave velocity due to anisotropy is an indicator for the mode of deformation in the lithosphere and the asthenospheric flow (e.g., [5,6]). Thus, the determination of this azimuthal variation for the PSP is the goal of the present study, and this azimuthal variation will be also anisotropically inverted [4,7] to determine the anisotropic structure of this plate.

2. Data, Methodology, and Results

The traces of 46 earthquakes (Supplement S1), registered by 30 stations (Supplement S2), have been selected to calculate the fundamental-mode surface wave group velocities, following the methodology described by Corchete [4]. In Supplement S3, the stations with a coordinate difference less than or equal to 0.4° in latitude and longitude were grouped in averaged stations (new station codes). Supplement S4 lists the surface wave paths determined for each station, with their recorded events (events involved) grouped by similar azimuth (differences < 0.4° of azimuth). The path coverage is shown in Figure 1a. Figure 1b,c show the number of paths (Supplement S4) calculated for each period of Love and Rayleigh waves. The group and phase velocities corresponding to the traces of the involved events (Supplement S4) have been determined as described by Corchete [4]. Figure 2 and Figure 3 show an example of this Love and Rayleigh group velocity computation, respectively, for the traces of event #40. Figure 4 shows the phase velocities corresponding to the final group velocities shown in Figure 2c and Figure 3c (magenta lines). Figure 5 shows the Love and Rayleigh phase velocities (dispersion curves) determined for the events involved in the path FAKI01 (Supplement S4). This method is followed to calculate the dispersion curves for all paths shown in Figure 1 (Supplement S4), and these curves are fitted to the following formula:

c(ω, θ) = A₁(ω) + A₂(ω) cos 2θ + A₃(ω) sin 2θ + A₄(ω) cos 4θ + A₅(ω) sin 4θ

(1)

where c is the phase velocity, ω = 2π/T, T is the period, and θ is the azimuth (Supplement S4) of the wave number vector [7]. Formula (1) expresses the azimuthal variation in the phase velocities through a set of coefficients A_i (with i varying from 1 to 5: Figure 6; with i varying from 1 to 3: Figure 7; and with i varying from 1 to 2: Figure 8) for each type of wave: Love or Rayleigh. Figure 9 shows the error ε determined between the phase velocity c_th given by (1), and the phase velocities c_ob determined for the paths shown in Figure 1a (the dispersion curves). This error ε is calculated by the following:

$$\epsilon (\mathrm{T})=\sqrt{\frac{\sum _{i=1}^N{\left[c_{ob}\right(T)-c_{th}(T)]}^2}{N}}$$

(2)

where N is the number of paths (Figure 1b,c) for each period T and for each type of wave (Love or Rayleigh). This error increases drastically (ε > 0.1 km/s) for periods less than 30 s (Love wave) and less than 20 s (Rayleigh wave). Consequently, the sets of coefficients A_i shown in Figure 6, Figure 7 and Figure 8 are considered only from 30 s for the Love wave, and from 20 s for the Rayleigh wave. In Figure 9, it should be noted that the error ε determined considering five (Figure 6) or three (Figure 7) A_i coefficients in Formula (1) is really very similar, i.e., the inclusion of A₄ and A₅ (Figure 6) in Formula (1) does not give better results in terms of error, and the errors in A₄ and A₅ (vertical lines, Figure 6) are greater than their values. On the other hand, the error ε increases when only two A_i coefficients (Figure 8) are considered. Thus, the best fit of the dispersion curves given by (1) is achieved with a set of coefficients shown in Figure 7 (three A_i coefficients). Figure 10 shows the azimuthal variation in the Love and Rayleigh phase velocities determined by Formula (1), with five (grey line, Figure 6) and three (black line, Figure 7) coefficients for some selected periods.

Table 1. Azimuths ${\mathrm{A}}_{\mathrm{z}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ and ${\mathrm{A}}_{\mathrm{z}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$ of the maximum (${\mathrm{c}}_{\mathrm{L}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$) and minimum (${\mathrm{c}}_{\mathrm{L}}^{\mathrm{m}\mathrm{i}\mathrm{n}}$) Love wave phase velocity, respectively, is determined from the azimuthal variation (Figure 10) calculated by Formula (1), with the coefficients shown in Figure 7.

Period (s)	${\mathbf{A}}_{\mathbf{z}}^{\mathbf{m}\mathbf{a}\mathbf{x}}$ (degrees)	${\mathbf{c}}_{\mathbf{L}}^{\mathbf{m}\mathbf{a}\mathbf{x}}$ (km/s)	${\mathbf{A}}_{\mathbf{z}}^{\mathbf{m}\mathbf{i}\mathbf{n}}$ (degrees)	${\mathbf{c}}_{\mathbf{L}}^{\mathbf{m}\mathbf{i}\mathbf{n}}$ (km/s)
30	160.00	4.42	69.09	4.29
35	163.63	4.46	73.63	4.33
40	163.63	4.49	73.63	4.37
45	163.63	4.52	73.63	4.41
50	163.63	4.54	73.63	4.42
55	163.63	4.57	73.63	4.43
60	163.63	4.59	73.63	4.44
65	163.63	4.61	73.63	4.46
70	163.63	4.63	73.63	4.47
75	163.63	4.64	73.63	4.50
80	163.63	4.66	73.63	4.52

lists the azimuths of the maximum and minimum Love wave phase velocity values (from 30 to 80 s) determined from this azimuthal variation (Figure 10) calculated by Formula (1), with the coefficients shown in Figure 7. It should be noted that the differences between these maximum and minimum velocities for each period are in general less than 3%. These small differences support the hypothesis of slight anisotropy, such as is defined by Babuska and Cara [8]. The Rayleigh wave is not listed because the difference between maximum and minimum is less than its error (Figure 10). The set of coefficients shown in Figure 7 will be considered as the observed data in the anisotropic inversion. For A₁, the values calculated for the periods greater than 100 s will be discarded for inversion because the number of paths N (Figure 1b,c) decreases rapidly while the error in the values increases (Figure 7) for this period range. For A₂, the values calculated for the periods greater than 80 s will be discarded for inversion because the errors in the Love wave values (vertical lines, Figure 7) are greater than these values from the 80 s period. For A₃, the Love and Rayleigh wave values are less than their errors (for all period ranges) and will be also discarded for inversion. The anisotropic inversion is calculated following the methodology detailed by Corchete [4,7], in which an isotropic model must be defined to calculate the anisotropic model as a small perturbation of this isotropic model. The methodology described by Corchete [7] is a revision of that published previously by Corchete and Badal [9], considering the problem of the non-uniqueness in geophysical inversions. More recently, this methodology [7] was revisited by Corchete [10], who presents a novelty in this issue considering the canonical harmonic components [11] ${\mathsf{\gamma }}_{\mathrm{S}}^{00\mathrm{c}}$, ${\mathsf{\gamma }}_{\mathrm{A}}^{00\mathrm{c}}$, ${\mathsf{\gamma }}_{\mathrm{S}}^{20\mathrm{c}}$, ${\mathsf{\gamma }}_{\mathrm{A}}^{20\mathrm{c}}$, ${\mathsf{\gamma }}_{\mathrm{A}}^{40\mathrm{c}}$ as linear functions of the P-velocities (α_H, α_V) and S-velocities (β_H, β_V) through the perturbations ${\gamma }_{ijkl}$ of the stiffness tensor [7,8,11]. Then, if a relation of $\mathsf{\alpha }=\sqrt{3}\mathsf{\beta }$ is assumed between the P- and S-velocities, the unknowns of the inverse problem can be reduced from five canonical harmonic components to two S-velocities, facilitating the fit of the observed data. This improvement was considered by Corchete [4] and applied in the present study, considering the isotropic model as that calculated from the isotropic inversion of the Rayleigh wave phase velocities shown in Figure 7 (A₁ coefficient, black triangles), as described by Corchete et al. [12]. In Supplement S5, the isotropic initial model necessary to perform this inversion is listed, and Figure 11 shows this inversion process, which results in the isotropic model (Supplement S6) used to perform the anisotropic inversion [4]. Figure 12 shows the results of this anisotropic inversion for layers 4 to 7 of Supplement S6 (from 15 to 240 km depth), and the corresponding values of the SH- and SV-velocities are shown in Figure 12a. Figure 12b–d show the satisfactory fit of the observed data, (A₁, A₂) for Love wave (black circles) and Rayleigh wave (black triangles), which was achieved by the theoretical values of (A₁, A₂) calculated from this inversion. In

Table 2. The SH-velocity (β_H) and SV-velocity (β_V) values shown in Figure 12a were calculated from the anisotropic inversion of the A₁ and A₂ coefficients shown in Figure 7 (triangles and circles), which are listed for the layers from 4 to 7 of Supplement S6. The parameter ξ is calculated as defined by Corchete [4].

Layer (n)	βH (km/s)	βV (km/s)	ξ (βH/βV)2
4	4.25 ± 0.07	4.11 ± 0.06	1.07
5	4.59 ± 0.08	4.45 ± 0.08	1.06
6	4.49 ± 0.08	4.21 ± 0.07	1.14
7	4.65 ± 0.08	4.44 ± 0.08	1.10

, the parameter ξ is calculated from the SH- and SV-velocities (Figure 12a) determined for the layers 4 to 7 of Supplement S6, as described by Corchete [4,10].

3. Interpretation and Discussion

Isotropic crust: depth range from 0 to 15 km. The azimuthal variation in surface wave velocities in the short-period range (<30 s Love waves, <20 s Rayleigh waves) is due to the lateral heterogeneity that occurred in an isotropic crust (Figure 12a, grey line), which has been already described in previous studies (e.g., [1,13,14]). The S-velocity values determined by Corchete [1] at the southwest of the PSP are higher than those shown for the other regions of the PSP because of the thin crust that exists in these areas. Corchete [1] determined S-velocities in the western part of the PSP to be higher than those in the eastern part because the crust is thinner in the western part. The eastern and northeastern parts of the PSP show a thickened crust, particularly in the ridges and their surrounding area.

Anisotropic lithosphere: depth range from 15 to 80 km. The anisotropy in the Earth’s upper mantle is a widely established result, and the azimuthal variation in surface wave velocities for the oceanic regions is due in many cases to anisotropy [8]. In the lithosphere, the main cause of anisotropy is the alignment of anisotropic crystals (generally olivine and/or orthopyroxene) approximately parallel to the direction of seafloor spreading, i.e., the lattice-preferred orientation (LPO) approximately parallel to the direction of seafloor spreading [15]. Most studies of azimuthal anisotropy that use surface wave data adopted the LPO interpretation because it is more consistent with the geothermal and rheological conditions at the depth range resolvable by the surface wave dispersion [6]. The fast axis of the seismic velocity is related to this LPO, and in the present study, this direction is ~163° of azimuth for the Love wave phase velocity (Table 1). This result suggests that the alignment of the crystallographic axes may occur in the lithosphere, not only in large oceanic plates (such as the Pacific plate) but also in smaller plates such as the PSP.

Anisotropic asthenosphere: depth range from 80 to 240 km. The seismic anisotropy can be derived from the LPO in response to the shear strains induced by mantle flow (e.g., [15]) and from the shape-preferred orientation (SPO) due to the presence of melt-rich layers embedded in the asthenosphere [16]. The fast axis of the anisotropic crystals is usually assumed as aligned with the mantle flow direction, and the seismic anisotropy is usually interpreted in terms of this flow pattern (e.g., [17]). Therefore, it is important to study this anisotropy in the asthenosphere to reveal its dynamic processes (flow patterns). There are many different processes in the context of plate tectonics capable of producing a mantle flow pattern (and its corresponding LPO). Also, there is a strong correlation between the seismic anisotropy (observed at asthenospheric depths) and the directions of current plate motions (e.g., [18]). In general, the preferred explanation for observed seismic anisotropy is the establishment of the LPO in response to the shear strains induced by mantle flow. In the present study, the fast axis of the seismic velocity related to this LPO is the direction of ~ 163° of azimuth for the Love wave phase velocity (Table 1). This result suggests that a mantle flow pattern may occur in the asthenosphere, and seems to be approximately parallel to the direction of seafloor spreading observed in the lithosphere.

Parameter ξ (Table 2): depth range from 15 to 240 km. The changes in this parameter with depth can be used to estimate the depth of the lithosphere–asthenosphere boundary (LAB; [19]), instead of the typical mapping of S-velocity with depth that is usually performed for a study area (e.g., [1]). In the present study, the values ξ clearly show a change between the lithosphere (1.06) and asthenosphere (1.14) at 80 km depth. This depth fits very well with the location in the depth of the LAB mapped in previous studies using Rayleigh wave tomography (e.g., [1]). The values of ξ determined in this study are in good agreement with other previous studies (e.g., [5]).

4. Conclusions

The azimuthal variation in the surface wave velocities was calculated and anisotropically inverted for the PSP to determine the anisotropic structure of this plate. This azimuthal variation in the short-period range (<30 s Love waves, <20 s Rayleigh waves) is due to the lateral heterogeneity occurring in an isotropic-type crust. For greater periods, this azimuthal variation is due to anisotropy in the upper mantle. In the lithosphere, the main cause of anisotropy is the alignment of anisotropic crystals approximately parallel to the direction of seafloor spreading. The fast axis of the seismic velocity is related to this LPO, and in the present study, this direction is ~163° of azimuth. In the asthenosphere, the seismic anisotropy can be derived from the LPO in response to the shear strains induced by mantle flow. The fast axis of the anisotropic crystals is then usually assumed as aligned with the mantle flow direction, and the seismic anisotropy is usually interpreted in terms of this flow pattern. This result suggests that a mantle flow pattern may occur in the asthenosphere, and seems to be approximately parallel to the direction of seafloor spreading observed in the lithosphere. Finally, the changes in ξ with depth are studied to estimate the depth of the LAB, observing a clear change in this parameter between the lithosphere and asthenosphere at 80 km depth. This depth fits very well with the location in depth of the LAB mapped in previous studies.