Azimuthal Variation in the Surface-Wave Velocity in the Arabian Plate

Abstract

This pioneer study determined the azimuthal variation in surface-wave fundamental-mode phase velocity for the Arabian plate, concluding that this variation is not due to seismic anisotropy but to lateral heterogeneity, which is compatible with anisotropic earth models of azimuthal isotropy. The study area was divided in six regions with similar surface-wave phase velocities. We determined their corresponding SH and SV-velocity models versus depth (from 0 to 260 km) by means of the anisotropic inversion of surface-wave phase velocities under the hypothesis of surface-wave propagation in slightly anisotropic media. We observed seismic anisotropy from 10 to 100 km depth. From these models, the parameter ξ was calculated for each region, and the most conspicuous features of the study area were described in terms of this parameter, such as the existence of the plume material propagation in the Arabian shield from the Afar plume, or the existence of a lithospheric keel, which was observed in previous studies beneath the Arabian platform, the Mesopotamian Plain and the Zagros belt.

1. Introduction

Seismic anisotropy can provide direct and independent information on geodynamics through the directional changes in seismic velocities, which can be related to the mantle flow and/or deformation (e.g., [1,2]). This information is particularly interesting for the Arabian plate, because its geodynamics are very complex due to the extensional/compressional regimes that exist around this plate [3]. Shear-wave splitting can be used to estimate anisotropy (e.g., [4]), but this technique provides limited constraints on the depth distribution of the anisotropy. This limitation is overcome if the velocity of the shear waves polarized vertically (β_V) and horizontally (β_H) is calculated versus depth, i.e., determining S-velocity distributions (β_V, β_H) with depth, such as those derived from surface-wave analysis. Thus, the goals of the present study are the determination of the azimuthal variation in surface-wave fundamental-mode phase velocity for the Arabian plate, and the parameter ξ = (β_H/β_V)² versus depth, from the Love- and Rayleigh-wave dispersion curves anisotropically inverted ([5,6]).

2. Data, Methodology and Results

The traces of 109 earthquakes (Supplement 1), registered by the station: RAYN (Supplement 2), have been analyzed to calculate the fundamental-mode surface-wave group velocities. The earthquakes’ epicenters have been grouped into 56 source zones (Supplement 3), as described by Corchete et al. [7]. These source zones are defined as a location in which seismic events with similar epicenter coordinates have occurred, i.e., seismic events with a coordinate difference less than or equal to 0.5 degrees in latitude and longitude. Thus, a path coverage of the study area of 56 source-station paths of surface-wave group velocities is determined (Figure 1a). Figure 1b,c show that the number of paths of Love waves decreases more rapidly than that corresponding to the Rayleigh waves. The group velocities corresponding to these paths have been determined by means of a combination of the Multiple Filter Technique (MFT; [8]) and the Time Variable Filtering (TVF; [9]), as described by Corchete et al. [7]. Figure 2 and Figure 3 show examples of the group-velocity calculation for the Love and Rayleigh waves, respectively. However, the methodology used to determine the seismic anisotropy [5], in the present study, considers phase velocities as observed data. Then, the phase velocities must be determined from their corresponding group velocities. This computation is performed as described by Corchete [6], and Figure 4 shows an example of the phase velocity computation for the group velocities shown in Figure 2c and Figure 3c (magenta line). Figure 5 shows the Love and Rayleigh phase velocities (dispersion curves) determined for the events involved in the path S23-RAYN (Supplements 2, 3 and Figure 1a), and this method is followed to calculate the dispersion curves for all paths shown in Figure 1a, and these curves are fitted to the formula [5].

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 of the wave-number vector. Formula (1) expresses the azimuthal variation in Love and Rayleigh phase velocities through a set coefficients Ai (with i varying from 1 to 5) for each type of wave: Love or Rayleigh. Figure 6 shows this azimuthal variation for the periods: 20, 40, 60 and 80 s; and Figure 7 shows the values of the coefficients Ai with the period T. Figure 8a shows the error ε determined between the phase velocity cth given by Equation (1) and the phase velocities cob (the dispersion curves) determined for the paths shown in Figure 1a. This error ε is calculated by

$$\epsilon (\mathrm{T})=\sqrt{\frac{\sum _{\mathrm{i}=1}^{\mathrm{N}}{\left[{\mathrm{c}}_{\mathrm{o}\mathrm{b}}\left(\mathrm{T}\right)-{\mathrm{c}}_{\mathrm{t}\mathrm{h}}\left(\mathrm{T}\right)\right]}^2}{\mathrm{N}}}$$

(2)

where Ν is the number of paths for each period T (Figure 1b,c) and for each type of wave (Love or Rayleigh). The error ε reaches a minimum value at ~40 s for Love and Rayleigh waves (Figure 8a), and from this value, it remains approximately constant with the period for Rayleigh waves (Figure 8a, blue line), while it increases with the period for Love waves (Figure 8a, red line), because the number of paths of Love waves (Figure 1b) decreases drastically with the period from ~40 s. A new fit of the dispersion curves using Equation (1) is calculated considering only three coefficients Ai (i varying from 1 to 3). Figure 8a (dashed lines) shows that the error ε is greater than that corresponding to the former fit, i.e., the fitting given by Equation (1) with five coefficients is better than that with three coefficients (Figure 8b). Nevertheless, Figure 6 shows that the azimuthal variation in phase velocities is not due to anisotropy but to lateral heterogeneity (Figure 9a; [10]), because Equation (1) does not fit the phase velocities satisfactorily within their errors in general. The best fit of Equation (1) is achieved at the period of 40 s when the coefficients Ai (with i varying from 2 to 5) are in general negligible within their error (Figure 7 and Figure 8a), and the error ε is greater for the period range in which those are not negligible within their error (e.g., 5–40 s; Figure 7 and Figure 8a). This lateral heterogeneity is compatible with anisotropic models of azimuthal isotropy (i.e., hexagonal symmetry or transversely isotropic [11]), which can be calculated if the study area is divided into regions (Figure 1a and Figure 9b). These regions are established considering the areas with similar Rayleigh-wave phase velocities. The Love-wave phase velocities are not considered because they show bigger scatter than the Rayleigh-wave ones (Figure 7 and Figure 8a). In Figure 10b, the Love (black circles) and Rayleigh (black triangles) phase velocities corresponding to the region 1 are shown. They are calculated with the mean of the values determined for each period for the paths plotted in the upper central part of Figure 10 and the small vertical bars present for the Rayleigh-wave values (Figure 10b), which confirms that the dispersion curves considered for this region have similar values. Then, for each region, an isotropic model is defined to calculate the anisotropic model as a small perturbation of this isotropic model ([5,6]). For region 1 (Figure 9b),

Table 1. Region 1 (Figure 9b): Isotropic model considered as initial model (α: P-velocity, β: S-velocity and ρ: density) for the anisotropic inversion of the Love and Rayleigh phase velocities determined for this region.

Thickness (km)	α (km/s)	β (km/s)	ρ (g/cm3)
5	5.63	3.25	2.30
5	5.72	3.30	2.77
20	6.58	3.80	2.85
25	7.36	4.25	3.20
45	7.88	4.55	3.35
60	7.45	4.30	3.40
100	8.31	4.80	3.53
140	8.31	4.80	3.60
100	9.41	5.09	3.64
100	9.72	5.26	3.84
40	9.97	5.26	4.08
30	10.54	5.70	4.16
130	10.68	5.85	4.22
200	11.10	6.26	4.43
200	11.48	6.44	4.61
200	11.78	6.54	4.74
200	12.06	6.64	4.83
$\infty$	12.32	6.75	4.92

shows this isotropic model, which is calculated from the isotropic inversion of the Rayleigh-wave dispersion, which is determined for the paths that are within this region (Figure 10b [7]). The S-velocity of this model (Figure 10a) is plotted only for depths above 260 km due to the poor resolution obtained for greater depths in this inversion process (Figure 10c). The Rayleigh-wave dispersion is properly fitted by this model, but the Love-wave dispersion is not fitted (Figure 10b), i.e., the Love- and Rayleigh-wave dispersions are not compatible with a unique isotropic model. This Love–Rayleigh discrepancy makes it necessary to consider the existence of seismic anisotropy. This anisotropy is considered with hexagonal symmetry [11], in the depth range from 10 to 100 km (Figure 11a [5,6]), to fit satisfactorily both dispersion curves (Figure 11b). For the other regions (Figure 9b), the same process is followed, selecting an isotropic model for each region (Supplements T1, T2, T3, T4 and T5) and calculating its perturbation in terms of S-velocities (Supplements F1, F2, F3, F4 and F5).

Table 2. Parameter ξ = (β_H/β_V)² calculated for the regions shown in Figure 9b, from the SV (β_V) and SH (β_H) velocities shown in Figure 11a and Supplements F1a, F2a, F3a, F4a and F5a.

Depth (km)	Region 1	Region 2	Region 3	Region 4	Region 5	Region 6
10–30	1.08 ± 0.08	1.05 ± 0.08	1.29 ± 0.10	1.25 ± 0.11	1.27 ± 0.10	1.05 ± 0.08
30–55	1.20 ± 0.10	1.02 ± 0.07	1.02 ± 0.07	1.00 ± 0.08	1.14 ± 0.07	1.05 ± 0.09
55–100	1.27 ± 0.10	1.14 ± 0.08	1.09 ± 0.07	1.09 ± 0.07	1.13 ± 0.07	1.00 ± 0.09

shows the values of the parameter ξε resulting from the S-velocities determined for each region of Figure 9b.

3. Interpretation and Discussion

Depth range: 10–30 km (crust). The parameter ξ (Table 2) shows higher values for the regions 3, 4 and 5. For the region 3 and 4, the higher values of ξ agree with the anisotropic perturbation determined for the Mesopotamian Plain by Kim et al. [3]. These higher values of ξ can be related to the lithospheric keel observed beneath the Mesopotamian Plain ([12,13,14]) and can be also related to the vertical alignment of minerals in the crust due to its horizontal shortening [3], caused by the collision between the Arabian and Eurasian plates from ~14 Ma, which has originated a horizontal lithospheric shortening of the Arabian platform, the Mesopotamian Plain and the Zagros belt. For region 5, the higher values of ξ can be related to shape-induced anisotropy, which is caused by small-scale isotropic heterogeneities preferentially oriented in a strain field [11], as can occur in folded zones such as the Oman-folded zone (OFZ, Figure 9a). This shape-induced anisotropy can exist for the crust and the subcrustal lithosphere. This kind of anisotropy is obviously difficult to interpret, because it is related to a complex geodynamic development, and the resultant pattern of deformations is also very complex.

Depth range: 30–100 km (upper mantle). The parameter ξ (Table 2) shows higher values for the regions 1 (30–100 km-depth), 2 (55–100 km-depth) and 5 (30–100 km-depth). For region 1, the higher values of ξ can be related to the plume material propagation in the Arabian shield, from the Afar plume ([14,15,16,17,18,19,20,21]), and to the Yemeni Oligocene Trapps, which was formed by the infiltration of Afar plume material ~30 Ma [22], and it may indicate the existence of magmatic underplating at crustal depths [23]. Also, these higher values of ξ can be related to the post-12 Ma volcanism in western Arabia [17]. For region 2, the higher values of ξ can be related to mantle plume material from the Jordan plume. Chang and van der Lee [17] determined a low-velocity anomaly in their model just beneath Jordan and northern Arabia, and they related this anomaly to the Jordan plume, suggesting that this plume may have formed the Syrian volcanic rocks. Also, these higher values of ξ can be related to the existence of a lithospheric keel, which was observed beneath the Arabian platform and the Taurus-Zagros folded zone (TZFZ) in previous studies ([12,13,14]). The fast axes directions of the shear-wave splitting data determined for this region in previous studies ([4,24,25,26,27,28]) are interpreted as toroidal flow around a lithospheric keel beneath this region by Kaviani et al. [27].

4. Conclusions

A study similar to the present study may be performed, for any plate, to determine whether the azimuthal variation in surface-wave velocities can be due to seismic anisotropy or to lateral heterogeneity. In the present study, this azimuthal variation is not due to seismic anisotropy but to lateral heterogeneity, which is compatible with anisotropic earth models of hexagonal symmetry (six models of SH and SV-velocity versus depth, from 0 to 260 km). From these models, the parameter ξ is calculated for each region, observing seismic anisotropy only from 10 to 100 km depth, and the following conclusions are obtained from the values determined for ξ:

Depth range: 0–30 km. For regions 3 and 4, the higher values of ξ can be related to the lithospheric keel that exists beneath the Mesopotamian Plain and to the vertical alignment of minerals in the crust due to its horizontal shortening, which is caused by the collision between the Arabian and Eurasian plates from ~14 Ma. For region 5, the higher values of ξ can be related to the shape-induced anisotropy that can occur in the Oman folded zone. This shape-induced anisotropy can exist for the crust and the subcrustal lithosphere.

Depth range: 30–100 km. For region 1, the higher values of ξ can be related to the plume material propagation in the Arabian shield from the Afar plume and to the Yemeni Oligocene Trapps. Also, these higher values of ξ can be related to the post-12 Ma volcanism in western Arabia. For region 2, the higher values of ξ can be related to mantle plume material from the Jordan plume. Also, these higher values of ξ can be related to the existence of a lithospheric keel observed beneath the Arabian platform and the Taurus–Zagros folded zone (TZFZ) in previous studies.