Wave Gradiometry / Wave Gradient Analysis

(1) Theory. (2) Application to the USArray.

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(2) Wave gradiometry applied to the USArray.

USArray provides an excellent test-bed for the Wave Gradiometry (WG) technique. In this section, we present results from waveforms recorded by USArray from 4 earthquakes from different azimuths. The ray paths of 4 earthquakes are shown in the Figure 1b. This method can ideally be applied to any identifiable phases. The applications for Rayleigh waves and body waves are present in section (2.1) and (2.2), respectively.

(2.1 ) Surface waves.

Figure 1a is a snapshot of the USArray. Figure 1b shows ray paths used in this study. Only results from one earthquake are discussed on this page though. The 4 WG parameter maps determined by WG are shown in the Figure 2. Figure 3 shows how the azimuth variations determined by WG can be associated with tectonic structure along wave paths.

Figure 1a: USArray and Western US (left). A snapshot of the USArray station coverage (dots) plotted on top of the topography (color). The magenta, black and blue lines are major faults, state boundaries and major rivers, respectively. Station coverage only represents the USArray on January 13, 2007. Waveforms recorded on these stations from the Kurile Island earthquake on this day are applied to WG method and results are plotted in the Figure 2.

Figure 1b: Ray paths of 4 earthquakes used in this study. But only results from the Kurile Islands earthquake are discussed on this page. More details refer to our paper (5).

Figure 2. Four WG parameter maps. Four maps derived from an earthquake from the Kurile Islands (see Figure 1b). Formula for four parameters are listed in equation (5a-5d). The geometrical spreading and radiation pattern should be understood as amplitude variations in the radial and azimuthal directions, respectively. See the “Interpretations” for details.

Figure 3: Ray paths and azimuth variations of the Kurile Islands earthquake. The azimuth variation map is the same as the Figure 2b. All rays south of the Aleutian subduction zone have negative azimuth variations, that is, smaller computed backazimuths than great circle backazimuths. Ray paths passing the subduction zone are far more complicated.

Interpretations:

(a) Phase velocity: Phase velocity perturbations (Figure 2a) with respect to an average velocity of 4.05km/s. The western coast of the US is dominated by high velocities while the Basins and Ranges province is characterized by low velocities with scattered high velocity bodies. The Snake River is associated with a very low velocity belt that separates velocity low and high to its south-southwest and north-northeast, respectively. These observations provide further evidences for the theory that the Snake River valley represents the track of the hot spot associated with the nowadays Yellowstone. The general feature observed in this study is also consistent with the velocity map inverted using traditional two station method using the USArray dataset [Yang, 2008a, Moschetti, etal, 2007].

(b) Azimuth variations: Strong path direction dependency is obvious for azimuth variations in Figure (2b). Figure 3 shows both ray paths and the azimuth variations. A velocity contrast of 0.25km/s between the oceanic lithosphere to west and the continental lithosphere to east is enough to account for the negative anomaly at California and western Nevada. On the other hand, for rays passing the Aleutian subduction zone, the patterns are complicated.

(c) Geometrical Spreading: The geometrical spreading map (Figure 2c) shows little distance dependency. Instead, strong anti-correlation between the phase velocity map and the geometrical spreading map is observed. For example, the high velocity western coast of US is associated with the negative geometrical spreading. Such relationship may be due to the focus and defocus of surface waves.

(d) Radiation Pattern: Similar to the azimuth variation, the radiation pattern (Figure 2d) is also strongly dependent on ray paths. This suggests that the dramatical azimuthal amplitude variation may be due to the scattering along the path. Similar to the azimuth variations, the Aleutian subduction zone may also play a big role to change the amplitude azimuthally.

(2.2 ) Body waves: in preparation.

References:

(1) Langston, C. A.(2007), Spatial Gradient Analysis for Linear Seismic Arrays, BSSA, Vol. 97, No. 1B, 265-280.

(2) Langston, C. A.(2007), Wave Gradiometry in Two Dimensions, BSSA, Vol. 97, No. 2, 401-416.

(3) Langston, C. A.(2007), Wave Gradiometry in the Time Domain, BSSA, Vol. 97, No. 3, 926-933.

(4) Langston, C. A. C. Liang (2008), Wave Gradiometry for polarized waves, in review.

(5) Liang, C., C. A. Langston (2008), Wave Gradiometry for USArray, in review.