Receiver functions are the time series that show the relative response of earth structure near the receiver. Computation of receiver function needs teleseismic earthquake events recorded at a three-component seismograph. An incident teleseismic P-wave will generate converted S wave at boundaries which have significant and sharp velocity contrast, like Moho discontinuity and basement[1]. The converted S wave will arrive at the seismometer right after the P wave arrival and the difference in travel time contains information about the depth of conversion point and P- and S-wave velocity. The receiver functions are computed by deconvolving the incoming P wave and converted S wave of the seismogram which removes the common part of the components while the resulting waveform is the receiver function[2].

Figure 1. The theoretical waveform of the receiver function of the two-layer model. Note that PpPhs, PpShs, PsPhs, PsShs are generated by multiple reflections.

## Method

Figure 2. Sketch illustrating the LQT coordinate system where L is aligned in direction of P wave propagation; Q is aligned in the direction of the SV phase movement; T is aligned in the direction of the SH phase movement.
Figure 3. Data example of an earthquake event data, waveform converted according to LQT coordinate system and receiver function result. a) North, East, and Vertical component of a teleseismic event. P wave coda in East and North component represent the converted S wave energy. b) Waveform converted according to LQT coordinate system. c) Radial receiver function time series from deconvolving L component from Q component.

As the P-wave passed upward in the mantle to Moho, it is partially converted into S wave, also known as the Ps phase in earthquake seismogram. Besides the P and Ps phase, other phases including PpPhs, PsPhs, and PpSs are generated by multiple reflections (Fig. 1). Both P wave and converted S wave is recorded by the seismometer near the conversion point while the converted S wave arrives the receiver later after the P wave arrival due to the velocity difference for P wave and S wave. Converted S wave is best recorded at the epicentral distance between 30° and 90° and is contained mainly in the horizontal components. The Ps energy can be isolated from direct P wave by rotating the seismograms recorded in three-component seismometer to LQT coordinate system (Fig. 2) where the L component is in the direction of the incident P wave; the Q component is perpendicular to the L and the T component is the third component of the LQT right-hand system. To eliminate the influence of the source and ray path, an equalization procedure is applied by deconvolving the R component with the P signal on the Z component. The resulting time series are named P receiver function (Fig. 3).

Figure 4. Example of a receiver function profile. Stacked receiver functions of each are displayed in a profile across north Oklahoma.

By integrating processing technics like H-k stacking, common conversion point stacking, move-out correction, migration, etc., the receiver function can provide a good estimation of Moho depth, crustal P-to-S velocity ratio, and imaging of crustal structures. 2D or 3D model of the depth of the Moho can be built with receiver functions of adjacent stations. A 2D cross-section image of the subsurface beneath the stations can be formed by putting receiver functions side by side, which shows the topography of Moho along with this profile (Fig. 4).

## Application

Receiver functions are widely used in deep earth structure studies as well as in studies that focused on inner-crust structures. For example, receiver functions were used to study the lithosphere-asthenosphere boundary (LAB) beneath the Philippine sea[3]. High-resolution receiver functions in near spaced seismometer are used to image the shallow crust structure in California[4]. Additionally, maps of seismic velocities and crustal thickness are useful as baseline data for additional seismological studies.