Virtual receiver functions via conditional diffusion transformers for robust crustal imaging

Abstract

Receiver functions (RFs) are widely used to image crustal and upper-mantle structure, and their variation with backazimuth and epicentral distance contains key information about layering and azimuthal anisotropy. In practice, however, RFs are contaminated by nuisance effects from unknown earthquake source signatures and seismic noise, which obstruct reliable crustal imaging. Sparse RF coverage across backazimuths and epicentral distances also leads to biased anisotropy estimates. We address these challenges using conditional diffusion models, conditioned on backazimuth, epicentral distance, and station coordinates, to produce high-quality virtual radial and transverse RFs. RFs from earthquakes with similar backazimuths and epicentral distances share consistent crustal responses but differ in nuisance effects, allowing the model to suppress the latter. Our framework generates virtual RFs within gaps in backazimuth and epicentral distance coverage, enhancing the interpretation of crustal anisotropy and layering. On synthetic RFs with realistic non-Gaussian noise, virtual RFs correlate more strongly with the true RFs than traditional linear or phase-weighted stacking. Applied to the Cascadia Subduction Zone, virtual radial RFs sharply image scattered S-waves from the dipping slab, with enhanced phase clarity and backazimuthal coverage relative to previous work. In southern California, anisotropy parameters inferred from virtual RFs are spatially coherent and consistent with regional fault geometry. Our approach leverages all available RFs, regardless of quality, to increase spatial coverage and support robust, automated RF analysis.

Figures (10)

• Figure 1: A schematic illustration of the diffusion-based generation of virtual RFs. The top box depicts the forward diffusion process, where the joint probability density function (pdf) of crustal and nuisance effects evolves over diffusion time steps $T$. The bottom box illustrates the generation process, where the trained diffusion model transforms random samples from a Gaussian pdf into realistic RFs conditioned on either $\mathbf{c}^{(i)}$ or $\mathbf{c}^{(j)}$. (a) Measured RFs for two conditions $\mathbf{c}^{(i)}$ and $\mathbf{c}^{(j)}$ (e.g., two different backazimuths) are shown as blue and black diamond markers. (b) and (c) The forward diffusion process gradually adds noise to the RFs in (a) leading to a joint pdf that becomes increasingly blurred and eventually converges to a Gaussian distribution at large $T$ as shown in (d). (e) During the generation process, we start with random samples drawn from the Gaussian distribution, and either condition using $\mathbf{c}^{(i)}$ (plus markers) or $\mathbf{c}^{(j)}$ (square markers), to gradually transform these samples into realistic RFs as shown in (f) and (g). (h) The generated RFs exhibit high variance along nuisance directions and low variance along crustal-effect directions, reflecting the structure in (a). By averaging these generated RFs for a specific condition, we obtain virtual RFs with reduced nuisance effects (plotted using star markers).
• Figure 2: Radial and transverse RFs from the synthetic experiment, derived using (a) diffusion transformer (b) linear bin-wise averaging and (c) phase-weighted averaging, are compared to (d) true RFs. A station with a dipping $30$km thick crustal layer is considered.
• Figure 3: Enhancement of RFs for the synthetic experiment, where the quality of the (a) radial and (b) transverse RFs, plotted in Fig. \ref{['fig:model1']}, is assessed using the normalized correlation coefficient. On average, the normalized correlation coefficient of the generated virtual RFs is higher than that of linearly averaged and phase-weighted RFs, indicating higher correlation with the true RFs. The backazimuth distribution of the synthetic dataset is realistic, with a highlighted gap between $100^{\circ}$ and $120^{\circ}$.
• Figure 4: Map illustrating the tectonic setting and positions of the stations (represented by black and white triangles) utilized in the study. This map also depicts the subduction of the Juan de Fuca plate beneath the North American plate, occurring at a rate of $42$ mm/yr DeMets1994 (indicated by a black arrow). The solid black line adorned with triangles marks the subduction boundary. Stations are from the POLARIS POL, C8 c8, CN cn, and UW uw networks. This paper plots RFs from stations marked by blue inverted triangles that are approximately positioned along a transect.
• Figure 5: (a) Virtual and (b) linearly averaged radial RFs at seismic stations (Fig. \ref{['fig:casmap']}) traversing the Cascadia subduction zone. The RFs in (b) are computed for the backazimuth bin centered at $300^{\circ}$. Panel (c) shows the epicentral-distance bin corresponding to (b). The virtual RFs in (a) span epicentral distances from $35^{\circ}$ to $85^{\circ}$, with the backazimuth fixed at $300^{\circ}$. Key seismic phases from the subducted slab (highlighted by colored lines) are more clearly resolved in the virtual RFs than in the linearly averaged RFs. The phase notation follows Bloch2023, as listed in Tab. \ref{['tab:phases_notation']}