A Generalized H‐κ Method With Harmonic Corrections on Ps and Its Crustal Multiples in Receiver Functions

Abstract

The H-κ method (Zhu & Kanamori, 2000, https://doi.org/10.1029/1999JB900322) has been widely used to estimate the crustal thickness (H) and the ratio of P to S velocities (V P /V S ratio, κ) with receiver functions. However, in regions where the crustal structure is complicated, the method may produce biased results, arising particularly from dipping Moho and/or crustal anisotropy. H-κ stacking in case of azimuthal or radial anisotropy with flat Moho has been proposed but not for cases with plunging anisotropy and dipping Moho. Here we propose a generalized H-κ method called H-κ-c, which corrects for these effects first before stacking. We consider rather general cases, including plunging anisotropy and dipping interfaces of multiple layers, and use harmonic functions to correct for arrival time variations of Ps and its crustal multiples with back azimuth (θ). Systematic synthetic tests show that the arrival time variations can be well fitted by cosθ and cos2θ functions even for very complex crustal structures. Correcting for the back azimuthal variations significantly enhances H-κ stacking. We verify the feasibility of the H-κ-c method by applying it to 40 permanent stations in various geological setting across the Mainland China. The results show clear improvement after the harmonic corrections, with clearer multiples and stronger stacking energy, as well as more reliable H-κ values. Large differences in H (up to 5.0 km) and κ (up to 0.09) between the new and traditional methods occur mostly in mountainous regions, where the crustal structure tends to be more complex. We caution in particular about systematic bias when the traditional method is used in the presence of dipping interfaces. The modified method is simple and applicable anywhere in the world.Plain Language Summary Crustal thickness and crustal V P /V S ratio are important parameters for regional geology and tectonics. We propose a method that corrects for the effect of crustal anisotropy and dipping interface on receiver functions, which results in more reliable estimation of crustal thickness and V P /V S ratio. Synthetic tests and application to real data suggest that this method is powerful and widely applicable.

Crustal Thickness Beneath the Dinarides and Surrounding Areas From Receiver Functions

“…These stations are mainly located in the External Dinarides where strong crustal discontinuities obscure or interfere with the signal from the deeper Moho interface, which is reflected in the uncertainty estimation (Figure b). In a recent paper, Li et al () warn that in the areas where Moho dip is considerable (as is the case here), and/or anisotropy is not negligible, application of traditional H − κ may produce biased results. Likewise, Ogden et al () showed that gradational Moho, as well as complicated crustal structure, will also have adverse effect on the accuracy and confidence of results.…”

“…Hopefully, our results will be updated with additional data from various other regional studies currently in progress, possibly also using novel approaches and methods. In particular, it seems that the H − κ– c algorithm (Li et al, ) that uses harmonic corrections for RFs to minimize the influence of dipping Moho as well as of the crustal S‐wave anisotropy, could be beneficial in this area of pronounced Moho topography.…”

“…Grad and Tiira () give an overview of other possible sources of error in H − κ analyses, and Lombardi et al () use synthetic PRFs to warn of overestimation of H by the H − κ method for dipping interfaces. Li et al () performed a thorough analysis of the adverse impact that Moho dip and crustal anisotropy have on estimated H and κ , and Ogden et al () also analyze the considerable influence of gradational Moho, heterogenous crust, and the choice of processing parameters on the final results. In our case, one of the important possible ambiguities stems from multilayered crust.…”

Crustal SiO2 Content of the Emeishan Large Igneous Province and its Implications for Magma Volume and Plumbing System

“…However, in the presence of complicated crustal structures or properties, such as the dipping Moho and crustal anisotropy, the H ‐ κ results can be biased owing to the deviation from the premise hypothesis of laterally homogenous and isotropic crust (Hammond, 2014; Tan et al., 2018). Here, we use a generalized H ‐ κ method with the harmonic correction, to minimize the biases due to the dipping Moho and crustal anisotropy (i.e., the H ‐ κ ‐ c method, J. Li et al., 2019). After correcting azimuthally dependent variations of the Moho Ps phase and crustal multiples in the 2 π or π periodicity, which could be induced by the interface inclination and azimuthal anisotropy, respectively (Savage, 1998), the H ‐ κ ‐ c method provides a more reliable H ‐ κ result based on more identical multiples and focused stacking energy (Figure 2).…”

Distinct Orogenic Processes in the South‐ and North‐Central Tien Shan From Receiver Functions

“…We also estimate crustal thickness (H) and Vp/Vs ratio (k) at each station using a modified H-k stacking scheme with harmonic corrections (H-k-c) (Li et al, 2019;Zhu & Kanamori, 2000). The algorithm resolves and removes the degree-1 and degree-2 back-azimuthal harmonic variations of Moho Ps and two crustal multiples and then performs the traditional H-k scheme on the harmonic-corrected RFs to calculate the optimal solution of H and k. Standard deviations are estimated using the bootstrapping resampling technique (Efron & Tibshirani, 1986).…”