A ten-degree dip on the Moho can move a station's crustal-thickness estimate by about two kilometres and its Vp/Vs by a few hundredths. That is enough to reclassify the crust as felsic when it is mafic. And the H-κ stack that produced the wrong number will look perfectly healthy, because the assumption it violated is baked in so deep that nobody sees it break.
The assumption you signed without reading
H-κ stacking [1] is the workhorse of crustal receiver-function analysis. Take a station's receiver functions and, for a grid of candidate crustal thicknesses H and Vp/Vs ratios κ, sum the receiver-function amplitude along the predicted arrival-time curves of the direct Ps conversion and its two crustal multiples, PpPs and PpSs+PsPs. Where the three phases stack constructively you get a maximum, and you read H and κ off it. It is elegant, it is fast, and it assumes, silently, in the moveout equations themselves, that the Moho is a flat horizontal layer beneath the station. That assumption is a signature you gave without reading the contract.
Dip breaks the moveout, backazimuth by backazimuth
Tilt the Moho and the geometry stops being azimuthally symmetric. A ray arriving from the up-dip direction hits the interface at a different depth and angle than one arriving from down-dip, so the conversion-point depth and the Ps delay time now depend on backazimuth, an effect documented in synthetic receiver-function experiments since the early broadband era [2]. The flat-layer moveout curves you are stacking along are correct for exactly none of these azimuths. Throw events from all backazimuths into one flat-layer stack and you are summing traces whose true moveouts disagree with each other and with the model. The stack maximum smears into an elongated blob instead of a tight peak. The instrument below shows this directly: at zero dip the stack is a crisp bullseye on the true H and κ; add dip and it stretches and slides off the cross that marks the truth.
The bias is not random, it has a direction
Here is what makes the trap dangerous rather than merely noisy: the smearing is biased, not scattered. The stack maximum does not just get fuzzier around the right answer; it moves systematically away from it. Depending on the azimuthal distribution of your events relative to the dip direction, an unmodeled dip pulls the apparent crustal thickness shallower or deeper and shifts κ, and the shift grows with dip angle. Because the error is systematic, stacking more events does not fix it. It hands you a more confident wrong answer. This is the worst failure mode in geophysics: a bias that masquerades as precision.
Why this bites asset teams specifically
Crustal thickness and Vp/Vs are not academic curiosities for an asset team. Vp/Vs is a composition and fluid proxy; a biased κ feeds straight into how you read the lower crust. Crustal thickness anchors the isostatic and thermal models that frame a basin's subsidence history. And a dipping Moho is not exotic. It is the norm near any orogen, passive-margin hinge, or inverted rift, which is to say near a great deal of interesting acreage. The stations that most need careful treatment are exactly the ones where the flat-layer assumption is least valid.
What the practitioner should actually do
The classical fixes are known and underused.
- Look before you stack. Plot the receiver functions against backazimuth before any grid search. A dipping interface announces itself: the Ps delay varies systematically with backazimuth, and energy appears on the transverse component with a polarity pattern organised by azimuth [3]. If the tell is there, a single all-azimuth H-κ number is already suspect.
- Bin by backazimuth. Stack within backazimuth bins so that each bin's geometry is quasi-consistent, then compare the per-bin H and κ values. Agreement licenses the flat model; systematic drift across bins is the dip talking.
- Invert for the interface. Where the drift is real, invert explicitly for dip and strike rather than assuming them away. Both this and binning cost more events and more care than one all-azimuth stack; that cost is the price of a number you can defend.
- Represent dip in the model. The scalable version, and the reason EarthScan treats crustal structure as a full inversion rather than a two-parameter grid search, is to let the model carry dip, anisotropy, and gradational boundaries as parameters the data can constrain, with calibrated uncertainty, so a dipping Moho shows up as a dipping Moho instead of a confidently mislocated flat one.
The trap is not the dip. The trap is a method that cannot represent it.
Limitations
- The bias magnitudes and the smear in the instrument are schematic illustrations of the documented dip effect, not a re-run H-κ stack on real data; the sign and size of the shift at a given station depend on its event distribution and velocity model.
- The headline figure, roughly two kilometres and a few hundredths at ten degrees of dip, is an order-of-magnitude guide, not a universal constant.
- Backazimuth-dependent receiver functions do not uniquely diagnose dip: dipping isotropic boundaries and anisotropic layers can produce similar azimuthal signatures and must be discriminated with care [3].
- Backazimuth binning divides the event catalogue; at quiet or young stations the per-bin stacks may be too noisy to compare, which pushes the problem toward explicit inversion.
By the numbers
Dip that shifts H by ~2 km
Vp/Vs shift at that dip
Phases summed in the stack
Parameters in the grid search
Key takeaways
- H-κ stacking assumes a flat horizontal Moho in its moveout equations, an assumption most users never consciously make and never check.
- Dip makes the Ps delay and conversion depth backazimuth-dependent, so an all-azimuth flat stack sums mutually inconsistent moveouts and smears the maximum.
- The resulting error is a systematic bias, not scatter; it grows with dip and does not average out with more events.
- Biased κ and H corrupt composition, fluid, and basin-history inferences, and dipping Moho is common precisely near tectonically interesting acreage.
- The fix is to represent dip, not assume it away: backazimuth binning, explicit dip inversion, or a full parameterized inversion with calibrated uncertainty.
References
[1] L. Zhu, H. Kanamori. Moho depth variation in southern California from teleseismic receiver functions. J. Geophys. Res., 2000. doi:10.1029/1999JB900322
[2] J. F. Cassidy. Numerical experiments in broadband receiver function analysis. Bull. Seismol. Soc. Am., 1992. doi:10.1785/BSSA0820031453
[3] M. K. Savage. Lower crustal anisotropy or dipping boundaries? Effects on receiver functions and a case study in New Zealand. J. Geophys. Res., 1998. doi:10.1029/98JB00795