Most receiver-function pipelines compute the transverse component, glance at it, and throw it away. The reasoning is textbook: under a flat isotropic crust the P-to-S conversion is polarised entirely in the radial-vertical plane, so the transverse receiver function should be zero, and whatever appears there is noise. The reasoning is also wrong the moment the crust stops being flat and isotropic, which is to say almost everywhere interesting. That transverse energy is not noise. It is the dip and anisotropy signal, and it arrives with a backazimuth signature that names the fabric direction if you read it.
Why it should be zero, and why it is not
The flat isotropic case is genuinely clean. A P wave converting at a horizontal boundary produces an S wave polarised in the vertical plane containing the ray, so rotating into radial and transverse puts every bit of converted energy on the radial and none on the transverse. A transverse trace that is not flat therefore means one of the assumptions has failed.
Two failures produce it. A dipping interface breaks the azimuthal symmetry, so the conversion point and polarisation depend on which direction the wave arrived from. Anisotropy, typically from aligned minerals or fractures, splits the converted shear wave and leaks energy onto the transverse regardless of interface geometry [1].
The signature is in the backazimuth, not the amplitude
Here is the part that turns a discarded trace into a measurement. Dip and anisotropy do not produce the same pattern as you walk around the compass. A dipping interface gives a transverse amplitude that repeats once per revolution, positive on one side and negative on the other, two lobes. Anisotropy with a horizontal fast axis gives a pattern repeating twice per revolution, four lobes, with nodes aligned to the fast axis itself.
So the diagnostic is periodicity, not loudness. A stronger transverse tells you something is there. The number of lobes tells you what, and where its axis points. Reading amplitude alone is how a real anisotropy measurement gets written off as a noisy station.
Transverse under flat isotropic crust
Lobes per revolution, dip
Lobes per revolution, anisotropy
What the nodes mark
Reading the harmonics is reading the fabric
Formally this is a harmonic decomposition: expand the transverse receiver function in backazimuth and the coefficients separate the contributions. The once-per-revolution term carries dip, the twice-per-revolution term carries anisotropy, and the axis falls out of the phase. Nothing here needs new data. It needs the component the pipeline already computed and then deleted.
The failure mode, and why it is expensive
The failure is mistaking one for the other. A pipeline that treats all transverse energy as a single quality metric will flag a strongly anisotropic station as poor and downweight it, discarding exactly the station with the most structural information. Conversely a genuinely noisy station can be read as fabric if nobody checks whether the pattern is coherent in backazimuth. Coherence across backazimuth is the test that separates them, and it costs nothing but keeping the trace.
Zooming out
Discarding the transverse is a data-efficiency failure of the ordinary kind: a channel recorded, processed, and thrown away because a simplifying assumption said it should be empty. The assumption is a good approximation in the settings where it holds and a poor one near orogens, margins and inverted rifts, which is where the interesting acreage tends to be. Keeping the component costs nothing. Reading its periodicity turns it into a measurement of fabric direction that no radial-only pipeline can produce.
Key takeaways
- The transverse receiver function is zero only under a flat isotropic crust, an assumption that fails near most structurally interesting settings.
- Non-zero transverse energy is signal: dipping interfaces and anisotropy both produce it, by different mechanisms.
- The diagnostic is backazimuth periodicity, not amplitude: two lobes per revolution for dip, four for anisotropy.
- Anisotropy nodes align to the fast axis, so the fabric direction falls out of the phase without new data.
- Treating transverse energy as a quality metric downweights exactly the stations carrying the most structural information.
References
[1] Bianchi, I. et al. Mapping seismic anisotropy using harmonic decomposition of receiver functions. Journal of Geophysical Research: Solid Earth, 2010.
