See also Hawaii Plume Discussion

29th June, 2010, Don L. Anderson
I have been waiting for someone better qualified than myself to comment in Science or Nature on the Wolfe et al. (2009) Hawaii paper, and others that basically use a vertical tomographic (ACH) approach to mantle structure. The claims in these papers are compelling to non-seismologists (including journal editors). Most seismologists have gone beyond the recent Science and Nature papers but they are still widely quoted, by non-seismologists, and even referred to as "the highest resolution studies out there...".

30th June, 2010, Adam M. Dziewonski
Don: It has been known for over 100 years (Herglotz-Wiechert) that you cannot uniquely determine a velocity profile if you do not have data for rays that bottom in a certain range of depths (low velocity zone). What you call "vertical tomography" is an attempt to circumvent this law. This is achieved by assuming a starting model and seeking perturbations to it by imposing additional conditions of minimum norm or minimum roughness.

The problem with studies such as that of Wolfe et al. (2009) is that they infer a structure for which they have only data with a very limited range of incidence angles at lower (and upper mantle depths).

This misconception has been propagated for over 30 years beginning with the 1977 paper by Aki and others. Using teleseismic travel times observed at NORSAR they inferred 3-D structure using rays with a very limited range of incidence angles. In contrast, Dziewonski et al. (1977) also used teleseismic travel times but limited their inversion to the lower mantle, in which it is possible to have all incidence angles from vertical to horizontal.

Structures obtained through inversion of data with a limited range of angles of incidence are highly nonunique, yet the tradition of such inversions continues with dozens of PASSCAL-type experiments. An example is the Yellowstone hotspot, where a slow structure had been claimed at depths exceeding the aperture of the array.

30th June, 2010, John R. Evans
Adam: I think you too overstate the issue but arrive at the correct bottom line (with minor exceptions).

The problem here is not ACH tomography and its numerous (almost exactly equivalent) offspring. The problem is the newbees to tomography (and folks outside that specialty), who do not understand the art and limitations of (restricted array) TT.

It has been known and widely stated from the very beginning that absolute velocities are utterly unknown in TT (and by corollaries that Ellsworth, I, and Uli Achauer established long ago that there are other structures that can effectively disappear or be misunderstood more easily than properly understood (I still think there is a lenticular mafic-silicic "heat exchanger" near Moho at Yellowstone, for example). The tradeoff in full-ray tomography at any scale from exploration to local to global is that the inverse problem becomes highly nonlinear and very sensitive to starting models and how cautious the driver is on that jeep track.

So please don't go throwing out baby with bathwater. TT is a powerful and highly linear, robust (in practice, if in not theory) method with a great deal to offer and has made major contributions where no other method yet dares to go. (Yeah, we'd all love to see full waveform tomography with all sources and constraints from other methods, but it ain't here yet. Even then, I guarantee that it will take 20 years of some curmudgeon like me hacking away to really understand the beast -- there is always more than meets the math.)

The problem is not the method but that newbees forget the art and the geology that are so essential to getting it right and simply go tunnel visioned on the maths, checkerboards, and pretty pictures (scaled for convenience and bias).

Every geophysical method has limitations, which must be well understood or it is useful in, garbage out. The Evans & Achauer (1993) chapter 13 in Iyer's great, pragmatic book on the art of tomography was an attempt to established a Perils and Pitfalls for TT, as was done famously and long ago for reflection seismology (e.g., no, the Earth actually is not composed largely of hyperbole ... only some papers!).

This subject really is worthy of a new paper of its own in a lead journal, a paper redolent in crisp, definitive statements to clarify some things that seem to have been forgotten in recent years.

2nd July, 2010, Jeannot Trampert
Don: I am not sure mere comments are going to change the perception of the subject. There seem to be two camps, the people who understand the limits of the techniques and those who project wishful thinking into the results obtained by the same techniques. There have been many comments and replies in the published literature but the debate has remained polarized.

The problem is of course that we do (could) not estimate uncertainties related to tomographic results. If people knew that anomalies carry uncertainties of the order of 1% (for example), they would refrain from interpreting anomalies of 0.5%. Very often resolution and uncertainty are confused. While there is a relation, they are not the same. You can infer a broad average very accurately, while a local property often carries a large uncertainty.

Checkerboard tests are very dangerous, because they are used to convince people that there is resolution while the mathematics tell you the opposite.

Rather than another comment, I think a tomographic study is needed with a complete uncertainty analysis. We are working on this here in Utrecht, but the calculations are long.

2nd July, 2010, John R. Evans
I agree with Jeannot. R is not C and both subsume a lot of physics and maths assumptions. I hope Jeannot and his colleagues have good success in a better evaluation.

6th July, 2010, Don L. Anderson
All this talk about resolution is nice but beside the point for this issue. It seems to be overlooked that the recent  Science paper, and earlier ones in Nature,  use only relative delay times over the small area investigated. Half of the arrivals are guaranteed to be later than the other half but it needs to be shown that these are slow in an absolute, global or regional sense. This has nothing to do with which approximation is used or what the resolution is. Confusing relative times with absolute times is about as fundamental an error as you can make.

If the shallow mantle is as heterogeneous and anisotropic as workers such as Ekstrom and Dziewonski say then one can show that the signals recorded by the Hawaiian array are created above 220 km depth. Furthermore, the tests by West et al. (2004) show that artifacts like those apparent in the results of Wolfe et al. (2009) are created by known shallow structures unless surface waves (and regional seismic phases) are used along with vertical body waves. Even the authors of the Wolfe et al. (2009) paper admit that complex shallow structures (of the very type imaged by surface waves and receiver functions) might (will, actually) explain the results. Montelli and colleagues acknowledge that little is known about structure above ~300 km but consider this unimportant. If you can't constrain the shallow mantle you cannot talk about the deep mantle (for these kinds of measurements). This is a fundamental.

6th July, 2010, Gillian R. Foulger
While I agree with Don, I have to disagree on what is the "Occam's razor" approach to debunking the results of Wolfe et al. (2009). Personally I think that it is surely more persuasive to point out that the experiment fundamentally cannot resolve a feature where they say one is, rather than arguing that there are geological complications (structure, anisotropy etc.) at shallow depth under Hawaii.

The latter approach will sound to most people like suggesting an ad hoc model that is not specifically supported, to explain away a plume-like structure which is similar to what many people expect to see. Yes, I know that there is evidence for anisotropy and shallow structure under Hawaii, but has anyone published a specific model that could be subtracted from the data of Wolfe et al. (2009) to make the "plume" vanish? And if so, why don't we need to appeal to such structures to make an Icelandic lower-mantle plume disappear, or a Yellowstone one?

This will sound to most people like:

Iceland = no LM plume seen
Yellowstone = no LM plume seen
Hawaii = LM plume IS seen, but we explain it away as anisotropy & shallow structure.

People simply won't find that convincing. Furthermore, this "plume" could be structure anywhere along the ray bundle – in the Chile trench, near the CMB etc. I don't see why it has to be shallow, or anisotropy. I think we cannot say where along the ray paths from the hypocenters somewhere in the circum-Pacific trench system to the surface stations at Hawaii, is the source of the tiny, much-smaller-than-the-corrections-and-the-errors "plume signal".

9th July, 2010, John R. Evans
I agree that sticking to the fundamentals is the best approach. Teleseismic Tomography (TT) simply CANNOT resolve location (at most it can tell direction) below the depth of good ray crossfire (about the array aperture). In addition to features actually present ANYWHERE below this array-aperture depth being candidates for the deeper features in models, note that TT WILL smear some of any unmodeled shallow perturbations not removed to those depths because it has no data to counter that solution and it shortens the model (in a damped inversion, it is "easier" [lower mismatch+length error metric] to split the shallow stuff between shallow and deepest than it is to put it all shallow, where it belongs).

The zealots will counter that they have removed ALL shallow structure by "crustal and upper-mantle stripping" and I can't argue against that very well without high-quality test models. In fact, I've made similar claims, though only for the regions WITH good ray crossfire where the inversion finds it harder to dump the leftovers.

Doing test models correctly requires full synthetics of P and S broadband waveforms (up to 2 or 3 Hz) received above a set of features present only in the crust and upper mantle (no CMB plume) and picking the arrivals, debugging the data, and inverting for structure as per normal.

The picking and debugging should be done two ways – the lazy, wrong way that is used now routinely (which subsumes systematic errors from the receiver function into the residuals) and the right way, by an experienced human in the painstaking way it was done for the first 15 years or so. Clearly that's a lot of work. Also, someone needs to step up for the synthetics (and instrument transfer functions) and someone needs to do other types of inversions with more sophisticated maths.

Note specifically that simple ray tracing or "ray front (potential) tracing" are not sufficient and will not reproduce a true field experiment in the way we need to nail this. (I think we might easily get away with using one input waveform to the bottom of the crustal/upper-mantle anomalous zone and do the full PDF work only above that depth. That is, assume perfectly one-dimensional lower crust, core, and source-zone velocity model. We have not talked about wavefront healing which would make this a good approximation even in the presence of modest perturbations in these places.

Other matters, like anisotropy, would simply confuse the matter and may not be relevant in any case if one is simply reading (with steep rays) a vertical alignment of olivine etc. in response to flow in a hypothetical plume. Such a feature would look almost exactly like a simple low or high and any distinction would be second order or less (one of the reasons that attempts to account for anisotropy have been pretty weak and not repeated).

6th July, 2010, Don L. Anderson
The ban of my life! Anisotropy is not a small effect nor one that can be corrected out (I wrote a book about that; Anderson, 1989). In the Pacific the anisotropy reaches 8% and the drop of Vs into the low-velocity anisotropic layer is also 8%. Vertical shear waves are 8% slower than near horizontal SH waves. Intermediate angle SV waves can be even slower. Simple arithmetic shows that S and SKS waves can vary by ~1-2 seconds through this kind of layer and another second or two can be added with the kinds of variations in lid thicknesses that are measured. Crustal, bathymetry and elevation are comparable. Heterogeneity below ~200 km then becomes a small perturbation, not the first order effect.

If one inverts for anisotropy first, and then for residual heterogeneity, rather than the reverse, one becomes a believer! As Dziewonski & I showed many years ago, if you have a lot of data and are allowed to fit 12 parameters (degrees of freedom), you get a much simpler model (structurally) and a better fit, if you use some of the parameters for anisotropy instead of a lot of isotropic layers (e.g., as Laske does for Hawaii).

Pacific anisotropy appears to require a laminated stack rather than oriented olivine crystals. Even with no lateral heterogeneity at all (a flat anisotropic layer) you can do a pretty good job at fitting the data of Wolfe et al. (2009). If the laminations tilt to the NW, as predicted, e.g., by Kohlstedt for melt-rich shear zones, then SKS is explained as well. Then, you can fiddle with heterogeneity to fit the rest of the residuals. This seems backwards if you grew up in an isotropic world.

I suspect that since anisotropy is such a big effect that if you do the usual of trying to find heterogeneity first you will have a funny model and then if you try to fit the residual with anisotropy you might conclude that "attempts to account for anisotropy [are] pretty weak"!

9th July, 2010, John R. Evans
I understand that, Don, though thank you for some new details.

I was simply trying to say: "Imagine a vertical plug in which the anisotropy is in one direction while it is some other but monotonous direction in all surrounding areas and further that is the ONLY difference between those regions. Because most of the rays in TT are quasi-vertical, that is still a binary model – the plug will look different from everything else around it whether that is (correctly) explained as anisotropy or (incorrectly) by an isotropic anomaly." You cannot tell the difference via TT at any meaningful level of certainty. To see anisotropy as clearly different from an isotropic anomaly, one must have a broader range of incidence angles.

8% is comparable to other (shallow) anomaly magnitudes and bigger than lower-mantle and most upper-mantle anomalies, so it may well be anisotropy, we simply can't distinguish.

So "second order" is not the right term, rather "effectively indistinguishable by TT". Where inversions for both isotropic anomalies and anisotropy have been tried (and you relate an example) the difference in model fit as a function of causality has not been resounding. Your Ekstrom & Dziewonski experiments of reversing the order or adding innumerable parameters to the fit both confirm my point – many anomalies can be explained in many ways and the problem is in distinguishing the various effects in the specific case of TT. Inter-parameter R and C are very weak with a typical TT data set. Something will be measured and modeled but we know not which among the many candidate causes to blame for it.

In contrast, the negative effects of the necessarily limited ray set in TT outside the well-sampled volume are as strong as the objects being (mis)interpreted – one need go no further than that to demonstrate the hypothesis – that the various "plume" results are unsupported by the data cited. I've measured anisotropy by splitting and know well that it is real – that's just not the point! KISS to penetrate the doubting reader's paradigm.

References

• Anderson, Don L., Theory of the Earth, Blackwell Scientific Publications, Boston, 366 pp., 1989.
• West, M., W. Gao, and S. Grand, A simple approach to the joint inversion of seismic body and surface waves applied to the southwest U.S., Geophys. Res. Lett., 31, L15615, doi:10.1029/2004GL020373, 2004.
• Wolfe et al., Mantle Shear-Wave Velocity Structure Beneath the Hawaiian Hot Spot, Science, 326, 1388 - 1390, 2009

last updated 12th July, 2010