Phases

A major feature of the TauP Toolkit is the implementation of a phase name parser that allows the user to define essentially arbitrary phases through the earth. Thus, the TauP Toolkit is extremely flexible in this respect since it is not limited to a pre-defined set of phases. Phase names are not hard-coded into the software, rather the names are interpreted and the appropriate propagation path and resulting times are constructed at run time. Designing a phase-naming convention that is general enough to support arbitrary phases and easy to understand is an essential and somewhat challenging step. The rules that we have developed are described here. Most of phases resulting from these conventions should be familiar to seismologists, e.g. pP, PP, PcS, PKiKP, etc. However, the uniqueness required for parsing results in some new names for other familiar phases.

In traditional whole-earth seismic phase names, there are 3 major interfaces: the free surface, the core-mantle boundary, and the inner-outer core boundary. Phases interacting with the core-mantle boundary and the inner core boundary are easy to describe because the symbol for the wave type changes at the boundary (i.e. the symbol P changes to K within the outer core even though the wave type is the same). Phase multiples for these interfaces and the free surface are also easy to describe because the symbols describe a unique path. The challenge begins with the description of interactions with interfaces within the crust and upper mantle. We have introduced new symbols to existing nomenclature to provide unique descriptions of potential paths. Phase names are constructed from a sequence of symbols and numbers (with no spaces) that either describe the wave type, the interaction a wave makes with an interface, or the depth to an interface involved in an interaction.

1. Symbols that describe wave-type:

   P	compressional wave, upgoing or downgoing, in the crust or mantle
   p	strictly upgoing P wave in the crust or mantle
   Ped	compressional wave, exclusively downgoing, in the crust or mantle
   S	shear wave, upgoing or downgoing, in the crust or mantle
   s	strictly upgoing S wave in the crust or mantle
   Sed	shear wave, exclusively downgoing, in the crust or mantle
   K	compressional wave in the outer core
   k	strictly upgoing compressional wave in the outer core
   Ked	compressional wave, exclusively downgoing, in the outer core
   I	compressional wave in the inner core
   y	strictly upgoing compressional wave in the inner core
   Ied	compressional, exclusively downgoing, wave in the inner core
   J	shear wave in the inner core
   j	strictly upgoing shear wave in the inner core
   Jed	shear wave, exclusively downgoing, wave in the inner core

2. Symbols that describe interactions with interfaces:

   m	interaction with the moho
   g	appended to P or S to represent a ray turning in the crust
   n	appended to P or S to represent a head wave, e.g. along the moho
   c	interaction with the core mantle boundary
   i	interaction with the inner core outer core boundary
   ^	underside reflection, used primarily for crustal and mantle interfaces
   v	topside reflection, used primarily for crustal and mantle interfaces
   V	critical topside reflection, used primarily for crustal and mantle interfaces
   diff	appended to P or S to represent a diffracted wave, e.g. along the core mantle boundary, or to K for a diffracted wave along the inner-outer core boundary
   kmps	appended to a velocity to represent a horizontal phase velocity

3. Exclusively upgoing and downgoing:

   The characters p, s, k, y and j always represent up-going legs.

   An example is the source to surface leg of the phase pP from a source at depth. P and S can be turning waves, but always indicate downgoing waves leaving the source when they are the first symbol in a phase name. Thus, to get near-source, direct P-wave arrival times, you need to specify two phases p and P or use the ttimes compatibility phases described below. However, P may represent a upgoing leg in certain cases. For instance, PcP is allowed since the direction of the phase is unambiguously determined by the symbol c, but would be named Pcp by a purist using our nomenclature. The phase k is similar to p but is an upgoing compressional wave in the outer core, while y and j are upgoing compressional and shear waves in the inner core. The name y is used as the lower case of the I phase is already used to indicate reflection from the inner-outer core boundary.

   With the ability to have sources at depth, there is a need to specify the difference between a wave that is exclusively downgoing to the receiver from one that turns and is upgoing at the receiver. The suffix ed can be appended to indicate exclusively downgoing. So for a source at 10 km depth and a receiver at 20 km depth at 0 degree distance the turning ray P does not have an arrival but Ped does.

4. Depths within the model:

   Numbers, except velocities for kmps phases (see 11 below), represent depths at which interactions take place. For example, P410s represents a P-to-S conversion at a discontinuity at 410km depth. Since the S-leg is given by a lower-case symbol and no reflection indicator is included, this represents a P-wave converting to an S-wave when it hits the interface from below. The numbers given need not be the actual depth, the closest depth corresponding to a discontinuity in the model will be used. For example, if the time for P410s is requested in a model where the discontinuity was really located at 406.7 kilometers depth, the time returned would actually be for P406.7s. The code taup time would note that this had been done via the Purist Name. Obviously, care should be taken to ensure that there are no other discontinuities closer than the one of interest, but this approach allows generic interface names like 410 and 660 to be used without knowing the exact depth in a given model.

5. Conversion at depth:

   If a number appears between two phase legs, e.g. S410P, it represents a transmitted phase conversion, not a reflection. Thus, S410P would be a transmitted conversion from S to P at 410km depth. Whether the conversion occurs on the down-going side or up-going side is determined by the upper or lower case of the following leg. For instance, the phase S410P propagates down as an S, converts at the 410 to a P, continues down, turns as a P-wave, and propagates back across the 410 and to the surface. S410p on the other hand, propagates down as a S through the 410, turns as an S, hits the 410 from the bottom, converts to a p and then goes up to the surface. In these cases, the case of the phase symbol (P vs. p) is critical because the direction of propagation (upgoing or downgoing) is not unambiguously defined elsewhere in the phase name. The importance is clear when you consider a source depth below 410 compared to above 410. For a source depth greater than 410 km, S410P technically cannot exist while S410p maintains the same path (a receiver side conversion) as it does for a source depth above the 410.

   The first letter can be lower case to indicate a conversion from an up-going ray, e.g. p410S is a depth phase from a source at greater than 410 kilometers depth that phase converts at the 410 discontinuity. It is strictly upgoing over its entire path, and hence could also be labeled p410s. p410S is often used to mean a reflection in the literature, but there are too many possible interactions for the phase parser to allow this. If the underside reflection is desired, use the p^410S notation from rule 7.

6. Non-conversion conversions:

   Due to the two previous rules, P410P and S410S are over specified, but still legal. They are almost equivalent to P and S, respectively, but restrict the path to phases transmitted through (turning below) the 410. This notation is useful to limit arrivals to just those that turn deeper than a discontinuity (thus avoiding travel time curve triplications), even though they have no real interaction with it.

7. Reflections:

   The characters ^, v and V are new symbols introduced here to represent bottom-side and top-side reflections, respectively. They are followed by a number to represent the approximate depth of the reflection or a letter for standard discontinuities, m, c or i. The lower-case v represents a generic reflection while V is a critical reflection. Note however, that V is critical in the sense of without phase conversion. In other words, PVmp is critical for ray parameters where a P wave cannot propagate into the mantle, regardless of whether or not S can propagate. A critical reflection phase using V is always a subset of the non-critical reflection using v. Reflections from discontinuities besides the core-mantle boundary, c; or inner-core outer-core boundary, i, must use the ^ and v notation. For instance, in the TauP convention, p^410S is used to describe a near-source underside reflection.

   Underside reflections, except at the surface (PP, sS, etc.), core-mantle boundary (PKKP, SKKKS, etc.), or outer-core-inner-core boundary (PKIIKP, SKJJKS, SKIIKS, etc.), must be specified with the ^ notation. For example, P^410P and P^mP would both be underside reflections from the 410km discontinuity and the Moho, respectively. Because of the difficultly of creating interfaces where critical underside reflections can occur in earth-like models, we have not added this capability.

   The phase PmP, the traditional name for a top-side reflection from the Moho discontinuity, must change names under our new convention. The new name is PvmP or PVmp while PmP just describes a P-wave that turns beneath the Moho. The reason the Moho must be handled differently from the core-mantle boundary is that traditional nomenclature did not introduce a phase symbol change at the Moho. Thus, while PcP makes sense since a P-wave in the core would be labeled K, PmP could have several meanings. The m symbol just allows the user to describe phases interaction with the Moho without knowing its exact depth. In all other respects, the ^-v nomenclature is maintained.

8. Core reflections:

   Starting in version 3.0, ^ and v are now allowed for for all disconuities in the model, including the crust, mantle and core. However, because “p is to P” is not the same as “i is to I”, a naming convention was created to use y as an exclusively upgoing leg in the inner core. For example in a model with a discontinuity at 5500 km depth in the inner core, the phases PKIv5500IKP and PKIv5500ykp are the same. Note that because standard models do not have discontuities in the core, these phases have not received the same level of testing.

9 Scattered phases:

Starting in version 3.0, o and O represent forward and back scattering, if the model is constructed with a scatterer (depth and distance). Forward scattering is in the sense that the phase continues around the earth in the same direction, while backscattering would reverse direction. Note that for some phases that go the long way around the earth, the sense of scattering may not match the positive anglular direction.

10 Core phase names:

Currently there is no support for PKPab, PKPbc, or PKPdf phase names. They lead to increased algorithmic complexity that at this point seems unwarranted, and TauP uses phase names to describe paths, but PKPab and PKPbc differentiate between two arrivals from the same path, PKP. Currently, in regions where triplications develop, the triplicated phase will have multiple arrivals at a given distance. So, PKPab and PKPbc are both labeled just PKP while PKPdf is called PKIKP.

11 Surface waves:

The symbol kmps is used to get the travel time for a specific horizontal phase velocity. For example, 2kmps represents a horizontal phase velocity of 2 kilometers per second. While the calculations for these are trivial, it is convenient to have them available to estimate surface wave travel times or to define windows of interest for given paths.

12 ttimes compatibility:

As a convenience, a ttimes phase name compatibility mode is available. So ttp gives you the phase list corresponding to P in ttimes. Similarly there are tts, ttp+, tts+, ttbasic and ttall.

The taup phase tool can be very helpful in understanding the phase naming convention by providing a detailed description of the path a phase takes through the model. It is also possible to generate a list of all possible phase paths within a model, using the taup find tool. This takes a --max n argument that speficies the maximum number of interactions that the phase has with discontinuities in the model, other than start, end and transmission without phase change.