mloc will use any phase for which a theoretical travel time can be provided, but travel time models always come with a set of “legal” phase names. Other than the teleseismic P and S phases, naming conventions for seismic arrivals have varied widely over time and among different organizations. There are also many cases in which arrival times are provided without any phase name. mloc contains a number of routines that process the the arrival time data read from event files to put them in a form which is usable for relocation.
The correctness of (most) phase identifications is less important than the consistency of those identifications, because most arrival time data are only being used as time differences for the estimation of cluster vectors.
The canonical set of phase names for observational seismology has been established by a working group in IASPEI. For most phases, mloc calculates travel times and derivatives using Tau-P software implementing the global 1-D model ak135 (Engdahl et al., 1998), which supports only a subset of the canonical set. When a custom crustal model is used (command lmod), the set of returned phases is limited to Pg, Pb, Pn, Sg, Sb and Sn, and the “Conrad Discontinuity” phases Pb and Sb are normally suppressed (see below). In addition, mloc can process Lg and T phase data, as well as S-P times and relative depth phase (e.g., pP-P).
Probability Density Functions for Phase Identification
When an arrival time reading occurs in a portion of the travel-time curve where only a single phase exists, the assignment of a phase name is trivial. Where two or more phase branches cross or come near one another, however, the problem is more difficult. in the early 1990s Ray Buland proposed using probability density functions (PDFs) for specific seismic phases in deciding, on the basis of arrival time only, what phase name should be assigned to a reading when this occurs. This approach was implemented in a limited way (for depth phases only) in the EHB algorithm (Engdahl et al., 1998). If a reading is in the vicinity of several possible phases, each of which has a separate PDF with varying amplitude and spread, the decision is made by assigning proportional segments of the number line 0-1 to the candidate phases and generating a random number on that range to make the selection. Thus it’s possible to select a phase which has lower probability over the most likely candidate. From the point of view of building catalogs in which the distributions of phases are free of cross-contamination around crossing points, this strategy makes great sense, but it is less obvious that it is a good way to obtain the most accurate locations for individual events. In any case, the necessary PDFs have never been developed for most phases.
Phase identification is done for single readings, i.e., there is no concept of groups of readings (primary and secondary readings at a station) being analyzed simultaneously. This was tried in earlier versions of mloc but it was found to be too complex. The current version of mloc uses a traditional “best fit” approach, but the code exists to take advantage of information on the probability distribution functions (PDFs) of different phases. The necessary research to establish the appropriate coefficients of the PDFs of all the needed phases has not been done. Therefore, at this time all PDFs are the same and the choice boils down to the classical “smallest residual” criterion.
The target arrival time is tested against all phases in the theoretical TT model for the corresponding focal depth and epicentral distance, regardless of arrival time order. Probability is calculated for each possible association, based on the candidate phases’s PDF, and the choice is made on the basis of highest probability. Depth phases should be handled separately if they are to be used for depth constraint. Phase type (P or S) is honored if a phase name has been provided in the event file. If the phasename matches the name of the first-arriving phase at that distance it is not changed. A phase name is not changed unless the probability of the new phase identification is 0.05 or greater.
The details of how teleseismic depth phases are analyzed in mloc to constrain focal depth are discussed elsewhere. With respect to phase identification the recommended approach is to use the ppri command to keep mloc from changing the phase name of pP and sP phases that are read from the event file. If they are to be renamed it should be done manually (editing the event file) after a suitable analysis.
Some arrival times come with a phase identification indicating that no phasename could be assigned or a phasename that cannot be translated into a legal one. If mloc is unable to associate such a reading with any legal phase, the reading is set to “UNKNOWN”, or in the case where a P or S character is indicated, “UNKNOWNP” or “UNKNOWNS”. Such readings will receive a “p” phase reading flag as well.