Travel Time Models
mloc uses three different approaches to calculate theoretical travel-times and derivatives, one based on a flat-layered crustal model that is adjusted to fit the observed data at local and near-regional distances, a global average model using the tau-p formulation to extract travel time information, and a linear model for Lg and T phases. Use of a crustal model is optional. The usage of a custom crustal model is discussed in a separate section.
By default, mloc uses the tau-p formulation of Buland and Chapman (1983) to calculate theoretical travel-times, based on the 1-D global average model ak135 (Engdahl et al., 1998). If the data set includes arrival times for phases that are not included in ak135, such as PPP, those readings are generally flagged (“p”) and ignored in the relocation. There are several cases (pwP and PKP precursors, see below) of commonly-reported seismic phases that do not exist in the ak135 phase set, but which are handled with minor adjustments to standard phases.
A global model other than ak135 could be used, if the user provides the necessary data files for the tau-p software:
These files must be stored in the subdirectory /tables/tau-p/; the command taup would be used to select it. It is a bit difficult to envision a circumstance where the use of a different global model would make a significant difference in the results of a calibrated relocation, because arrival time data at epicentral distances for which the global model would be used are converted to travel time differences. In other words, baseline differences are ignored.
Multiples of the teleseismic pP phase that reverberate in the water column of oceanic areas, named “pwP”, were first reported by Mendiguren (1971). Such phases are not included in the ak135 model, which has no water layer, but Engdahl et al., 1998 found that the ISC Bulletin contains many instances of pwP that are mis-identified as pP, causing over-estimation of the focal depth for many oceanic events. The EHB location protocol includes the pwP phase, calculating travel time by making a correction to the pP phase travel time based on the water depth at the bouncepoint. This capability also exists in mloc, through the bptc command. The swP phase is not supported, nor are multiples (pwwP, pwwwP, etc.) of the pwP phase.
In the distance range 125-145° precursors to the main PKP arrival are frequently observed (e.g., Cleary and Haddon, 1972). They are sometimes identified as likely precursors with names like “PKPpre”, but often appear as PKP with large negative residuals. mloc renames “PKPpre” as “PKPdfpre” and calculates a residual relative to PKP but it does not use them for relocation; they are automatically flagged (“p”). Depending on how they are reported in the data set, the phase naming algorithm may fail to catch some precursors and the user may need to edit the incoming phase name in the MNF file so that mloc handles these arrivals correctly. If not, they will often end up being flagged as outlier readings in the cleaning process.
Several corrections are made to the travel times calculated from the global model. mloc does not support traditional station corrections or the patch corrections (regionalized station corrections) utilized in the EHB algorithm (Engdahl et al., 1998), since mloc takes a much different approach to the problem of determining hypocenters that are minimally biased by unknown Earth structure.
Ellipticity corrections (in real function ellip in mloclib_tt.f90) are based on the formulation presented by Dziewonski and Gilbert (1976), with code adapted from Engdahl’s EHB location code (based in turn on code by D.J. Brown, B.L.N. Kennett and W. Spakman). Ellipticity corrections are always made. They are typically ~0.1 s or less. These corrections have almost no effect on the relative locations of a cluster or on a calibrated relocation, but they are necessary if mloc is used to do a “traditional” teleseismic location.
The code (in get_elev_corr in mloclib_tt.f90) used to calculate station elevation corrections is based on the algorithm used in the new ISC locator written by Istvan Bondar. The corrections are based on P- and S-velocities that can be specified by the user with the command secv. Station elevation corrections can be turned off with the corr command.
Bounce Point Corrections for Depth Phases
In the global model, travel times of teleseismic depth phases (pP and sP) are calculated under the assumption that the “short leg” is reflected from the reference ellipsoid (i.e. zero elevation). In developing a refined method of analyzing teleseismic depth phases for the EHB algorithm, Engdahl attempted to reduce the biasing effect of varying elevation at the surface bounce points. Travel time is increased when the bounce point is above sea-level, reduced when it is below sea-level (i.e., in oceanic areas). This correction is available in mloc, through the command bptc, with topography (and bathymetry) taken from the ETOPO5 digital elevation model.
In rare circumstances it may be suspected, or even confirmed, that the timing system of a station was out of calibration when an arrival time reading was made. The command terr is provided to explore the consequences of such errors. If the timing of a station cannot be trusted it would be far preferable to flag the reading (“t”) and not use it rather than try to correct it.
Linear Travel-time Models
Neither the continental Lg phase nor the oceanic T phase are included in the ak135 global model, but mloc is able to use both phases in a relocation because their travel-times can be predicted fairly accurately with simple linear-with-distance models. Lg is a very commonly reported phase and contributes significantly to many relocations. T phase arrivals have been studied since the early 1950s but have only recently begun to appear in open seismic bulletins such as the ISC Bulletin. They have been shown to have value in localizing seismic sources in the oceans when there is adequate azimuthal coverage by T phase stations (hydrophone arrays) and they play a role in nuclear monitoring (Okal, 2001) but limited experience so far indicates that these data have almost no value (because of large scatter) in high-resolution relocations when combined with traditional “solid Earth” arrival time data (the skip * T * command is often used). Nevertheless, the ability to carry T phase readings through a relocation analysis may eventually lead to improvements in this regard.
Both Lg and T phases are modeled with a linear model (y = ax + b) parameterized by a zero-distance intercept (usually near zero) and a derivative in epicentral distance (s/deg). Default values of these parameters are provided but it is usually desirable (especially with Lg) to derive an improved model from the observed travel times and input them with the commands lgtt and tptt. Use the command ttou to create a file with the distance and travel-time data for a phase of interest, read the data into a program that can do basic line fitting.