Here we summarize answers to frequently asked questions related to various aspects of ISOLA
Import Data
Records imported to ISOLA (e.g. SAC files) should have their start time at least 30s before origin time. The records
must have a known orientation of the components (most often NS,EW,Z, positive to N, E and up; or, if not
NS,EW,Z, then user must know the orientation angles and apply rotation into N,E,Z system).
Try filters
A tool to find out a frequency range suitable for inversion (together with the S/N ratio tool). It is also extremely
useful to make a preliminary analysis of waveforms (SAC format) in SeisGram 2K beta version software of A.
Lomax. For example, broad-band records should be integrated (using full frequency band, without instrument
correction, after removal of the record mean), and this analysis effectively discovers low-frequency disturbances
(’mice’) described by zahradnik_plesinger_bssa2005 and bssa2010. Such records should be removed from inversion.
If kept in the inversion, and using band-pass filtration, the disturbances are often overlooked and even single station
like that might destroy the inversion.
Crustal model
1D model composed of layers with constant velocities; 1st column contains depths of layer top (not thicknesses).
Multiple crustal models
Different source-station paths may have different models (maximum 4 models).
Event Info
Lat, Lon, Depth of hypocenter (H) are specified. Epicenter serves as origin of the Cartesian coordinate system (x
positive to N, y positive to East) in which we describe the source and station positions. ISOLA is able to search
sources, i.e., ISOLA is not computing moment tensor only at the hypocenter, or below epicenter, but in a much more
general way. That is why inaccurate H position (and origin time) is not necessarily critical for success of the ISOLA
modeling.
Station Selection
It must be always preceded by specifying EventInfo, because the station coordinates are expressed in the coordinate
system whose origin is at the epicenter.
Time Window Length
(selecting from prescribed options, e.g. 245.76 seconds, 409.6 s, etc.)
TWL is the length of temporal interval starting at origin time, in which make waveform modeling. TWL must be
greater than P_travel_time + Seismo_Duration at the most distant station. By Seismo_Duration we mean duration of
the complete waveform (P, S, surface waves). For example, for epicentral distances up to ~300km a typical value of
TWL is 327.68s.
The offered values look strange, they are not rounded numbers; it is because we prefer to have rounded time step dt,
and TWL=8192 * dt. The 8192 factor =(2^13) relates to usage of the Fast Fourier Transform.
Choosing smaller TWL than necessary creates undesired time aliasing effects and may harm the inversion.
Time step dt (the basic time step), implied by the choice of TWL, is used in ISOLA when re-sampling all waveforms
and to make all calculations.
Green function computation
In fact this tool creates convolution of Green function with 6 elementary moment tensors and produces the so-called
elementary seismogram (one elemse**.dat file for each trial source of the sequential number **). All elementary
moment tensors have the same moment-rate function (elementary time function): either delta function, or a
symmetric triangle of a prescribed duration. If working at frequencies well below the corner frequency of the event,
Delta is applicable. If not, the triangle duration should be chosen, or varied during inversion to optimize the data fit.
Inversion - frequency range
One of the most critical parameters. The lower are the usable frequencies (with signal above the noise level) - the
better, because the modeling is then less sensitive to poorly known velocity model.
The lowest usable frequency is determined by the noise (either natural or instrumental). The highest usable frequency
is determined by maximum epicentral distance - smaller distances can be modeled up to higher frequencies.
Examples - very rough estimates:
weak near event (up to 10km): ~0.4-1.0 Hz
moderate (M3-5) events at near-regional distances (up to 300km): ~0.04-0.10 Hz
large (M6-7) events at regional distances (up to 1000km): ~0.004-0.010 Hz
Each case needs its own careful analysis of the admissible range, or testing several ranges.
ISOLA makes it possible to apply also the station-dependent frequency ranges, which is
very useful when mixing near and distant stations, or mixing broad-band and strong-motion data.
Inversion - time search
Time search (determination of the =centroid time) is an important ingredient of ISOLA. It is necessary because
ISOLA searches the optimum position of the source (among trial sources). Time search has its start, step and end.
These values are expressed as multiples of the basic time step dt, discussed above (dt=TWL/8192). This 'time-search
window' has nothing to do with the above discussed Time Window Length! Time search is usually made in vicinity
of origin time to reflect the fact that the hypocenter and origin time provided by location tools might be in error. The
time search refers to the source. It has nothing to do with time shifts at stations; ISOLA does not include any station
time shifts ('artificial time alignment between data and synthetics to compensate for inaccurate crustal models',
because the authors consider them to be almost always poorly justified, if not even wrong.
Inversion - weights
If used, weights in ISOLA are computed as proportional to epicentral distance in order to down-weight near stations
with large amplitudes which (without weighting) might dominate the inversion. However, weighting should be used
with caution, or avoided at all.
Correlation diagram
Its main purpose is not only to visualize correlation as a function of space and time, but also to warn that the formally
optimal solution might have correlation almost identical with many other solutions (resolution problem).
Time function
Some applications allow calculation of the source time function represented by a linear combination of the (identical)
elementary time functions. For example, a M7 event might be well modeled by a suite of a few (e.g. 2-3) mutually
shifted 10-s elementary triangles of different amplitude, having effective duration of 15s. This time function might
be better than a single 15-s triangle. The advantage of the linear combination is even more pronounced when the
studied event is complex and the elementary triangles do not superimpose (e.g., the event consists of two 10-s
triangles with a mutual shift of 15 s between their centers). This case obviously cannot be represented by any single
triangle (neither 10-s, nor 25-s), but the time-function calculation can manage such a case. Moreover, the method
used to calculate the time function for two sources simultaneously in ISOLA (the NNLS method) is preferable over
standard iterative deconvolution. For more details, see Appendix of zahradnik_sokos_GJI2013.
Uncertainty Estimation
It is based on linear assessment (6D error ellipsoids), see Appendix of zahradnik_custodio_bssa2012 paper. The
unknown input parameter, the data variance is computed in ISOLA GUI by Eq. (13) of the cited paper using a free
scaling parameter C. Most often C=1 is a reasonable choice for obtaining a meaningful relative uncertainty
assessment.
FMVAR-STVAR index
This is accessible in Plot results window and represents another measure of the solution uncertainty, including spacetime variation of the moment tensors. See sokos_zahradnik_srl2013.
Plot moment tensor
Plots *best.ps, representing summary of results, provides FMVAR, STVAR but also S/N ratio and CN (condition
number). All these parameters, together with variance reduction (VR) are useful measures of the solution reliability.
FMVAR, STVAR and CN should be as small as possible, while SNR and VR should be as large as possible. Future
experiments are needed to unify them in a single-parameter measure of the solution quality.