The fociMT algorithm is point-source moment tensor inversion and the fault rupture processes (e.g. directivity or spatial changes in elementary moment tensors) are NOT considered. As such, the algorithm is valid for events with simple source time functions that can be represented by a single pulse. Therefore, it is suggested to use the algorithm for events with moment magnitudes not exceeding Mw 4.

“omega” parameter which is a part of ASCII input file is basically the area below the first P-wave ground displacement pulse (in time domain) or equivalently the spectral level taken from the amplitude spectrum of ground displacement pulse. The unit of “omega” parameter is [m * s] (meter times second), and it comes from the fact that we multiply the amplitude of first P-wave pulse using ground displacement seismogram in [m] by the half of duration of the first P-wave pulse in [s]. Regardless of whether time or frequency domain was used to extract the “omega” value, the parameter should contain the sign information. The sign of “omega” is in accordance with the seismological convention, i.e. it is positive for the positive first P-wave ground displacement amplitude (i.e. ground motion AWAY from the seismic source) and negative otherwise (ground motion TOWARDS the seismic source).

In case of simple impulsive source time functions it is typically not necessary to calculate the integral of ground displacement first P-wave pulse. Instead, the amplitude D (cf. picture) including sign information of first P-wave pulse may be taken from ground displacement seismogram (the seismogram should be calibrated to [m]) and multiplied by the the rise time (i.e. time interval between the P-wave onset and P-wave amplitude, t_max-t_ons in seconds [s]). In this case, the integral of the pulse is simply replaced by the area of the triangle.

The MATLAB wrapper focimt.m has no option for changing the decomposition scheme, which is currently fixed to Jost and Herrmann’s (1989) approach. However, the focimt application has implemented an alternative decomposition scheme based on Vavrycuk’s (2001) approach. In focimt application this is specified by option -d D or -d Y (see the documentation of focimt application for details). Therefore, the hardcoded decomposition scheme in focimt.m may be changed from Jost and Herrmann’s to Vavrycuk’s approach simply by changing the following line from (note change from “D” to “Y” in option -d):

commandline = ['-i ' temp '.txt -d DWAFTUMVE -o ' temp ' -s ' solutions ' -n ' normfunc ' ' bbsize ' ' bbformat ' ' bbproj ' ' jacknife ' ' bootstrap ' ' vmodel ' ' ball];

to

commandline = ['-i ' temp '.txt -d YWAFTUMVE -o ' temp ' -s ' solutions ' -n ' normfunc ' ' bbsize ' ' bbformat ' ' bbproj ' ' jacknife ' ' bootstrap ' ' vmodel ' ' ball];

Future version of focimt.m implement the decomposition switch parameter.

The takeoff angle is measured in degrees from dowgoing ray (towards the center of Earth) direction. The seismic ray leaving the source purely up (towards the Earth surface) has takeoff angle of 180 degrees. The ray leaving earthquake source towards center of Earth has a takeoff angle of 0 degrees.

The azimuth of a vector from the seismic hypocenter to the seismic station is measured in degrees, and it is positive from north towards east. 0,90,180, and 270 degrees corresponds to the station located North, East, South, and West from the earthquake hypocenter.

The angle of incidence in RAW ASCII input file follows the standard seismological convention. The angle of incidence to the sensor is measured in degrees from down direction (towards center of Earth). In other words, the seismic ray pointing directly up (perpendicular towards the surface) has 0 degrees incidence angle and pure horizontal ray (parallel to the surface) has 90 degrees incidence angle.

Note #1: In case of pure horizontal ray (incidence = 90) one should not expect P-wave arrival to be visible on vertical component. Phases with incidence angle = 90 degrees should be disregarded from processing.

Note #2: Large values of incidence angle (>80 degrees) leads to high corrections for “omega” parameter, as the “omega” is divided by the cosine of the angle of incidence. This typically leads to overestimation of total and scalar seismic moment, as well as it may influence the moment tensor decomposition.

If you get error similar to this:

>> drawhudsonnet;
??? Error: File: drawhudsonnet.m Line: 119 Column: 3
Expression or statement is incorrect--possibly unbalanced (, {, or [.

it is likely due to the fact that your version of MATLAB does not support empty output arguments that are specified in MATLAB as “~” (tilde character). If possible, please update your MATLAB to the newest version that handles empty output arguments. Alternatively, please change every null output variable “~” to any valid and not used variable name, e.g. “dummy”:

[~,DD] = eig(M);

to

[dummy,DD] = eig(M);

This problem will be resolved in future version of hybridMT.

Consider a scenario of executing the drawstereonet.m function:

[X,Y] = drawstereonet([10 20 30 40],[50 60 70 80]);
??? Error using ==> drawstereonet at 43
Argument 'AZM' failed validation with error:
Undefined function or method 'ismatrix' for input arguments of type 'double'.

This error results from the fact your MATLAB version does not contain ismatrix() routine. If it is possible, please update the MATLAB to the newest version. Alternatively, you can try to disable the validation routine. In case of example above, by changing line:

p.addOptional('AZM', [], @(x) ismatrix(x) && isnumeric(x) );

to:

p.addOptional('AZM', [], @(x) isnumeric(x) );