pyacs.gts.lib.trajectory module

Non linear trajectory models for Geodetic Time Series

pyacs.gts.lib.trajectory.trajectory(self, model_type, offset_dates=[], eq_dates=[], H_fix={}, H_constraints={}, H_bounds={}, component='NEU', verbose=False)[source]

Calculates the parameters of a (non-linear) trajectory model for a Geodetic Time Series. The trajectory model is:

y(t) =

trend : trend_cst + trend * ( t - t0 ) +

annual: a_annual * cos( 2*pi + phi_annual ) +

semi-annual: a_semi_annual * cos( 2*pi + phi_semi_annual ) +

offset : Heaviside( t - t_offset_i ) * offset_i +

post-seismic_deformation as decaying log (psd_log): psd_eq_i * np.log( 1 + Heaveside( t - eq_i )/tau_i )


model_type – string made of the key-word the parameters to be estimated.

Key-word parameters are


‘trend-seasonal-offset-psd_log’ will do the full trajectory model.

  • offset_dates – a list of offset_dates in decimal year

  • eq_dates – a list of earthquake dates for which post-seismic deformation (psd_log) will be estimated

  • H_fix – a dictionary including the name of the parameter to be hold fixed and the value.

For instance to impose the co-seismic offset (North-East-Up) and relaxation time of 100 days for the first earthquake use:

H_fix = { ‘psd_log_offset_00’:[10., 15., 0.] , ‘psd_log_tau_00’:[100., 100., 100.]}


H_constraints – a dictionary including the name of the parameter to be constrained.

For instance to impose a 50 days constraints around 500 days on the relaxation time of the second earthquake for all NEU components use: H_fix = { ‘psd_log_tau_01’:[[500.,50], [500.,50] , [500.,50]]}


H_bounds – a dictionary including the bounds.

For instance to impose a relaxation time for the third earthquake to be in the range of 2 to 3 years, for all NEU components use: H_bounds = { ‘psd_log_tau_02’:[[2*365.,3*365.], [[2*365.,3*365.] , [[2*365.,3*365.]]}

  • component – string , component for which the trajectory model will be estimated.

  • verbose – verbose mode


Unlike most pyacs.gts functions, trajectory returns 4 elements: the results as a dictionary, the model Gts,

the residual Gts and a Gts with model predictions at every day.