model_par.mle_point: Model Parameter Maximum Likelihood Estimation (Point Data)
In amignan/rseismTLS: Induced Seismicity Traffic Light System

Description Usage Arguments Details Value References See Also

Provides the maximum likelihood estimates (MLE) of the parameters of the statistical model of Mignan et al. (2017) using the negative log likelihood function negloglik_point.val() for one of the three possible time windows (full sequence, injection phase or post-injection phase).

model_par.mle_point(
  data,
  theta.init = list(a_fb = -1, tau = 1, b = 1),
  window = "full sequence"
)

data

a list containing all the necessary point data:

seism an earthquake catalogue data frame of parameters t (time in days) and m (magnitude)
inj matching injection profile data frame of parameters t (time in days), dV (flow rate in cubic metre/day) and V (cumulative injected volume in cubic metres)
m0 the minimum magnitude cutoff of the earthquake catalogue
ts shut-in time (in days) (not required for "injection")
Tmax upper range of the time window (in days) (not required for "injection")
lambda0 seismicity rate (per day) at shut-in (only required for "post-injection")

theta.init

an optional list of the initial values for the parameters to be optimized over

a_fb the underground feedback activation (in /cubic metre)
tau the mean relaxation time (in days)
b the slope of the Gutenberg-Richter law

window

the window to be used: "injection", "post-injection", or "full sequence"

Optimization done using the 'optim()“ function of the stats package.

a list of the parameters' MLEs:

a_fb the underground feedback activation (in /cubic metre)
tau the mean relaxation time (in days)
b the slope of the Gutenberg-Richter law
nLL the negative log likelihood value for the optimized parameters

Broccardo M., Mignan A., Wiemer S., Stojadinovic B., Giardini D. (2017), Hierarchical Bayesian Modeling of Fluid‐Induced Seismicity. Geophysical Research Letters, 44 (22), 11,357-11,367, doi: 10.1002/2017GL075251

Mignan A., Broccardo M., Wiemer S., Giardini D. (2017), Induced seismicity closed-form traffic light system for actuarial decision-making during deep fluid injections. Sci. Rep., 7, 13607, doi: 10.1038/s41598-017-13585-9

negloglik_point.val, negloglik_hist.val, model_par.mle_hist

amignan/rseismTLS documentation built on July 4, 2020, 1:04 p.m.