model_par.mle_hist: Model Parameter Maximum Likelihood Estimation (Histogram...
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 Non-Homogeneous Poisson Process (NHPP) derived from the statistical model of Mignan et al. (2017) using the negative log likelihood function negloglik_hist.val() for one of the three possible time windows (full sequence, injection phase or post-injection phase).

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

data

a list containing all the necessary histogram data:

seism.binned an earthquake-rate histogram data frame of parameters t (time in days) and rate (per time bin)
inj.binned matching binned injection profile data frame of parameters t (time in days), dV (flow rate in cubic metre/time bin) and V (cumulative injected volume in cubic metres)
b the b-value of the earthquake catalogue (not required for "post-injection")
m0 the minimum magnitude cutoff of the earthquake catalogue (not required for "post-injection")
ts shut-in time (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)

window

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

Optimization done using the 'optim()“ function of the stats package. In contrast to point-data MLE parameter optimization, the b-value is here an input instead of an output.

a list of the parameters' MLEs:

a_fb the underground feedback activation (in /cubic metre)
tau the mean relaxation time (in days)
nLL the negative log likelihood value for the optimized parameters

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_hist.val, negloglik_point.val, model_par.mle_point, data.bin

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