Problem 1. There are a number of seismic recordings from earthquakes and from mining explosions in the R package "astsa". All of the data are in the dataframe "eqexp", but two specic recordings are in "EQ5" and "EXP", the fth earthquake and the sixth explosion, respectively. The data represent two phases or arrivals along the surface, denoted by P (t = 1.., 1024) and S (t = 1025,..., 2048), at a seismic recording station. The recording instruments are in Scandinavia and monitor a Russian nuclear testing site. The general problem of interest is in distinguishing between these waveforms in order to maintain a comprehensive nuclear test ban treaty. To compare the earthquake and explosion signals, - (a) Plot the two series separately in a multigure plot with two rows and one column. . (b) Plot the two series on the same graph using different colors or different line types. - (c) Consider the signal plus noise model: art 2 at i wt, where wt ~ WN(0, 1). Simulate and plot the following two models. Model (i): :17; 2 st +wt,where wt ~ WN(0, 1) {0, t:1,...,125 St = t125 10 3 25 005(27rt/4), t : 126, . . . ,250 Model (ii): :3; 2 st +wt,where wt ~ WN(0, 1) {0, t=1,...,125 St : e125 10 e' 250 cos(27rt/4), t = 126, . . . ,250. Compare the general appearance of the series of model (i) and (ii) with the earthquake series and the explosion series