Modeling a Seismic Signal with a Ricker Wavelet Assignment

Assignment Task

A. A seismic signal is modeled by a Ricker wavelet:

a. The constant k is adjusted to obtain a wavelet of a given frequency. Calculate this constant so that the spectrum of the signal is approximately centered on 40 Neatly plot the original signal and its amplitude spectrum.

NB: A Ricker wavelet is the second derivative of a Gaussian function, and its theoretical spectrum can be easily calculated analytically (cf. attached document).

b. An explosion of a buried charge is approximated by the source How does the spectrum change with the existence of a ghost, i.e., the reflection on the free surface? (We will construct a sampled signal at 1000 Hz, taking into account the ghost; for example, we will take a depth of 20 m and a surface velocity of 1200 m/s.

NB: The ghost corresponds to an additional secondary source equal to the primary signal (neglecting attenuation and spherical divergence), delayed by the round-trip time and multiplied by the reflection coefficient e1 on the free surface. Vertical paths will be considered.

c. What type of filter does the ghost effect make you think of? Determine a discrete MA filter by its expression in z that artificially recreates this ghost effect and expresses its spectral

PS: Questions a) to c) will be solved both theoretically (establishment of literal formulas) and numerically.

d. The files T20.txt and T25.txt represent recordings of buried charges, at depths respectively ranging from 28 to 20.60 m (20 kg of explosive) and from 31 to 21.75 m (25 kg of explosive). Perform spectral analysis on the first arrivals and determine if a ghost effect exists on the recordings (we will test on the Z component measured in free field (the 3rd column of the file, with time being the 2nd) at 4154 and 4191 m from the source, respectively).

B. The signal recorded in the file is the recording made by a Vibraloc vibration controller. Three channels are recorded (in mm/s) corresponding to the 3 geophones (V)ertical and horizontal, (L)ongitudinal and (T)ransverse. The signals are sampled at 997 Hz. A fourth channel can be used for sound recording using a microphone. The recording is triggered by the detection of ground vibration on a threshold crossing criterion. Channels V, L, and T correspond to the 1st, 2nd, and 3rd columns of the file, respectively.

• Using the modified Welch method, calculate the power spectral density of the signal detected on channel Explain the chosen parameters and neatly plot this spectrum, correctly indicating the units of the numerical values on the axes.
• What is the frequency corresponding to the maximum PSD?
• By performing an appropriate calculation, determine if the signals recorded on channels L and T are correlated in a certain frequency band.

This Engineering has been solved by our PhD Experts at My Uni Paper.