Signal-to-noise ratios of seismic waves
Refer to given Exercise. Suppose an additional independent variable is considered, as follows:
x3 = Time interval (seconds) between seismic waves
(a) Write the first-order model plus interaction for E(y) as a function of x1, x2, and x3.
(b) Write the complete second-order model plus interaction for E(y) as a function of x1, x2, and x3.
Exercise
Signal-to-noise ratios of seismic waves. Chinese scientists have developed a method of boosting the signal-to-noise ratio of a seismic wave (Chinese Journal of Geophysics, Vol. 49, 2006). Suppose an exploration seismologist wants to develop a model to estimate the average signal-to-noise ratio of an earthquake's seismic wave, y, as a function of two independent variables:
x1 = Frequency (Cycles per second)
x2 = Amplitude of the wavelet
(a) Identify the independent variables as quantitative or qualitative.
(b) Write the first-order model for E(y).
(c) Write a model for E(y) that contains all first order and interaction terms. Sketch typical response curves showing E(y), the mean signal-to-noise ratio, versus x2, the amplitude of the wavelet, for different values of x1 (assume that x1 and x2 interact).
(d) Write the complete second-order model for E(y).