Question

Identify the CORRECT assumption(s) supporting the convolutional model of zero-offset seismic data from the following statements.

• A. Seismic data consist of a single temporal frequency
• B. There are no sharp changes in the material properties in the subsurface
• C. Density is constant in the subsurface
• D. The source waveform is stationary, that is, the source waveform does not change as it travels in the subsurface

Hint:

The convolutional model assumes a stationary source wavelet, meaning it remains unchanged as it propagates. This makes seismic data representation as a convolution possible.

Answer 1

The Correct Option is D

Step 1: Understanding convolutional model of seismic data
In the convolutional model, the recorded seismic trace is expressed as: \[ s(t) = w(t) * r(t) \] where \(w(t)\) = source wavelet, \(r(t)\) = reflectivity function, and \(*\) = convolution operator.
This model assumes that the source waveform remains unchanged as it propagates through the medium. Step 2: Check each statement
(A) Seismic data consist of a single temporal frequency
This is incorrect. Seismic data are typically broadband, not consisting of a single temporal frequency. (B) There are no sharp changes in the material properties in the subsurface
This is incorrect. The convolutional model actually works because of reflectivity, which arises due to sharp changes in material properties (like velocity and density contrasts). (C) Density is constant in the subsurface
This is not a required assumption. The convolutional model can handle varying densities. Assuming constant density is sometimes used for simplicity, but it is not fundamental. (D) The source waveform is stationary
This is correct. The convolutional model assumes that the source waveform does not change as it travels through the subsurface. This assumption of stationarity is key to the model's validity. Step 3: Conclusion
Thus, the correct assumption is: \[ \boxed{\text{(D) The source waveform is stationary.}} \]