## GEOL882.3

Fall 2016/2017:

*
*Linear Filtering in Applied Geophysics

Students will learn and discuss basics of the linear
filtering theory in application forward and inverse seismic and geophysical
problems. Each of the students will make three presentation and perform a
short practical exercise by using Matlab or Octave software.

Study topics:

- Transforms (Part 1 in the text):
- Fourier, Z-, and Laplace transforms
- Hilbert transform; instantaneous amplitude and
instantaneous frequency
- The t-
*p* transform
and its inverse

- Linear filtering (Parts 4 and 5):
- Requirements (linearity, time-invariance, causality)
- Impulse responses and frequency responses
- Inverse filters
- Special types (zero-phase, time-shift, minimum-phase,
all-pass)
- Cascaded and parallel application of filters
- Recursive and rational filters

- Optimal filters (Part 6):
- Wiener optimum filter
- Shaping filters
- Kalman filters

- Deconvolution (Part 7):
- Exact deconvolution
- Optimum deconvolution
- Homomorphic deconvolution
- Applications to reflection seismics: ghost reflection
suppression, wavelet estimation, predictive deconvolution, dynamic
deconvolution

#### Text:

Buttkus, B., 2000. Spectral Analysis and Filter Theory in
Applied Geophysics, Springer-Verlag, ISBN 3-540-62674-3

From this book, we will use Parts 1 and 4 through 7.

#### Marking scheme:

- 80% for three presentations
- 20% practical exercise