Page 220 - Acquisition and Processing of Marine Seismic Data

CHAPTER

4

Fundamentals of Data Processing

OUTLINE

4.1 Autocorrelation 213 4.6 2D Fourier Transform 222
4.2 Crosscorrelation 215 4.7 z Transform 230
4.3 Convolution 215 4.8 Hilbert Transform 231

4.4 Fourier Series 216 4.9 τ-p Transform (Slant Stack) 232
4.5 1D Fourier Transform 219 4.10 Sampling Theory 235

In seismic data processing, some fundamental such as auto- and cross-correlations and convolu-
processes and the determination of processing tion, some generalized functions such as the
parameters are accomplished by analyzing spe- Dirac Delta or unit impulse, box-car or sinc func-
cific correlation functions and frequency compo- tion, and some of the most common transforms
nents of the input seismic data. Correlation can be such as the Fourier, Hilbert or τ-p transforms
handled by computing auto- or cross-correlation and their characteristics, as well as application
functions, while the frequency characteristics of fields, are explained.
the data are investigated by computing the Fou- Signal processing in geophysics is generally
rier transform, which moves the data from the achieved by carrying out a number of mathe-
time to the frequency domain. In addition, some matical processes applied to the geophysical sig-
of the processing steps such as bandpass filtering nal, which is generally in the form of discrete
or deconvolution in the time domain are imple- time series. Based on the environment where
mented by convolution. Since these applications the signal is observed, the data is a function of
are the main tools of data processing, their funda- either time or space: that is, the data is defined
mental concepts and basic properties have signif- in time or distance domains, respectively. If
icant importance for a seismic processor. In this the observed signal is a function of frequency,
section, some of the basic mathematical processes then the frequency domain is considered. It is

Acquisition and Processing of Marine Seismic Data 211 # 2018 Elsevier Inc. All rights reserved.
https://doi.org/10.1016/B978-0-12-811490-2.00004-9