GEOL 340 Sedimentology and Stratigraphy
Lecture 28
1. Fourier Analysis
2. Cyclostratigraphy Case Studies
1. Fourier Analysis
Time Series = record of continuously varying signal
sampled at regular intervals
(Example: bedding thickness, grain size, isotope composition,
etc.)
Spectral Analyses allow two approaches to time series
a. time domain - the data series itself
bed thickness
transformation of bed thickness into time units
(extrapolation between layers of time control)
b. frequency domain - spectral density function of periodic
components, function of:
assumed underlying model
time-domain into frequency-domain transformation
graphic display of spectral density is called the power spectrum
Fourier Analysis
a. Jean Baptiste Fourier (1768-1830)
b. any continuous single values function can be expressed as the sum of harmonically related Fourier sinusoids, each with fixed amplitude, frequency, and phase
Fundamental Problem
a. lack of information and control on rates of sedimentation
b. when hiatuses occur, spectra beased on bed thickness are not
useful
Considerations
a. sinusoidal wave (duration = infinity; one cycle = period or
wavelength = 500 years)
b. power spectrum shows one peak with frequency = 2 cycles/ka
c. power spectrum peak height = wave amplitude
d. frequency = 1/wavelength = number of waveforms per unit time
e. noise = natural variations in the geologic attribute being measured
f. identifies cyclicity but not the process
g. absence of sedimentary cyclicity does not prove absence of cyclic processes
2. Cyclostratigraphy Case Studies
a. Deep-Water
KT Spain
Mid to Late K Piobicco, Moria, Umbria, Niobrara
b. Shallow-Water
Triassic Latemar Dolomites
Permian Castile