"Mathematical Techniques and Their Application in Geophysical Data Processing"

M. Turhan Taner, Hon. PhD.

20-21 / 06 / 2005

OBJECTIVE OF THE SEMINAR:

Objective of the seminar is to present mathematical techniques developed during my 40+ years as a Seismic Data Processing Research Geophysicist to the young researches, in the hope that it may help them in their work. I am not a seismic Interpreter, hence interpretation of the processing results will be left to the experienced interpreter. However, I am familiar with their needs, which directed me to the subjects to investigate. The lecture will not have many integrals, but sufficient amount of theory with more physical and geometrical analogy. Since I have been educated by the ITU as an Engineer, I will discuss more practical applications then abstract theory.

I will provide copies my papers written on each of the subjects discussed in the seminar.

1) MATHEMATICAL TECHNIQUES IN GEOPHYSICS (with applications):

Least Squares, conjugate gradient, Eigen analysis, principal component analysis, Fourier and z transform, minimum phase, zero phase concepts.
Joint time frequency analysis, complex functions, discrete vs. continuous functions their differences, Gabor–Morlet spectral decomposition, spectral
analysis of non-stationary data, spectral balancing, human hearing perception. Other joint time-frequency methods, Radon transform, linear, parabolic and hyperbolic, and their uses in Geophysical data processing and Interpretation.

2) SEISMIC DATA PROCESSING (fundamentals):

Objective oriented processing steps, processing for structural, stratigraphic and lithologic interpretations. Selection of processing parameters, use and abuse of some processes. Surface consistency.

Following lecture items will follow the processing steps:

3) WAVELETS:

Wavelet estimation from shot records, wavelet characteristics, wavelet estimation from stack section, between well logs and seismic data, phase estimation, wavelet shaping, higher resolving wavelets, surface consistent processing.

4) DECONVOLUTION AND MULTIPLE SUPPRESSION:

Surface connected multiples, inter-bed multiples, multiple suppression methods, deconvolution , spiking, predictive, multi-channel deconvolution, adaptive deconvolution, characteristics of multiple prediction operators. New ideas of utilization of multiples, characteristics of auto, cross correlation.

5) STATICS:

Near surface problems, various types of statics, common problems, different methods, amplitude, phase and time statics, reflected and refracted wave statics, near surface imaging with refracted waves, surface consistency, consistent delay estimation.
6) VELOCITY ANALYSIS:

Average, RMS, interval velocities, time and depth average velocities. Velocity analysis for CDP, time and depth migration, travel time-offset relations, velocities for long offsets.

7) ATTENUATION-DISPERESION OF SEISMIC WAVES, AND Q:

Attenuation and dispersion of seismic waves, intrinsic and extrinsic attenuation, attenuation-dispersion relationship, Q computation and compensation form seismic data.

8) SEISMIC ACOUSTIC INVERSION:

Simple inversion by recursion, by integration and their practical uses.
9) NEURAL NETWORKS:

Basics of neural networks, supervised and unsupervised networks,  network training, their utilization on various problems. Multi layer perceptron, Kohonen’s Self Organized Map method, Learning Vector Quantizing network, probabilistic network, Radial basis function networks. computation methods. Simulation of human hearing perception. Data mining and knowledge discovery.

10) AMPLITUDE-VERSUS-OFFSET (AVO):

AVO computations and approximations, experiment with various parameterizations. Aki-Richard, Fatti and Shuey approximations for P, S wave reflectivities, density and various elastic modulo estimations, seismic inversion.

11) SEISMIC ATTRIBUTES AND THEIR UTILIZATION IN INTERPRETATION:

Physical, geometric, wavelet attributes, special purpose composite attributes,, continuity discontinuity attributes, Eigen attributes, Principal component analysis, attribute characteristics.