Understand the two main objectives of geophysical data processing-namely, enhancement and modeling and parameter estimation.
	Gain experience in computer usage to solve numerical problems in geophysics.
	Develop greater familiarity with certain mathematical tools and constructs [Vectors, Matrices, Transforms] as used in geophysical computation.
	Understand the basic principles of geophysical data inversion, parameter estimation, assessment of solution goodness.
	Understand the basic principles of filtering and its applications for data enhancement.

In addition to the course prerequisites stated in the Bulletin, students are expected to have completed their general mathematics and physics course requirements.

Vector Analysis   Vector algebra, calculus and operators. Some important concepts and theorems: the gradient, the divergence, and the curl; Gauss, Green, and Stockes’ theorems. Examples of geophysical applications of vectors: Gravity and Magnetic fields and field equations. SVD; Paleomagnetic data analysis.	1
Matrix Computation   Basic concepts from linear algebra: vector space, bases vectors, and linear independence. Matrix algebra: addition, multiplication, and inversion of matrices. Matrix rank and linear dependence: singular matrices and some special types of square matrices. Matrix functions: their integration and differentiation.	2
Elements of Statistics   Basic Concepts: classification of data, histograms, and frequency distribution; mean, variance, standard deviation, and moments. Elements of probability theory and sampling: sample space, sample point and events; conditional probability and independence of events. Discrete and continuous random variables: important probability distribution of random variables.	1
Elements of Inverse Theory    Basic concepts: observational data, random error, model parameters, and measures of vector length. Classification and Formulation of inverse problems: The implicit and the explicit linear linear forms. Overdetermined, Evendetermined, and Underdetermined linear inverse problems. Solutions of LIP: prediction error, vector norms, and the solution of the Overdetermined problem; priori information, constraints, Lagrange multipliers, and the solution of the Underdetermied problem. Generalized inverse: measures of goodness of resolution and covariance; the data resolution, the model resolution, and the unit covariance matrices. Description of some Linear Inverse Problems [LIP] in geophysics with examples from gravity, magnetic and seismic exploration methods. Generalized inverse: measures of goodness of resolution and covariance: the data resolution, the model resolution, and the unit covariance matrices. Description of some Linear Inverse Problems [LIP] in geophysics with examples from gravity, magnetic and seismic exploration methods.	4
Fourier Transform   Fourier Analysis and Synthesis: The Fourier series and properties; expansion of functions; discrete form; computation of coefficients by inversion. Applications: Continuation of potential fields. Fourier transform and inverse transform: transform pairs of special functions, even, odd and mixed functions; useful properties of the Fourier transform. The Discrete (DFT) and Fast Fourier (FFT) Transforms; some algorithms for their computation.	2
Filtering Fundamentals   Basics of Signal analysis: amplitude, period, wavelength, cycle, spatial, temporal, and angular frequencies. Sampling Theorem: sampling rate and aliasing. Basic concepts of linear systems: convolution, and digital filtering; Low Pass, High Pass, and Band Pass filters. Geophysical Examples: continuation and derivatives of potential fields, data smoothing, signal separation. Spectral Analysis: autocorrelation, crosscorrelation and power spectrum, windowing, simple methods of spectral estimation. Power spectra and the interpretation of magnetic anomalies.	4