Yaoguo Li - Courses Taught
I am currently teaching two courses on gravity
and magnetic methods of exploration. The undergraduate course,
GPGN303 focuses on basics of the potential field methods and aim
to familiarize students with different aspects of these techniques.
The graduate course, GPGN511, concentrates on a number of selected
topics to introduce students to some of the newly developed numerical
methods for processing and interpretation.
- GPGN303: Introduction to Gravity and Magnetic
- This two-part course covers the basics of
gravity and magnetic exploration methods. In the first part,
we begin with Newton's law of gravitational force and study the
variations in earth's gravity field and move on to the small-scale
perturbations that are the signal of gravity exploration methods.
This leads to the study of methods and instruments for measuring
these variations and the associated field procedures. Subsequently,
the correction and processing of the observed data will be discussed.
This section concludes with the basic techniques for interpreting
gravity data, which include the calculation of source parameters
for simple anomalies. The second part of the course studies the
magnetic methods of exploration. We begin with the fundamentals
of magnetic field and study the earth's magnetic field and its
variations. Aspects of instrumentation, survey procedure, data
reduction, and interpretation will be studied. With the basic
understanding of both gravity and magnetic methods, we examine
the mathematical connection between the two methods, and study
the integrated interpretation.
- The course consists of the following sections:
- Part-I: Gravity methods.
- (1) Theory of gravitational field: gravitational
force, Newton's law, gravity potential and Poisson's equation.
- (2) Earth's gravitational field: its global
variations and various components for describing the field.
- (3) Principles of gravimeters.
- (4) Survey design and field procedures.
- (5) Gravity data reduction.
- (6) Processing techniques for gravity data.
- (7) Numerical modeling of gravity data.
- (7) Interpretation and inversion of gravity
- Part-II: Magnetic methods:
- (1) Theory of magnetic field: magnetic field
produced by a loop current and its dipolar approximation.
- (2) Sources of magnetic field in exploration
geophysics: magnetic susceptibility and magnetization.
- (3) Earth's magnetic field: basic parameteres
of the field and its spatial and temporal variations.
- (4) Principles of magnetometers.
- (5) Data reduction and processing.
- (6) Poisson's relation between gravity and
- (7) Numerical modeling of magnetic data.
- (8) Intepretation and inversion of magnetic
data: simple parameter estimation and examples of generalized
- Follow this link
to see pictures of students working during 1999 class.
- GPGN511: Advanced Gravity and Magnetic
- This course focuses on newly-developed processing
and interpretation techniques for gravity and magnetic data.
A number of selected topics will be discussed that cover different
stages from data reduction, processing, to interpretation. The
common foundation for these techniques is the inverse theory
applied to the problems in gravity and magnetic exploration.
Within this context, regularized inversion, fast numerical methods
for large-scale problems, and the interior-point method of optimization
will be discussed.
- The course consists of following five sections:
- (1) Introductory review on the basics
of the gravity and magnetic methods: Basic theory, data processing,
areas of application, and outstanding problems.
- (2) Stable downward continuation:
This section treats an age-old problem while introducing the
basic concepts of regularized inversion and demonstrating how
it can be used to tackle ill-posed problems in gravity and magnetics.
- (3) Stable reduction to the pole of magnetic
data at low latitudes: This is one of the best-known difficult
problems in gravity and magnetics. Formulation as a regularized
inversion allows one to extend this operation to the magnetic
equator while providing a framework for understanding previous
approaches in the literature.
- (4) Construction of equivalent sources:
This processing technique has seen increased use in recent years
due to the increased computing power and more efficient numerical
techniques. We discuss its solution using wavelet transforms
and regularized inversion. This also serve to introduce the wavelet-based
fast algorithms for large-scale problems.
- (5) 3D Inversion of gravity and magnetic
data: This topic utilizes the numerical techniques introduced
in the previous sections, and tackle the penultimate problem
of constructing a 3D distribution of physical properties from
the surface or borehole measurements of gravity or magnetic data.
Aspects of 3D inversion, depth weighting function, imposition
of bound constraints using interior-point methods, and fast numerical
solution using wavelets are discussed.
Last update: March 18, 2000.