## 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 GPGN511

• GPGN303: Introduction to Gravity and Magnetic Methods
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 data.

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 magnetic fields.
(7) Numerical modeling of magnetic data.
(8) Intepretation and inversion of magnetic data: simple parameter estimation and examples of generalized inversion.

Follow this link to see pictures of students working during 1999 class.

• GPGN511: Advanced Gravity and Magnetic Exploration
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.