Download Rock Physics

School of GeoSciences Board of Studies
Proposal for a New Course or Major Course Change
Please use the following headings for your Proposal. Where it is not obvious, some indication
is given of the information that is needed under each heading.
Course Name:
Rock Physics
Course Rationale (including academic justification and any enhancements to the student
learning experience)
This is a core course for the MSc degree programme in Exploration Geophysics, and it is also
available for other post-graduates in the school (MScs + PhDs) as an optional course.
Benefits to the School
This course is to support the MSc degree programme in the school, and the School will be
benefited through increased financial income from MSc students.
Quotas and Prerequisites
30-35; successful completion of the course in Fundamental mathematics, and other
conversion courses, as well as the compulsory courses defined in the relevant degree
programme.
Resource Implications
The course will be taught jointly by an existing staff member in the school and an external
expert in this field.
Consultation
We have consulted widely in the development of this course, including discussion with the
geophysics team and the subsurface research group, as well as the teaching organization.
Several consultation sessions have been held with the MSc programme director, the HoS, and
the Teaching Organisation.
Risk Assessment
This is normal classroom teaching. Health and safety procedures are in place in the School
and no specific risks arising from the proposed the course have been identified.
Teachability Assessment
On completion of this course, the students should achieve the following learning outcomes:

A familiarity with how rocks and pore fluids behave under stress in the subsurface.

An understanding of how rock and fluid properties affect the propagation of geophysical
fields, as an aid to interpreting geophysical images.

An understanding of mathematical, physical, computational and experimental concepts
and tools required to model the behaviour of reservoir rocks.
Disabled students will not be at a disadvantage for the majority of the course, as it is lecture
and classroom-based
Quality Assurance Arrangements
The course will be assessed by continuous assessment, and assessment will be by members of
academic staff using the University’s common marking scheme. The assessed group
presentation component will be marked by 2 or more of the lecturing staff for that course,
with feedback provided to students on the reasons for their assigned mark.
Student questionnaires will be used to provide feedback on the quality of the course, teaching
and supervision.
External examiners will also be used to ensure the quality of the overall programme and
suitability of MSc grading.
Course summary
Rock Physics (10 credits) - Semester 2: Block 4
Syllabus
Part A – Rock deformation and fluid flow (led by Ian Main)
1. Introduction – concepts of stress, strain, elasticity of isotropic media
2. Simple rheological models – the generalised Burgers body
3. Rock failure – brittle and ductile
4. Experimental Rock deformation: laboratory methods and demonstration (Ian Butler)
5. Coulomb friction
6. Failure criteria for ideal elastic materials
7. Fracture nucleation
8. Static fatigue
9. Percolation theory and numerical modelling
10. Fluid flow in porous, fractured media
Part B – Geophysical properties of porous, fractured media (led by Mark Chapman)
-
include anisotropy, what determines velocity resistivity etc., damage mechanics, effective
medium theory, poroelasticity, seismic wave propagation, effect of P and T, upscaling etc.
Outline of the 10 lectures:
1. Intuitive definition of anisotropy; causes of anisotropy in the Earth’s crust; Importance of
anisotropy; Symmetry classes, HTI, VTI, orthorhombic, monoclinic together with likely
causes; outline of the course.
2. Introduction of elastic tensor; formal definition of anisotropy in terms of invariance under
rotation; standard matrix form of the elastic tensor; Christoffel equation, plane wave
solutions; slowness surfaces and polarisations; Definition of Thomsen parameters; weak
anisotropy.
3. Distinction between phase and group velocity; wavefront construction; singularities;
observable seismic effects, shear-wave splitting, AVO vs azimuth, azimuthal variations in
interval traveltime.
4. Mathematical description of fractured media through use of equivalent medium theories;
energy approaches; volumetric averaging approaches, Backus averaging technique;
fundamental limitations of equivalent medium theory.
5. The Eshelby inclusion; Budiansky-O’Connell model; Hudson’s theory for fractured rock;
high concentration extensions, self-consistent, coherent potential, differential scheme;
Linear-slip model; estimates of Z N , ZT .
6. Poroelasticity; Biot-Gassmann theory; dispersion/attenuation and the slow P-wave;
concept of effective stress; experimental basis, role of fluid mobility; squirt-flow concept;
fractures in porous media; frequency-dependence
7. Resistivity of porous rock; Formation factor; Hashin-Shtrikman bounds on resistivity;
simple inclusion models; Archie equation, generalized Archie; Humble formula; empirical
relations; resistivity anisotropy; importance of resistivity anisotropy in light of modern
resistivity logs- 3D explorer.
8. Effects of fluids and stress on seismic and electrical properties; Gassmann/anisotropic
Gassmann; fluid estimates from Hudson, effect of aspect ratio; Nur’s theory for closing of
microcracks and extensions; pressure sensitivity of fracture compliance; laboratory
measurements of stress and fluid sensitivity.
9. Fracture characterisation in applied geophysics; shallow seismic refraction for civil
engineering applications; Rock damage, RQD index; Barton-Bandis model; construction
of fracture maps for oil reservoirs from anisotropy measurements; coherencey cube;
techniques based on curvature attributes and geostatistics; estimation of fracture spacing
from analysis of coda.
10. Finite difference modelling of wave propagation in fractured rocks; Coates-Schoenberg
technique; building discrete fracture network (DFN) models from seismic and log data;
flow simulations through DFN models, link to anisotropic permeability; future directions
– fracture characterization from seismic to simulator.
Tutorials
Three tutorials on suitably constructed problems along the following lines (all of these should
be able to be done with pen and paper):
1. Manipulation of elastic tensor; construction from Thomsen parameters; identification of
symmetry class from standard matrix form; demonstration of invariance of TI tensor
under certain rotations, but not others.
2. Calculations of effective elastic tensors for a) a given layered medium using Backus, b) a
given fractured medium using Hudson. Solve the Christofell equation for various
directions of propagation. Develop relationships between crack properties and resulting
variations of velocity with direction.
3. Anisotropic fluid substitution exercise. Give them some laboratory velocity data (5
velocity measurements, dry), get them to construct the elastic tensor assuming transverse
isotropy, use anisotropic Gassmann to change the fluid, then calculate the same 5
velocities but for water saturation.