Page 20 - Reservoir Geomechanics

5 The tectonic stress field

chapters. While there are many excellent texts on elasticity and continuum mechanics
that discuss stress at great length, it is useful to set forth a few basics and establish a
consistent nomenclature for use throughout this book. Next, the relative magnitudes
of in situ stresses are discussed in terms of E. M. Anderson’s simple, but powerful,
classification scheme (Anderson 1951) based on the style of faulting that would be
induced by a given stress state. This scheme leads naturally to some general constraints
on stress magnitudes as a function of depth and pore pressure. These constraints will
be revisited and refined, first in Chapter 4 where we will discuss constraints on stress
magnitudes in terms of the strength of the crust and further refined when we incorporate
information about the presence (or absence) of wellbore failures (Chapters 7 and 8).
In the next section of this chapter I briefly review some of the stress indicators that
will be discussed at length in subsequent chapters. I do so in order to review synoptically
some general principles about the state of stress in the crust that can be derived from
compilations of stress information at a variety of scales. The overall coherence of the
stress field, even in areas of active tectonic deformation and geologic complexity is now
a demonstrable fact, based on thousands of observations from sites around the world
(in a wide range of geologic settings). We next briefly review several mechanisms that
control crustal stress at regional scale. Finally, we consider the localized rotation of
stress in the presence of near frictionless interfaces, such as salt bodies in sedimentary
basins such as the Gulf of Mexico.

Basic definitions

In simplest terms, stress is defined as a force acting over a given area. To conform
with common practice in the oil and gas industry around the world I utilize throughout
the book calculations and field examples using both English units (psi) and SI units
(megapascals (MPa), where 1 MPa = 145 psi).
Tobemore precise,stressisatensorwhichdescribesthe densityofforces actingonall
surfaces passing through a given point. In terms of continuum mechanics, the stresses
acting on a homogeneous, isotropic body at depth are describable as a second-rank
tensor, with nine components (Figure 1.1, left).

 
s 11 s 12 s 13
 
S =  s 21 s 22 s 23  (1.1)
s 31 s 32 s 33

The subscripts of the individual stress components refer to the direction that a given
force is acting and the face of the unit cube upon which the stress component acts. Thus,
any given stress component represents a force acting in a specific direction on a unit
area of given orientation. As illustrated in the left side of Figure 1.1,a stress tensor can