Anderson's Theory of Faulting

 

The Simple Theory That Explains Earth's Faults: An In-Depth Look at Anderson's Model

Just an imaginary sketch of Anderson

I. Introduction: The Deep Dialogue Between Theory and Reality

Earth's surface is a dynamic canvas, a landscape of towering mountain ranges, sprawling valleys, and continents in slow, grinding motion. These dramatic features are the result of immense, unseen forces acting on the planet's crust. When these forces become too great, the brittle rock breaks, leaving behind a fracture known as a fault. While the grinding motion of these faults can unleash the destructive power of earthquakes, they are also a fundamental part of the geological processes that shape our world. To understand them is to understand the language of our planet.

At the heart of this understanding lies a remarkably simple yet profound framework: Anderson's Theory of Faulting. Developed by Ernest Masson Anderson in his seminal 1951 work, Dynamics of Faulting and Dyke Formation with Application to Britain, this theory provides the foundational principles for a first-pass classification of faults. Far from being a historical artifact, its elegant logic continues to serve as a cornerstone of structural geology and seismic interpretation. It allows geologists to relate the sense of slip on a fault to the underlying regional stress field, providing a crucial link between the visible surface features and the invisible forces that create them. This report delves into the elegant core of Anderson's model, exploring its foundational concepts, its key assumptions and limitations, and its enduring legacy in modern geological science.

II. The Blueprint of Brittle Failure: Understanding Stress

To grasp Anderson's theory, one must first understand the concept of stress, which in geology is simply defined as the force applied to a material. Deep within the Earth, rocks are subject to immense pressure from all directions, a state known as confining stress. However, deformation and failure, such as the creation of faults, occur when there is an imbalance in these forces, leading to compressional (squeezing), tensional (pulling apart), and shear (sliding) stresses.

Anderson's theory is built upon the concept of principal stresses. A stress field at any point in the Earth's crust can be mathematically represented, but it can always be simplified to three primary, mutually orthogonal directions where the shear stress is zero. These are the principal stresses, conventionally labeled and ordered by magnitude:

• σ1​ (Sigma 1): The maximum principal stress, representing the direction of greatest compression.

• σ2​ (Sigma 2): The intermediate principal stress.

• σ3​ (Sigma 3): The minimum principal stress, representing the direction of greatest tension or least compression.

The orientation of these three principal stresses with respect to each other and the Earth's surface is the key to predicting fault formation. The mechanical behavior that governs this process is the Mohr-Coulomb failure criterion, a principle stating that a rock will fail when the shear stress across a plane overcomes two forces: the rock's internal cohesive strength and the frictional resistance along that plane. The theory posits that rocks will fail on two symmetric planes at a specific angle to the direction of greatest compression, a concept central to Anderson's model.

III. Anderson's Three Faulting Regimes: An Elegant Classification

Anderson's most profound contribution was the recognition that the Earth's surface functions as a "free surface," meaning it cannot support shear stress. This critical boundary condition forces one of the three principal stress axes to be oriented vertically (perpendicular to the surface). The other two principal stresses must then lie on a horizontal plane. This simple but elegant constraint reduces the infinite number of possible stress orientations to just three primary configurations, each defining a distinct faulting regime.

Normal Faults

Normal faults occur in an extensional stress regime where the Earth's crust is being stretched. In this scenario, the greatest compressive stress (

σ1​) is vertical, and the least compressive stress (σ3​) is horizontal. Under these tensional forces, a block of rock known as the hanging wall slides downward relative to the block below, called the footwall. The theory predicts a characteristic dip angle of approximately 60 degrees for these faults, an angle that is a direct consequence of the Mohr-Coulomb failure criterion and the assumed friction of the rock.

Reverse Faults

A reverse fault is the product of a compressional stress regime where the crust is being squeezed. In this case, the greatest compressive stress (

σ1​) is horizontal, and the least compressive stress (σ3​) is vertical. This configuration causes the hanging wall to be thrust upward relative to the footwall, resulting in a shortening of the crust. According to Anderson's model, reverse faults are predicted to form with a shallower dip angle of approximately 30 degrees. When a reverse fault has a particularly shallow dip, typically less than 45 degrees, it is often referred to as a thrust fault.

Strike-Slip Faults

Strike-slip faulting represents a shearing environment where blocks slide horizontally past each other. This occurs when both the greatest compressive stress (

σ1​) and the least compressive stress (σ3​) are horizontal, and the intermediate stress (σ2​) is the vertical principal stress. Since the movement is purely lateral, there is no vertical displacement, and thus the concepts of a hanging wall and footwall do not apply. The theory predicts a perfectly vertical (90-degree) dip for these faults, a testament to the elegant relationship between the stress field and the orientation of the fault plane.

The following table provides a quick guide to Anderson's three primary fault types and their relationship to the principal stress axes and predicted dip angles.

Fault Type	Principal Stress Regime	Resulting Motion	Predicted Dip Angle
Normal	${\sigma }_1$ is vertical, ${\sigma }_3$ is horizontal	Hanging wall moves down relative to footwall	~60°
Reverse	${\sigma }_1$ is horizontal, ${\sigma }_3$ is vertical	Hanging wall moves up relative to footwall	~30°
Strike-Slip	${\sigma }_1$ and ${\sigma }_3$ are horizontal, ${\sigma }_2$ is vertical	Lateral, horizontal movement	~90°

IV. Beyond the Perfect Model: Assumptions and Exceptions

While Anderson's theory is a remarkably powerful tool, it is, by design, an idealized model. Its predictive power rests on several key assumptions that are not always met in the complex reality of Earth's crust:

• The rock is homogenous and isotropic.

• The fault blocks are perfectly rigid.

• Faults are straight, planar surfaces.

• The model addresses a "frozen state," neglecting the dynamic processes of fault initiation, propagation, and growth over time.

The most significant and well-known challenge to Anderson's model comes from the existence of low-angle normal faults. The theory predicts that normal faults should dip at approximately 60 degrees, yet many are observed with dips less than 45 degrees. This apparent contradiction has led to the development of more complex models to explain these geological phenomena, which, in turn, demonstrates the evolution of structural geology.

Modern explanations for these exceptions include:

• Elevated Pore Fluid Pressure ($P_f$): Anderson's model does not explicitly account for the presence of fluids within the rock. However, fluids in the pore spaces of rocks exert pressure that effectively "pushes back" against the normal stress holding a fault plane together. This reduces the

  effective normal stress (${\sigma }_{eff}={\sigma }_n-P_f$) and, consequently, lowers the frictional resistance to slip. A high fluid pressure can therefore enable a fault to slip at a mechanically unfavorable, shallower angle. This mechanism is a critical factor in understanding how seismic activity can be triggered, a key area of modern research.

  

• Pre-existing Anisotropy: Real rocks are not homogenous materials as the theory assumes. They contain pre-existing weaknesses, such as bedding planes, foliation, or older, inactive fault zones. It may be easier for the rock to fail along one of these weak planes, even if its orientation is not optimal according to the stress field, rather than forming a new fault at the predicted angle. This highlights how a rock's intrinsic structure can be a more dominant factor in determining a fault's orientation than the overarching stress field.

• The Rolling-Hinge Model: For low-angle normal faults, this model offers a dynamic, time-dependent explanation. It proposes that an initially steep, Andersonian-style normal fault can progressively flatten over time as it slips, with the fault plane rotating to a gentler angle. This kinematic model accounts for the evolution of a fault system, complementing Anderson's static, "frozen-in-time" perspective.

Beyond the three primary faulting regimes, a lesser-known but fascinating part of Anderson's original work also explored the concept of stress trajectories around a single fracture. He correctly inferred the location and orientation of where secondary, or "splay," faults would form in the stress shadow of a major fault, an observation that demonstrates his profound foresight and meticulous understanding of rock mechanics.

V. Where the Theory Meets the Real World: Case Studies

The enduring relevance of Anderson's theory is best demonstrated by its ability to explain the fundamental tectonic forces shaping iconic geological landscapes around the globe.

The Basin and Range Province (Normal Faulting)

The Basin and Range Province, a vast region spanning the western United States, is a textbook example of crustal extension and normal faulting. Here, tensional forces have stretched the crust, creating a series of parallel, alternating mountain ranges (horsts) and valleys (grabens). This distinctive topography is the direct result of large-scale normal faults, perfectly consistent with Anderson's model of a tectonic regime where the maximum compressive stress is vertical.

The Himalayas (Reverse Faulting)

On the other side of the globe, the formation of the Himalayas provides a perfect illustration of a compressional stress regime. The ongoing collision of the Indian and Eurasian plates is a titanic compressional event. This force is accommodated by immense reverse and thrust faults that have pushed huge sheets of rock up and over, resulting in the crustal shortening and spectacular uplift that created the world's highest mountains.

The San Andreas Fault (Strike-Slip Faulting)

Perhaps the most famous fault in the world, the San Andreas Fault in California, is the quintessential example of strike-slip faulting. This fault marks the boundary between the Pacific and North American tectonic plates, which are sliding horizontally past one another. This lateral movement, driven by horizontal stresses, is the primary source of the major earthquakes that define the region and is a clear, large-scale confirmation of the Andersonian strike-slip regime.

VI. Conclusion: Anderson's Enduring Legacy

Anderson's Theory of Faulting stands as a testament to the power of a simple, elegant model to illuminate a complex natural process. It provides an indispensable first-pass framework for understanding how stress is translated into brittle failure and a clear method for classifying the three fundamental types of faults. While the theory's simplifying assumptions mean it does not explain every faulting phenomenon, particularly in the face of modern discoveries like low-angle normal faults and the effects of pore fluid pressure, it remains a cornerstone of geological education and research.

Refrence: 

• Structural Geology - Haakon Fossen
• Structural Geology of rocks and regions – G. H. Davis
• Structural Geology, fundamentals & modern development -  S K Ghosh
• Structural Geology – M. P. Billings