Seismic Waves
An application of an external force, on part of a medium (elastic medium), leads to creation of internal opposing forces which intend to resist the deformations caused by that external force. Typical forms of the resulting deformations are changes in volu
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Seismic Waves
2.1
The Fundamental Conditions
An application of an external force, on part of a medium (elastic medium), leads to creation of internal opposing forces which intend to resist the deformations caused by that external force. Typical forms of the resulting deformations are changes in volume and/or in shape which are created at the affected location. In consequence, the medium will return to its original condition after the external force is removed. This property of resisting of changes in volume and in shape and return to original conditions after removal of the external force is called (elasticity). Provided that the changes are small, rock media in nature are considered to be perfectly elastic in nature. As a result of the elasticity property of media, the changes (volume and shape changes) oscillate about their neutral positions and, at the same time, propagate away from the energy source-location. Energy transfer in this manner (motion that leaves out no permanent distortions) is commonly referred to as (wave motion). The fundamental condition for the creation and propagation of seismic waves (seismic field) is a source of mechanical energy of impulsive type which is initiated within an elastic medium. The energy source may be natural (as in earthquake-generated waves) or artificial (as in firing of a dynamite charge). In both cases wave
motion of elastic waves are generated and can be recorded by the appropriate detection instruments. These are normally referred to as the (seismic waves).
2.2
Theory of Elasticity
As it is stated above, the fundamental conditions for a seismic field to be created is that the medium must possess the elasticity property. Two main concepts are governing the propagation of seismic waves in an elastic medium: the (stress) and the (strain). Stress represents the external force applied to the elastic medium, and strain is the resulting changes in volume and in shape. The relation between stress and strain, for a particular medium (perfectly elastic medium), gives evaluation expressions for the elasticity property of that medium. The stress-strain proportionality constants are the elastic coefficients which serve as measures of the elasticity of a particular medium. The principal types of changes experienced by a medium due to passage of a seismic wave are re-distribution of the internal forces (stress changes) and modification of the volume and geometrical shape (strain changes). The theory of elasticity deals with analysis of these principal effects and the related physical changes.
© Springer International Publishing Switzerland 2017 H.N. Alsadi, Seismic Hydrocarbon Exploration, Advances in Oil and Gas Exploration & Production, DOI 10.1007/978-3-319-40436-3_2
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2.2.1
2 Seismic Waves
Stress
In the broad sense, stress is represented by a force (called traction) which is acting on a finite area occupying an arbitrary position within the medium. However, for more precise definition, the stress (T) is defined to be a limiting value of the ratio of a force (F) acting
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