Seismic method The seismic method of exploration , exploit the fact that the velocity of elastic waves is different in different rocks .
What are seismic waves? Many people have experienced an earthquake but are probably unaware that the shaking they Feel and The damage To structures Are caused By the Arrival of Various seismic waves, a general term encompassing all waves generated by an earthquake. When movement on a fault takes place, energy is released in the form of two kinds of seismic waves that radiate outward in all directions from an earthquake’s focus. Body waves, so called because they travel through the solid body of Earth, are somewhat like sound waves, and surface waves, which travel along the ground surface, are analogous to undulations or waves on water surfaces.
What are the two types of body waves? An earthquake generates two types of body waves: P-waves and S-waves : P-waves, or primary waves, -are the fastest seismic waves and can travel through solids, liquids, and gases. -P-waves are compressional , or push–pull, waves and are similar to sound waves in that they move material forward and backward along a line in the same direction that the waves themselves are moving.
-Thus the material through which P-waves travel is expanded and compressed as the waves move through it and returns to its original size and shape after the waves pass by. - In fact, some P-waves emerging from Earth are transmitted into the atmosphere as sound waves, which at certain frequencies can be heard by humans and animals. S-waves, or secondary waves, are somewhat slower than P-waves . - S-waves can travel only through solids. S-waves are shear waves because they move the material perpendicular to the direction of travel, thereby producing shear stresses in the material they move through . Because liquids (as well as gases) are not rigid, they have no shear strength, and S-waves cannot be transmitted through them.
-The velocities of P- and S-waves are determined by the density and elasticity of the materials through which they travel. -For example, seismic waves travel more slowly through rocks of greater density but more rapidly through rocks with greater elasticity. Elasticity is a property of solids, such as rocks, and means that once they have been deformed by an applied force, they return to their original shape when the force is no longer present. Because P-wave velocity is higher than S-wave velocity in all materials, P-waves always arrive at seismic stations first .
what are the two major types of surface waves ? -Surface waves travel along the surface of the ground, or just below it, and are slower than body waves. Unlike the sharp jolting and shaking that body waves cause, surface waves generally produce a rolling or swaying motion, much like the experience of being in a boat. Several types of surface waves are recognized. The two most important are Rayleigh waves and Love waves, named after the British scientists who discovered them, Lord Rayleigh and A. E. H. Love. Rayleigh waves (R-waves) are generally the slower of the two and behave like water waves in that they move forward while the individual particles of material move in an elliptical path within a vertical plane oriented in the Direction of wave movement. The motion of a Love wave (L-wave) is similar to that of an S-wave, but the individual particles of the material move only back and forth in a horizontal plane perpendicular to the direction of wave travel. This type of lateral motion can be particularly damaging to building foundations.
Theory of elastisty The fundamental physical property mainly utilized in methods is the elastic wave transmission through the solid earth. The basis of the seismic methods is the theory of elasticity , which is governed by Hooke s law. Hookes law states that stress is proportional to strain, and the constant of proportionality being known as the elastic modulus.
Stress and strain Stress : a force acting a body, or a rock unit, that tend to change the size or the shape of the body , or the rock unit. Force per unit area within the body. S = F / A
Strain : Change in size (volume) or shape of the body in response to stress. Є
Propagation of seismic waves Propagation of seismic waves are controlled by the following concepts of geometrical optics: Huygens principal Fermat s principal Snell s law
1-Huygens's principal: every point on an advancing wavefront can be regarded as the source of secondary wave and that a later wavefront is envelope tangent to all the secondary waves. the line perpendicular to wavefront are wave paths or rays. waves are often represented by these rays. 2- Fermat ‘s principal: The ray pats which seismic energy will follow between two points is that for which the travel time is minimum . If the intervening medium, but will be such that the travel time is minimized. Snell ‘s law follow from this principal .
Attenuation and dispersion Attenuation of wave: A reduction of the amplitude of seismic waves, produced by divergence reflection, Scottering and absorption. Attenuation is often thought to be linear with frequency, sometimes thought to be quadratic with frequency. The following relationship is sometimes suggested:
Where : I= amplitude at distance ® I 0= initial amplitude R= distance travelled by wave Q= constant of the medium.
Sources of seismic attenuation may be grouped as follows: Inelastic processes Spherical divergence and spreading of energy over large area. Reflection and transmission losses at bound aries depending on reflectivity and reflection coefficient. Dispersion of waves The distortion of the Sharpe of a wave because of the variation of velocity with frequency.
Velocity of seismic waves
Refraction and reflection Seismic techniques generally involve measuring the travel time of certain types of seismic energy from surficial shots through the subsurface to arrays of ground motion sensors or geophones . In the subsurface, seismic energy travels in waves that spread out as hemispherical wavefronts (the three dimensional version of the ring of ripples from a pebble dropped into a pond). The energy arriving at a geophone is described as having traveled a ray path perpendicular to the wavefront ( a line drawn from the spot where the pebble was dropped to a point on the ripple). In the subsurface, seismic energy is refracted and/or reflected at interfaces between materials with different seismic velocities ( different densities).
The refraction and reflection of seismic energy at density contrasts follows exactly the same laws that govern the refraction and reflection of light through prisms. Note that for each seismic ray that strikes a density contrast a portion of the energy is refracted into the underlying layer, and the remainder is reflected at the angle of incidence . The reflection and refraction of seismic energy at each subsurface density contrast, and the generation of surface waves (or ground roll), and the sound (i.e. the air coupled wave or air blast ) at the ground surface all combine to produce a long and complicated sequence of ground motion at geophones near a shot point. The ground motion produced by a shot is typically recorded as a wiggle trace for each geophone .
Seismic Reflection Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves . . In reflection survey , the geophone separations I small compared to the depth. It is most extensively used geophysical technique. It give direct and detailed picture of sub surface
4.The main limitations to seismic reflection are its higher cost than refraction (for sites where either technique could be applied), and its practical limitation to depths generally greater than approximately 50 feet . 5.the correction of reflection method is topographic correction and weathering zone correction .
Seismic Refraction Refraction is the change in direction of waves that occurs when waves travel from one medium to another. Refraction is always accompanied by a wavelength and speed change . Diffraction is the bending of waves around obstacles and openings The shock waves which return from the top of rock are refracted waves, and for geophones at a distance from the shot point, always represent the first arrival of seismic energy
Seismic refraction is generally applicable only where the seismic velocities of layers increase with depth. Therefore, where higher velocity (e.g. clay) layers may overlie lower velocity (e.g. sand or gravel) layers, seismic refraction may yield incorrect results. In addition, since seismic refraction requires geophone arrays with lengths of approximately 4 to 5 times the depth to the density contrast of interest (e.g. the top of bedrock), seismic refraction is commonly limited (as a matter of practicality) to mapping layers only where they occur at depths less than 100 feet
Fermat's principle states that “light travels between two points along the path that requires the least time, as compared to other nearby paths.” From Fermat's principle, one can derive (a) the law of reflection [the angle of incidence is equal to the angle of reflection ] and (b) the law of refraction [Snell's law ]. This is problem