Directional geophone responses to different waves

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	2
Pages	7 - 46
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 2.15

Assume three geophones so oriented that one records only the vertical component of a seismic wave, another only the horizontal component in the direction of the source, and the third only the horizontal component at right angles to this. Draw the responses of the three geophones for the following cases:

1. A P-wave traveling directly from the source to the geophones
2. A P-wave reflected at a deep horizon
3. An S-wave generated by reflection of a P-wave at an interface
4. A Rayleigh wave generated by the source
5. A Love wave generated by the source

Assume a simple waveshape, that there is a small vertical velocity gradient, that the source generates an initial compression for the direct wave, and an initial up- and away-thrust for the horizontal phone that is in line with the source. Compare the relative magnitudes of the components for short- and long-offset distances.

Background

A converted S-wave is generated in a solid medium when an incident P-wave strikes an interface at an angle (see problem 2.10). A Love wave is a type of surface wave (see Sheriff and Geldart, 1995, Section 2.5.4) in which the earth motion is parallel to the surface and perpendicular to the direction of wave travel.

Standard polarity for a minimum-phase waveshape (see problem 9.11) is that a compression produces a negative deflection.

Solution

The components of the waves (Figure 2.15a) are all in-phase except for the Rayleigh wave, where they are $90^{\circ }$ out-of-phase.

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Rayleigh-wave relationships	Tube-wave relationships
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Introduction	Partitioning at an interface
Table of Contents (book)

Also in this chapter

• The basic elastic constants
• Interrelationships among elastic constants
• Magnitude of disturbance from a seismic source
• Magnitudes of elastic constants
• General solutions of the wave equation
• Wave equation in cylindrical and spherical coordinates
• Sum of waves of different frequencies and group velocity
• Magnitudes of seismic wave parameters
• Potential functions used to solve wave equations
• Boundary conditions at different types of interfaces
• Boundary conditions in terms of potential functions
• Disturbance produced by a point source
• Far- and near-field effects for a point source
• Rayleigh-wave relationships
• Tube-wave relationships
• Relation between nepers and decibels
• Attenuation calculations
• Diffraction from a half-plane

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