Geophysical Ray Tracing - Wave Propagation in Drilling, Well Logging and Reservoir Applications - page 306

6
Geophysical Ray Tracing
Here we introduce fundamental concepts from the “kinematic wave
theory” developed in Chapter 2 to geophysics problems at borehole, interlayer
and crosswell scales; that is, we deal with the physics of “slowly varying
wavetrains” in modern seismic applications (not to be confused with “slow”
waves). Elementary notions in geophysics, e.g., eikonal methods, ray tracing,
Fermat' s principle, and so on, are also developed from first principles as needed.
We emphasize that our treatment is not intended to replace standard geophysics
curriculum materials. Instead, our complementary discussions aim at
highlighting the underlying formulation aspects and implicit assumptions of a
mathematical subject which are often subtle. Thus, we will not develop eikonal
methods in their fullest detail, leaving that task to many well written topics
already available. We will not derive the general equations governing P and S
waves, introduce specialized techniques used in migration, nor will we delve
into the attenuative behavior of seismic waves in oil saturated rocks. The
subjects presented for discussion were selectively chosen to guide novices and
experts in geophysics on key ideas essential to formulating correct boundary
value problems. An attempt is made to expand upon traditional equation-based
modeling methods, by introducing more powerful kinematic wave formalisms
that allow immediate use of empirically measured r (k) and i (k) functions in
seismic modeling. The limitations of conventional modeling methods are
examined in light of modern kinematic wave theory.
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