# Expanding an Elastic Definition

Seismic stratigraphy has been an important seismic-interpretation science since the 1975 AAPG annual meeting, when its principles were introduced in a series of presentations  --  and particularly since its documentation two years later as AAPG’s Memoir 26.

Emerging interest in multicomponent seismic technology now allows (and demands) the science of seismic stratigraphy be expanded to include all modes of a multicomponent seismic wavefield. The term “elastic wavefield seismic stratigraphy” is now used when the total elastic wavefield, not just the  P-wave component, is used in seismic stratigraphy applications.

In elastic wavefield seismic stratigraphy, a seismic sequence is still defined as a succession of relatively conformable seismic reflections bounded by unconformities or their correlative conformities, just as Robert M. Mitchum (this year’s AAPG Sidney Powers Memorial winner) defined the term for P-wave seismic stratigraphy decades ago  --  only now the definition is expanded to include interpretation and utilization of S-wave seismic sequences in addition to P-wave sequences.

A seismic facies is still defined, using Mitchum’s original definition, as any seismic attribute that distinguishes one succession of reflection events from another. The only difference now is the term is expanded to include interpretation and use of S-wave seismic facies as well as P-wave facies.

Two arguments help explain why  P-wave sequences and facies often differ from S-wave sequences and facies:

• First, assume an elastic wavefield is traveling vertically through a horizontally layered medium. The  P-wave particle displacement vector associated with that wavefield then senses the fabric of the medium in a direction normal to the layering, and the S-wave particle displacement vector senses the fabric in a direction parallel to the layering.

The elastic constants of the medium (i.e., the fabric of the medium) differ in these two directions. For example, forces of different magnitudes have to be applied to flex a deck of playing cards or the sheets of a notepad when those forces are directed normal to and parallel to layering (figure 1). In this simple test, the medium is the same at the common point where forces are applied, but the fabric (or strength) of the material is not the same in the two force directions.

Thus, P-wave seismic sequences and facies sometimes differ from S-wave sequences and facies simply because orthogonal P and S particle-displacement vectors sense and react to different elastic properties at the same subsurface Earth coordinates.

• Second, the reflectivity of each mode of an elastic wavefield at an interface differs from the reflectivities of its companion modes.

The principle is illustrated in figure 2; the vertical axis Ri,S is the S-wave reflectivity at an interface, the horizontal axis b is the ratio of the velocity ratio VP/VS across that interface (VP = P-wave velocity and VS = S-wave velocity), and the quantity Ri,P labeled on each curve is the P-wave reflectivity at the interface.

These curves show there are interfaces that:

• Are invisible to P waves (the curve labeled Ri,P = 0) but are not invisible to S-waves unless b = 1.0.
• Are invisible to S waves (the horizontal line Ri,S = 0) but are not invisible to P waves unless b = 1.0.
• Cause P and S reflections to be in phase (shaded parameter region) and others that cause P and S reflections to be opposite polarity (unshaded parameter region).
• Are robust P reflectors but weak  S reflectors (elliptical domains A) and others that are robust S reflectors but weak P reflectors (elliptical domains B).

Thus, any combination of P and S sequences and facies can be encountered in elastic wavefield seismic stratigraphy, depending on how the VP/VS velocity ratio varies across interfaces illuminated by a multicomponent seismic wavefield.

An example of elastic wavefield seismic stratigraphy interpretation is illustrated in figure 3. P-P and P-SV images shown in this example come from a deep-water, 2-D, four-component ocean-bottom-cable profile. The unique geometry of depositional unit C allows that unit to be defined confidently in each image space, even though P-P  and P-SV image-time coordinates are drastically different.

There is an obvious facies change in the P-SV image that segregates the interval above unit C into two distinct seismic facies A and B. Sequence boundary 1 is defined at the common boundary between these two P-SV seismic facies.

An equivalent facies break is not obvious in the P-P image. Boundary 1 drawn across P-P image space and the two P-P units labeled A and B are inferred from the P-SV interpretation. An interpreter would be hard pressed to justify P-P units A and B are different facies only on the basis of the P-wave data.

This is only one example whereby expanding seismic stratigraphy beyond the confines of P-wave seismic data provides increased insight into depositional architecture and lithofacies distribution.

The U.S. Department of Energy provided funding that allowed the Exploration Geophysics Laboratory to initiate the elastic wavefield seismic stratigraphy research that is partly described here (Contract DE-FC26-03NT15396).