# Depth Registration of P and S Data

## Abstract

Two critical assumptions are involved in elastic wavefield stratigraphy: (1) Across some stratigraphic intervals, one mode of an elastic wavefield might show different seismic sequences and facies than its companion modes do, and (2) S-wave seismic sequences and facies are just as important in geologic interpretation as P-wave seismic sequences and facies are.

Once those two assumptions are accepted, a serious interpretive challenge then is encountered — depth registration of P and S images. An interpreter must be confident that a targeted data window in P-wave image space is depth equivalent to a data window selected from S-wave image space before seismic sequences and seismic facies in the respective data windows can be combined into an elastic wavefield stratigraphy analysis. Until depth-equivalent P and S data windows are defined, no meaningful geologic interpretation of P and S sequences or facies can be done.

To effectively combine P and S reflection data into a unified stratigraphic interpretation of a prospect, it is necessary to identify the specific P-wave time window and the specific S-wave time window that span each targeted stratigraphic sequence that is to be interpreted. For example, to calculate reliable *V*_{P}/*V*_{S} ratios over a reservoir interval, it is essential to identify P and S reflection events that define the top and base of the reservoir sequence as accurately as possible. The interpreter's dilemma is to decide which S-wave reflection event occurs at the same stratigraphic boundary where a P-wave reflection event has been interpreted.

This requirement for a methodology that accurately transforms

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# Multicomponent Seismic Technology

A principle that is emphasized throughout this book is that the physics of any multicomponent seismic technology cannot be understood unless that technology is viewed in terms of the particle-displacement vectors associated with the various modes of a seismic wavefield. This material therefore begins with a discussion of seismic vector-wavefield behavior to set the stage for subsequent chapters.

Several approaches can be used to explain why each wave mode of nine-component (9C) and three-component (3C) seismic data that propagates through subsurface geology provides a different amount and type of rock/fluid information about the geology that the wave modes illuminate. Some approaches appeal to people who have limited interest in mathematics. Other options need to be structured for people who have an appreciation of the mathematics of wavefield reflectivity. Another argument that can be used focuses on the fundamental differences in P-wave and S-wave radiation patterns and the distinctions in target illuminations associated with 9C and 3C seismic sources. We will consider all of those paths of logic.

A principle that will be stressed is that each mode of a multicomponent seismic wavefield senses a different earth fabric along its propagation path because its particle-displacement vector is oriented in a different direction than are the particle-displacement vectors of its companion modes. Although estimations of earth fabric obtained from various modes of a multicomponent seismic wavefield can differ, each estimate still can be correct because each wave mode deforms a unit volume of rock in a different direction, depending on the orientation of its particle-displacement vector. Those deformations sense a different earth resistance in directions parallel to and normal to various symmetry planes in real-earth media. The logic of that nonmathematical approach appeals to people who are interested in the geologic and petrophysical information that multicomponent seismic data can provide and are less concerned about theory and mathematics.

A second approach that is helpful for distinguishing one-component (1C), 3C, and 9C wavefield behavior focuses on the mathematics of the reflectivity equation associated with each mode of the full-elastic seismic wavefield. The mathematical structure of the reflectivity equation associated with each seismic wave mode describes why and how petrophysical properties of the propagation medium affect different wave modes in different ways. The logic of that analytical approach is appreciated by scientists who are comfortable with mathematics.

All of these concepts lead to the development of a new seismic-interpretation science based on multicomponent seismic data called elastic wavefield seismic stratigraphy.