Fresnel zone effect on seismic velocity resolution

Abstract

For impedance, velocity resolution depends on Fresnel zone considerations. A change of velocity can be distinguished only if its size is greater than the Fresnel zone. This is demonstrated on synthesized examples where a single velocity anomaly is introduced in a homogeneous medium. (Although unrealistic, this model was designed to exhibit the physical phenomenon in its simplest configuration.) The presence of the velocity anomaly breaks the wavefront into two main parts. The first part, which travels through the anomaly, corresponds to the specular ray and gives rise to an event which we call the ray event since it can be predicted by standard ray‐tracing techniques. The second, which emanates from outside the anomaly, does not correspond to a ray event. Therefore, we call it the nonray event. It travels at the speed of the background medium. The relative amplitude of the two events depends upon the size of the anomaly compared to the size of the Fresnel zone. When the anomaly is larger than the Fresnel zone, then the ray event dominates and the velocity variation is detectable. On the other hand, when the anomaly is smaller than the Fresnel zone, then the nonray event dominates and everything occurs as if there were velocity variation, leading to the wrong velocity model. The physical phenomenon underlying the presence of the nonray event is very pervasive and does not depend on the velocity contrast. It has already been referred to as wavefront healing, but its consequences in terms of velocity resolution have not been outlined in the domain of seismic reflection. The paper is organized in the following way. First, we present the phenomenon and its consequences on velocity analysis on a single model. Then, by changing the model parameters, we show how the respective amplitudes of the nonray event and the ray event and, therefore, the detectability of velocity variations depends on the size of the anomaly. Finally, we present two approaches to describe the physics of the phenomenon: (1) geometrical considerations based on Huyghen’s principle to explain the wave‐front healing phenomenon and (2) a discussion on the Kirchhoff integral to explain how the amplitude ratio of the ray event to the nonray event (and in turn the detectability of the velocity variation) depends on the size of the anomaly compared to the size of the Fresnel zone. In the final part of the paper we give two potential applications of this theory: (1) the use of the Fresnel zone diameter as the minimum length for smoothing velocity horizons and (2) a theoretical scheme for velocity analysis that should improve the velocity resolution: a combination of velocity estimation and wave equation redatuming. No implementation of this scheme has yet been tested.