Seismic tomography with co-located soft data

Introduction

Seismic data contain a wide range of uncertainties which directly affects the quality of seismic images. Previous studies have tried to extract more information from raw seismic data to reduce the uncertainty in the seismic-imaging problem (Aki and Richards, 2002; Yilmaz, 2001). Since velocity analysis plays a fundamental role in seismic imaging, uncertainties in velocities lead to significant inaccuracies in seismic images. Without an accurate velocity estimate, seismic reflectors are misplaced, the image is unfocused, and seismic images can easily mislead earth scientists (Clapp, 2001; Claerbout, 1999). Defining a reliable velocity model for seismic imaging is a difficult task, especially when sharp lateral and vertical velocity variations are present. Moreover, velocity estimation becomes even more challenging when seismic data are noisy (Clapp, 2001).

In areas with significant lateral velocity variations, reflection tomography methods, where traveltimes are mapped to slowness, are often more effective than conventional velocity-estimation methods based on measurements of stacking velocities (Clapp, 2001; Biondi, 1990). However, reflection tomography may also fail to converge to a geologically reasonable velocity estimation when the wavefield propagation is complex.

Unfortunately, the reflection tomography problem is ill-posed and under-determined. Furthermore, it may not converge to a realistic velocity model without a priori information, e.g., regularization constraints and other types of geophysical properties, in addition to seismic data (Clapp, 2001). Better velocity estimation can be achieved by integrating co-located soft data, such as non-seismic geological data, in the reflection tomography problem.

Lack of an analytical relationship between different measured geological properties limits our ability to use co-located soft data. Besides the conventional probabilistic relations, similarity-measurement tools can be used to enforce the structural information contained in soft data into seismic velocity estimates. Based on these tools, differences in two images are classified as structural differences and non-structural differences. Since gradient fields are a good choice for geometrical (structural) comparisons, the cross-gradient function is one useful similarity-measurement tool. This is true because the variations of geophysical properties can be described by a magnitude and a direction (Gallardo and Meju, 2007,2004).

Here we use the cross-gradient function to integrate a given set of soft data--the resistivity field measured by magnetotelluric (MT) sounding in our case--into the reflection tomography problem. This integration requires consideration of differences in frequency in seismic and resistivity data. In the following sections we study the behavior of cross-gradient functions in different cases and then give an overview of how an understanding of these differences can be used to improve velocity estimates given by seismic tomography.

Seismic tomography with co-located soft data