Discrete tomography and joint inversion for loosely connected or unconnected physical properties: application to crosshole seismic and georadar data sets

Abstract

SUMMARY Tomographic inversions of geophysical data generally include an underdetermined component. To compensate for this shortcoming, assumptions or a priori knowledge need to be incorporated in the inversion process. A possible option for a broad class of problems is to restrict the range of values within which the unknown model parameters must lie. Typical examples of such problems include cavity detection or the delineation of isolated ore bodies in the subsurface. In cavity detection, the physical properties of the cavity can be narrowed down to those of air and/or water, and the physical properties of the host rock either are known to within a narrow band of values or can be established from simple experiments. Discrete tomography techniques allow such information to be included as constraints on the inversions. We have developed a discrete tomography method that is based on mixed‐integer linear programming. An important feature of our method is the ability to invert jointly different types of data, for which the key physical properties are only loosely connected or unconnected. Joint inversions reduce the ambiguity in tomographic studies. The performance of our new algorithm is demonstrated on several synthetic data sets. In particular, we show how the complementary nature of seismic and georadar data can be exploited to locate air‐ or water‐filled cavities.

Joint inversion of crosshole radar and seismic traveltimes acquired at the South Oyster Bacterial Transport Site

“…A natural extension to two-and three-dimensional applications has been to assume that the earth can be divided into sub-volumes of uniform properties with geometries that are common for all physical properties in the inversion (e.g., Hyndman and Gorelick, 1996;Musil et al, 2003). Such approaches are certainly useful, but physical properties can vary gradually in space and not all data are necessarily sensitive to the same changes in lithology and state variables.…”

Borehole seismic monitoring of CO2 storage within a saline aquifer at Ketzin, Germany

“…This leads to an overestimation of the velocity and therefore to an underestimation of the amplitude of velocity anomalies in an inversion problem. For media with structures a size smaller than the Fresnel volume, this effect is intensified by the forward calculation of travel times based on the standard ray theory, which is derived using a high-frequency approximation (Musil et al (2003), Spetzler et al (2008)). …”

“…This leads to an overestimation of the velocity and therefore to an underestimation of the amplitude of velocity anomalies in an inversion problem. For media with structures a size smaller than the Fresnel volume, this effect is intensified by the forward calculation of travel times based on the standard ray theory, which is derived using a high-frequency approximation (Musil et al (2003), Spetzler et al (2008) At the Nagaoka CO 2 injection site, sonic logging indicated a sound speed reduction of 21 % due to CO 2 injection. An inversion of crosshole data with 3D finite-frequency wavefield theory found a velocity decrease of 18 %, whereas the inversion with standard ray theory observed only a velocity change in the order of 3 % (Spetzler et al (2008)).…”

Non-invasive means of detecting subterranean border crossing tunnels

“…To date most of these methods utilize a cross borehole or borehole design in their method of detection which for the cross borehole means that one side again contains a source and the other an array of sensors or for the one utilizing a single borehole the sources located in the borehole and the sensors are located on the surface [13,14,31,33]. The seismic methods are much more effective for penetrating deeper into the soil than the GPR, however, since many of them use boreholes or cross borehole methods it means that large amounts of prep time are needed before each test can be run.…”

“…An active seismic means of detection can be used in several ways, including cross borehole logging, where two bore holes are drilled in parallel at a set distance apart with one side as the source side and the other borehole of the receiver side with an array of geophones or accelerometers in the receiver side [13,14]. Knowing the type of soil one can ascertain the average velocity through that soil and with a set distance it could be determined how long it should take the wave to arrive at the sensors.…”