Seismic Imaging of Subsurface Porosity

Reliable estimates of subsurface porosity is an important problem in the geosciences. Transport processes such as heat and water flow, or migration of particles are studied in many environmental applications, and rely on accurate porosity estimates. Furthermore, seismic site response studies, which determine a change in ground displacement due to stress changes during earthquakes, depend on porosity of the material under investigation. Yet current methods to determine subsurface porosity rely on point or line measurements in boreholes which are extrapolated to larger distances. It is clear that this method is very limited and produces questionable results at best. Therefore, an approach is needed that provides in-situ porosity measurements at larger scales and dimensions. In the current study, we present a method to estimate porosity over large areas based on scattered seismic energy. Subsurface porosity occurs on all scales from micro-pores to large cavities. If information on the background material is available (e.g. the seismic velocity of the background matrix) it is possible to image the concentration of the larger pores in space. In this model the background information already contains the effect of micro-scale porosity and possible fracturing. Examples of larger pores are present in volcanic deposits where cooling processes have introduced gas inclusions that vary in size between a few inches up to one foot or more. Limestone deposits may also exhibit a high degree of porosity created by leaching or washout mechanisms. These voids represent strong scatterers and the application of linearized methods like the Born approximation, for example, will produce doubtful results. We explore a possibility to apply scattering theory to estimate the porosity without considering interaction between scatterers (single scattering theory). The voids in the medium affect the amplitudes as well as the phases of the scattered seismic waves , and in the Rayleigh regime the relationship between the concentration of porosity and phase shift becomes attractively simple. Thus porosity can be directly estimated from travel time measurements. We present modeling results based on laboratory data that estimate the distribution of porosity from travel times of seismic waves. A general finding is that the relative change in seismic velocity is approximately equal to 50% of the porosity value.