A. Vesnaver

A geostatistical framework for incorporating seismic tomography auxiliary data into hydraulic conductivity estimation

Abstract A geostatistical approach is presented for the inclusion of seismic tomography data and sonic log data into the estimation of hydraulic conductivity. The procedure accounts for the errors in seismic tomography inversion and for the correlation of such errors. The proposed methodology consists of two steps: (1) the cross-variogram inference is carried out using only the data at the wellbore (both hydraulic and seismic); (2) a co-kriging procedure takes the cross-well data into account to interpolate between boreholes. No postulated a- priori relationship is needed. In order to illustrate the methodology a synthetic data set is generated on the basis of evidence from published case studies and simplified physical considerations. The numerical experiments show that the choice of the excitation frequency is critical. A trade-off exists between the need for a high-resolution survey (asking for higher frequencies) and the need for a good correlation between hydraulic conductivity and seismic properties (asking for frequencies below the squirt frequency of the medium). In the simulation using seismic data with the best excitation frequency (1 kHz in this case), the mean squared error of the hydraulic conductivity estimate is two-thirds lower than using hydraulic data alone. It is important to note also that only a part of the interwell region is adequately sampled by the tomographic experiment. Such a region can be readily identified by calculating the energy of the quasi-null space, through singular value decomposition of the tomographic matrix. In planning this type of experiments, it is necessary to carefully verify case by case whether the adopted range of high frequencies does not prevent the seismic energy from propagating effectively from sources to receivers.

Staggered or adapted grids for seismic tomography

Often a prisoner can see the sky from jail only through a grid. Thus, the grid may hide the moon or some landscape detail. In this case, he can solve the problem by moving his head just a bit. He will lose some other detail but will see the desired one. Because he remembers details seen before, his mind can reconstruct the image he would get out of the jail—without the grid. Actually, there is another way for reducing the grid annoyance; he could stretch the grid so that it does not hide any interesting view. However, this is more difficult (and less legal) and is usually adopted for other goals (e.g., escapes).

Time-lapse tomography

In time-lapse analysis, we have to distinguish the seismic response changes due to oil and gas production at a reservoir over the years from several other causes, such as the recording signature and random noise. In this paper, we focus our attention on the velocity macromodel provided by seismic tomography, which is a basic tool for the data regularization, its depth or time migration, and a possible final subtraction among different vintages. We show first that we cannot use just a single velocity model for all data sets, because of seasonal variations of the overburden velocity (which is mainly due to seawater temperature in marine cases and to the water table depth in land cases). However, we can exploit the basic assumption of time-lapse analysis for constraining reflection/refraction tomography, i.e., by imposing the constraint that the layer structure and the local velocities do not change outside the reservoir (and in the shallowest part) over time. We thus get coupled models that are physically consistent, with a better spatial coverage and higher information redundancy. The new method is illustrated by a marine case history from the North Sea.

Tomographic imaging by reflected and refracted arrivals at the North Sea

We discuss some processing steps of a marine 3-D data set from the Oseberg field, North Sea. We compare the prestack depth‐migrated images obtained by the velocity fields provided by different tools: velocity spectra, reflection tomography, and joint tomographic inversion of reflected and refracted arrivals. The last ones are definitely better. We also produced a synthetic example by modeling the estimated earth structure and the actual recording geometry, and we reached similar conclusions. The correlation between reflected and refracted signals may be unclear for later arrivals because of their reciprocal interference and multiple reflections. We adopt a technique based on a surgical mute in the τ-p domain, which allows coupling the signals coming from the same elastic interface.

The contribution of reflected, refracted and transmitted waves to seismic tomography: a turorial

Introduetion Traveltime inversion usually treats only reftected and transmitted arrivals. This is due to two main reasons: first, in conventional hydrocarbon exploration, acquisition and processing parameters are optimized for these type of waves, whereas others (e.g. refracted or diffracted) are attenuated as an undesired noise; secondly, the most popular ray tracing techniques (based on Snells law or on the eikonal equation) are not ab Ie to model refracted or diffracted waves. During the last few years, various techniques based on Fermats principle have been proposed which enable us to exploit these events also (see among others Moser 1989, 1991; Saito 1989; Asakawa and Kanawaka 1993; Fisher and Lees 1993). The algorithm adopted here, in particular, allows us to trace the minimum time paths of refracted and diffracted waves in irregular grids (Vesnaver 1993).

Reflection tomography versus stacking velocity analysis

The travel-time inversion of reflected arrivals reconstructs the structure of the main interfaces with a precision comparable to the seismic wavelength. The resolution of the conventional stacking velocity analysis is lower, i.e. of the order of the seismic spread length. Furthermore, the stacking velocity field is defined in the time domain, and its conversion to the depth domain is not straightforward. Both methods require selecting: this is quite difficult and time consuming for the pre-stack reflected events, but simpler and inexpensive for the velocity spectra. There is thus a tradeoff between the two approaches in terms of costs and benefits. In this paper we compare the main features of the two methods by applying them to different synthetic models of increasing complexity. We modelled the related seismograms using the Fourier pseudo-spectral method.

Full 3D relocation of microseisms for reservoir monitoring

An optimal hydrocarbon production is achieved by injecting fluids (as brine or CO2) in the reservoir. The resulting pressure gradient may induce cracks that cannot be imaged by conventional surface or borehole seismic, but only by a seismological approach. The hypocenter location of induced microseisms reveals the pathways of fluids. Petroleum engineers have been measuring microseismicity to check the fracking fluid efficiency in the last decade, but only very close to the wells, where 1D reservoir models from well logs only may be sufficient. Monitoring an entire reservoir requires an extended network of receivers, placed both at the surface and in wells, and the capability of modeling complex 3D structures as salt domes or stratigraphic traps. Classical seismological tools as Hypo71 (Lee and Lahr, 1972) HypoInverse-2000 (Klein, 2002) can deal with 1D models only, composed of plane parallel layers, without sharp lateral variations of Pand S-wave velocities, nor 3D variations of the Vp/Vs ratio. Limitations exist also for receivers’ geometry, as the must be placed on a plane only. A more recent and flexible tool as NonLinLoc (Lomax et al., 2000) can deal with regular grids only. Here we present an algorithm able to deal with irregular 3D models and arbitrary recording geometries, which allows integrating any kind of active seismic (3D surface, VSP, and crosswell surveys) with passive seismic from surface and boreholes.

Null Space Reduction in the Linearized Tomographic Inversion

The null space is the origin of the non-uniqueness of solutions of linearized tomographic inversion. Usually its negative effects are dealt by introducing a priori information by means of constraints, covariance matrices and damping factors. In this paper a singular values analysis is introduced which allows to identify the null space causes: uncrossed pixels and linearly dependent rays. Both can be controlled or eliminated modifying properly the tomographic grid, accordingly to the estimated local reliability. Some synthetic examples are presented with a velocity distribution which is typical of the sea water, and the relationship between the acquisition geometry, the pixel distribution and the quality of results is discussed.

Tomographic inversion of the water layer in the 4D analysis

The variations of the seawater velocity in space and time are often uncared for in the conventional processing of marine data, because their influence may be negligible for imaging targets at large depths. However, in the time-lapse monitoring of hydrocarbon reservoirs, subtle effects must be observed, as the variations of the local velocities and the Gas/Oil or Oil/Water contact. We show here by a real example that the velocity anomalies in the seawater should be measured and compensated: otherwise, their effect can distort significantly the time-lapse analysis.

Travel Time Inversion of Marine Seismic Data for Ocean Sound Speed Reconstruction

Tomographic inversion of marine seismic data is carried out to explore possible hydrocarbons reservoirs in the geological formations below the sea floor. The vertical velocity variations in the water structure are usually neglected, because they are much smaller than those at the targets of the oil and gas industry. In this paper we study the possibility of exploiting data and techniques of seismic exploration for oceanographic purposes. The depth of the sea floor is estimated by the reflection tomography at first, and then the velocity distribution in the sea water is computed by travel time inversion of both transmitted and reflected arrivals. Encouraging preliminary results are presented, obtained from a seismic profile acquired by OGS at the Ross Sea (Antarctica).