This paper presents a method for combining seismic and electromagnetic measurements to predict changes in water saturation, pressure, and CO 2 gas/oil ratio in a reservoir undergoing CO 2 flood. Crosswell seismic and electromagnetic data sets taken before and during CO 2 flooding of an oil reservoir are inverted to produce crosswell images of the change in compressional velocity, shear velocity, and electrical conductivity during a CO 2 injection pilot study. A rock properties model is developed using measured log porosity, fluid saturations, pressure, temperature, bulk density, sonic velocity, and electrical conductivity. The parameters of the rock properties model are found by an L1-norm simplex minimization of predicted and observed differences in compressional velocity and density. A separate minimization, using Archie's law, provides parameters for modeling the relations between water saturation, porosity, and the electrical conductivity. The rock-properties model is used to generate relationships between changes in geophysical parameters and changes in reservoir parameters.Electrical conductivity changes are directly mapped to changes in water saturation; estimated changes in water saturation are used along with the observed changes in shear wave velocity to predict changes in reservoir pressure. The estimation of the spatial extent and amount of CO 2 relies on first removing the effects of the water saturation and pressure changes from the observed compressional velocity changes, producing a residual compressional velocity change. This velocity change is then interpreted in terms of increases in the CO 2 /oil ratio. Resulting images of the CO 2 /oil ratio show CO 2 -rich zones that are well correlated to the location of injection perforations, with the size of these zones also correlating to the amount of injected CO 2 . The images produced by this 3 process are better correlated to the location and amount of injected CO 2 than are any of the individual images of change in geophysical parameters.

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The process of acquiring a crosswell seismic direct‐arrival traveltime data set can be approximated by a series of truncated plane‐wave projections through an interwell slowness field. Using this approximation, the resolution and uniqueness of crosswell direct‐arrival traveltime tomograms can be characterized by invoking the Fourier projection slice theorem, which states that a plane‐wave projection through an object constitutes a slice of the object’s spatial spectrum. The limited vertical aperture of a crosswell survey introduces a small amount of nonuniqueness into the reconstructed tomogram by truncating the plane‐wave projection. By contrast, the limitations on angular aperture have a significant effect on resolution. The reconstructed tomogram is smeared primarily along the limiting projection angles, with the amount of smearing dependent upon the well spacing and the angular aperture. The amount of smearing was found to be inversely proportional to tan Δϕ, where Δϕ is the angular aperture illuminating a sector of the interwell plane. Consequently, the amount of smearing can be large where the angular aperture becomes small, such as at the top and bottom of the tomogram. For interwell sectors illuminated by large angular apertures, Fresnel zone effects will generally be the limiting factor in crosswell tomogram resolution. However, in some circumstances, angular aperture effects may control the tomogram resolution. The effects of angular aperture and direct‐arrival Fresnel zones produce tomograms with spatial resolution that is dependent upon the well spacing. This study indicates that direct‐arrival traveltime tomography will not usually produce tomograms with substantially greater resolution than surface seismic techniques for normal oil and gas well spacings.

Conventional crosswell direct‐arrival traveltime tomography solves for velocity in a 2‐D slice of the subsurface joining two wells. Many 3‐D aspects of real crosswell surveys, including well deviations and out‐of‐well‐plane structure, are ignored in 2‐D models. We present a 3‐D approach to crosswell tomography that is capable of handling severe well deviations and multiple‐profile datasets. Three‐dimensional pixelized models would be even more seriously underdetermined than the pixelized models that have been used in 2‐D tomography. We, therefore, employ a thinly layered, vertically discontinuous 3‐D velocity model that greatly reduces the number of model parameters. The layers are separated by 2‐D interfaces represented as 2‐D Chebyshev polynomials that are determined using a priori structural information and remain fixed in the traveltime inversion. The velocity in each layer is also represented as a 2‐D Chebyshev polynomial. Unlike pixelized models that provide limited vertical resolution and may be overparameterized horizontally, this 3‐D model provides vertical resolution comparable to the scale of wireline logs, and reduces the degrees of freedom in the horizontal parameterization to the expected in‐line and out‐of‐well‐plane horizontal resolution available in crosswell traveltime data. Ray tracing for the nonlinear traveltime inversion is performed in three dimensions. The 3‐D tomography problem is regularized using penalty constraints with a continuation strategy that allows us to extrapolate the velocity field to a 3‐D region containing the 2‐D crosswell profile. Although this velocity field cannot be expected to be accurate throughout the 3‐D region, it is at least as accurate as 2‐D tomograms near the well plane of each 2‐D crosswell profile. Futhermore, multiple‐profile crosswell data can be inverted simultaneously to resolve better the 3‐D distribution of velocity near the profiles. Our velocity parameterization is quite different from pixelized models, so resolution properties will be different. Using wave‐modeled synthetic data, we find that near horizontal raypaths have the largest mismatch between ray‐traced traveltimes and traveltimes estimated from the data. In conventional tomography, horizontal raypaths are essential for high vertical resolution. With our model, however, the highest resolution and most accurate inversions are achieved by excluding raypaths that travel nearly parallel to the geologic layering. We perform this exclusion in both a static and model‐based manner. We apply our 3‐D method to a multiple‐profile crosswell survey at the Cymric oil field in California, an area of very steep structural dips and significant well trajectory deviations. Results of this multiple‐profile 3‐D tomography correlate very well with the independently‐processed single profile results, with the advantage of an improved tie at the common well.

Abstract. This paper proposes a new method that combines check- pointing methods with error-controlled lossy compression for large-scale high-performance Full-Waveform Inversion (FWI), an inverse problem commonly used in geophysical exploration. This combination can signif- icantly reduce data movement, allowing a reduction in run time as well as peak memory. In the Exascale computing era, frequent data transfer (e.g., memory bandwidth, PCIe bandwidth for GPUs, or network) is the performance bottleneck rather than the peak FLOPS of the processing unit. Like many other adjoint-based optimization problems, FWI is costly in terms of the number of floating-point operations, large memory foot- print during backpropagation, and data transfer overheads. Past work for adjoint methods has developed checkpointing methods that reduce the peak memory requirements during backpropagation at the cost of additional floating-point computations. Combining this traditional checkpointing with error-controlled lossy compression, we explore the three-way tradeoff between memory, precision, and time to solution. We investigate how approximation errors introduced by lossy compression of the forward solution impact the objective function gradient and final inverted solution. Empirical results from these numerical experiments indicate that high lossy-compression rates (compression factors ranging up to 100) have a relatively minor impact on convergence rates and the quality of the final solution.