John K. Washbourne

Pressure and fluid saturation prediction in a multicomponent reservoir using combined seismic and electromagnetic imaging

This paper presents a method for combining seismic and electromagnetic (EM) measurements to predict changes in water saturation, pressure, and CO2 gas/oil ratio in a reservoir undergoing CO2 flood. Crosswell seismic and EM data sets taken before and during CO2 flooding of an oil reservoir are inverted to produce crosswell images of the change in compressional velocity, shear velocity, and electrical conductivity during a CO2 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 Archies law, provides parameters for modeling the relations between water saturation, porosity, and electrical conductivity. The rock‐properties model is used to generate relationships between changes in...

Characterization of resolution and uniqueness in crosswell direct-arrival traveltime tomography using the Fourier projection slice theorem

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 illuminat...

Crosswell traveltime tomography in three dimensions

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.

Treasure hunting with direct-arrival transmission imaging

During the past five years, the Engineering Geoscience group at the University of California, Berkeley has been applying seismic technology in the search for two hoards of buried treasure — in the challenging desert terrain of southeast New Mexico where we searched for the Victorio Peak Treasure, and in the jungles of the Philippines looking for Yamashita’s Treasure (gold and jewels supposedly hidden by the Japanese military in underground tunnels during World War II).

Crosswell seismic imaging in three dimensions

Summary The simultaneous acquisition of multiple profile, high-resolution datasets from highly deviated or horizontal wells is the new crosswell seismic frontier. These datasets have motivated development of a 3D modeling approach that is consistent “from the ground up”, an altogether different approach than interpolating 2D results. For several reasons, we believe it is more desirab le to develop new modeling and processing techniques than to extend the typical 2D methods into 3D. We have developed an efficient means of integrated 3D interwell imaging that we term a “common earth model”. The model formulation consists of closely spaced (~2 m.) 3D surfaces which mimic structural contours, and a series of 2D velocity functio ns between each layer. Both the surfaces and the velocity functions are represented by Chebyshev polynomials, and hence any spatial derivatives required for both the ray tracing and traveltime inversion can be determined analytically in closed form. The velocity inversion algorithm is well determined while still providing high spatial resolution. An additional algorithmic advantage of our formulation is the “natural” application of continuation constraints to regularize the traveltime inversion and increase spatial resolution (after Bube and Langan, 1994).

Weyburn field horizontal-to-horizontal crosswell seismic profiling: Part 2 - data processing

This paper is the middle of a three-part case study. Detailed information about the horizontal well crosswell acquisition at the Weyburn field is discussed in Part 1 (Majer et al., 2001), and the interpretation and analysis of the data, including comparison with reservoir models and surface seismic data, are given in Part 3 (Li et al., 2001). We provide here an overview of the data processing, including a description of the procedure used to generate the baseline P-wave direct-arrival tomogram. We also discuss some processing issues related to repeat acquisition and processing of the time-lapse surveys.

High resolution crosswell reflection imaging in the presence of anisotropy: The Santa Rosa gas field, Eastern Venezuela

Seismic anisotropy in sand/shale sequences causes structural imaging problems when an isotropic earth is assumed. Three high resolution crosswell seismic profiles were acquired in the Santa Rosa gas field in eastern Venezuela. The main objective is to gain detailed structural images in a seismically difficult data zone, where the deep target horizons are obscured by a near-surface gas column. Isotropic imaging techniques were applied to the crosswell data with relatively poor results. The imaging target comprises sands from 5 to 50 ft thick in a 1800 ft thick deltaic, mainly shaley sequence unconformably overlying a predominantly fluvial Oligocene sand-rich sequence. The abundance of shales and fine layering has resulted in significant anisotropy. We have performed perhaps the first anisotropic reflection imaging of crosswell seismic data. Due to the structure and well deviations we use a fully 3-D modeling and imaging framework to produce both velocity and crosswell reflection images. Initial tomographic inversion revealed strong evidence of anisotropy, which correlated well with sonic log information. Differences between vertical and horizontal velocities range from 1623% in the upper shale-rich sequence, dropping to less than 5% in the lower sands.

Wave‐like rays in traveltime tomography

Modeling seismic propagation is critically important to our work, and unhappily we must trade simulation accuracy for reduced computational expense. We present a seismic modeling method that is as simple and computationally efficient as raytracing, but provides propagation paths and arrival times that are more consistent with finite bandwidth data. A significant benefit of finite frequency wave-like rays is the increased stability of propagation times and paths with respect to small changes in velocity. This leads to increased robustness of tomography and depth imaging, and can improve confidence in downstream interpretation. We refer to the modeling method as “wavetracing”, and illustrate the advantages with field data examples for the crosswell seismic geometry.

Surface-to-Borehole Traveltime Inversion For Velocity And Receiver Location

The surface-to-borehole seismic survey geometry can provide much higher frequency data for analysis and interpretation than traditional surface seismic because the overall propagation distance of both transmitted and reflected energy is greatly reduced. The higher frequency data obtained from surface-to-borehole surveys will translate into improved vertical and lateral imaging resolution, provided certain conditions are met. One very important condition is the reduction of uncertainties in both borehole deviation information and in correct positioning of receivers within the borehole.

Wavetracing: Ray tracing for the propagation of band‐limited signals: Part 2 — Applications

Summary The computation of travel times and travel paths is fundamental to a wide variety of seismic imaging techniques. There is a tradeoff in modeling seismic propagation that balances computational expense against accuracy. Often the accurate modeling of finite bandwith signals requires greater computational expense. We present a new method for seismic modeling that is as simple and computationally efficient as raytracing, and provides propagation paths and arrival times consistent with real data of finite frequency. We refer to this method as “wavetracing”.