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received April 17, 1998

revised June 16, 1998

accepted June 22, 1998

Abstract

Introduction

Rapid ground subsidence over areas of petroleum and gas extraction has been observed previously [Mayuga and Allen, 1970; Pratt and Johnson, 1926; Vanhasselt, 1992]. The effects are most noticeable on a coastline where a small elevation decrease may cause inundation, first described over an oilfield near Houston, Texas [Pratt and Johnson, 1926]. Parts of the city and port of Long Beach, California, suffered major problems due to rapid (up to 0.75 m yr^-1) land subsidence related to extraction of oil from the underlying Wilmington oil field [Mayuga and Allen, 1970]. Problems were caused both by inundation and by horizontal strains on the sides of the subsidence bowl. Subsidence over petroleum extraction zones can also cause significant damage to extraction infrastructure itself, including expensive well failures. In this paper, we report subsidence rates as high as 40 mm in 35 days or an annual rate of > 400 mm yr^-1 in two California oilfields.

Synthetic Aperture Radar (SAR) images can be combined using interferometric analysis to measure surface deformation remotely [Gabriel et al., 1989]. An advantage of SAR interferometry (IntSAR) is that it can provide a geographically comprehensive map of the deformation, with a sampling rate far more dense than the most detailed surveys. One disadvantage is that SAR interferometry only measures one displacement component, but the operating satellite systems are most sensitive to vertical motions, which is appropriate for subsidence. While most applications of IntSAR to-date have been to study nearly instantaneous deformation due to earthquakes and rapid motion of glaciers, gradual subsidence and uplift of the earth's surface have also been measured [Briole et al., 1997; Carnec et al., 1996; Fruneau et al., 1996; Galloway et al., in press; Lu et al., 1997; Massonnet et al., 1997; Peltzer et al., 1996; Vadon and Sigmundsson, 1997](also M. van der Kooij, Atlantis Scientific, unpublished, 1997). Here we demonstrate interferometric mapping of rapid surface deformation related to petroleum extraction.

The Lost Hills and Belridge oilfields are located in western Kern County, California, on the west side of the San Joaquin Valley (Plate 1). The major oil reservoir in both fields is diatomite [McGuire et al., 1983]. The extraction of large volumes of fluid, aided by hydrofracturing, from diatomite formations located at shallow depths (about 700 m below the surface) in Lost Hills and Belridge fields, causes a reduction in the pore fluid pressure, resulting in significant compaction of the reservoir rocks under the weight of the overburden. A subsidence bowl forms at the surface [Bondor and de Rouffignac, 1995; Holzer and Bluntzer, 1984; Martin and Serdengecti, 1984]. Subsidence at the South Belridge field was first noted in the 1980's [Bondor and de Rouffignac, 1995; Bowersox and Shore, 1990].

Interferometric Observations

We corrected the interferograms for the phase signature due to orbital separation and earth curvature, but we did not remove the very small topographic phase component. The topographic contribution to phase over the oilfields is negligible, because there is < 30 m of relief in the Lost Hills and even less at Belridge and because the IntSAR pairs have very small orbital separations or baselines. The ambiguity height or amount of elevation that will cause one fringe of phase change of these pairs (Table 1) highlights their low sensitivity to elevation. Topographic maps show up to 30 m (100 ft) of relief for Lost Hills (north of the subsidence bowl). This relief corresponds to a maximum of ~ 54 ° of phase or < 4 mm of range change [Zebker et al., 1994b]. The remaining phase includes the satellite line-of-sight (range) component of surface motion plus changes in radar propagation.

Quantifying and correcting the apparent surface motion due to changes in atmospheric radar propagation delay is difficult because knowledge of atmospheric conditions at the resolution of the radar pixels is unavailable. Phase change is primarily due to changes in tropospheric water vapor distribution [Goldstein, 1995, Zebker et al., 1997]. Because the atmosphere is so spatially variable, we sample the atmospheric delays in this area with a Tandem interferogram with a 1-day interval and a short spatial baseline (see Table 1). The observed signal over the flat San Joaquin Valley can be assumed to be almost entirely due to atmospheric delays. Over areas the size of Lost Hills and Belridge, the observed variation is roughly 5 mm of delay, and we expect a similar level of atmospheric effects in the other interferograms. These delays are similar to those estimated by Goldstein [Goldstein, 1995] for eastern California. The atmospheric conditions during the two images of Tandem pair may not be typical, but these effects are small compared to the > 40 mm of observed range change over the oilfields.

The short spatial scale of the surface deformation at Lost Hills ( ~ 2 x 5 km) and Belridge ( ~ 2 x 15 km) requires processing of interferograms at the highest possible resolution. Cross-track (range) resolution for the ERS SAR is 7.9 m in slant range divided by sin(23°) ~= 20 m on the ground for ERS. Along-track (azimuth) resolution is much higher, roughly 4 m on the ground, so we average 5 pixels in azimuth to give approximately 20 x 20 m square pixels (see Plate 1). For the longer time intervals (8-months and 26-month interferograms), this resolution is inadequate to resolve the most intense deformation gradients in the oilfields with the 56 mm wavelength of ERS (see Plate 2).

Conclusions

Directly mapping the deformation in areas of rapid subsidence (Plate 3) over long time intervals would require a SAR system with a longer wavelength or higher spatial resolution (or both). Another possibility would be to sum multiple measurements over short time periods, which would require a satellite with a tightly controlled orbit that allowed interferograms to be formed between every consecutive pair of orbits.

Interferometric measurements of rapid subsidence over oilfields can provide valuable information for understanding the response of the reservoir and overlying rocks to various petroleum extraction strategies. The ability to map the subsidence distribution from satellite data powerfully complements ground-based techniques and permits measurements in areas where access is difficult or expensive. In addition, IntSAR provides an instantaneous measurement that is not possible with campaign-style traditional surveys that take a significant time to complete. The synoptic mapping of deformation with IntSAR is also vital for associating it with the underlying causes. A geodetic point measurement for tectonic deformation in or near an area of subsidence can give spurious results, while an IntSAR map can show the anomalous pattern caused by non-tectonic deformation. This new application of IntSAR should be of interest to the petroleum industry, regulatory agencies, and geodesists.

Acknowledgments. We are grateful to P. Rosen and S. Hensley for the use of their ROI_pac interferometry software, and R. Crippen and K. Burke for helpful comments.This work was performed at the Jet Propulsion Laboratory, California Institute of Technology under contract with the National Aeronautics and Space Administration.

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Figures

Plate 1 The 35-day ascending ERS interferogram with phase converted to range change in satellite line-of-sight direction and geocoded. Colors show relative apparent motion of surface, with the yellow and red areas moving away, hence downward relative to dark purple areas. Overlays show major roads (gray lines) and California aqueduct (red line). Irregular areas in white are regions where the phase could not be reliably unwrapped, due to decorrelation. This is primarily in agricultural fields where the ground surface has been significantly modified by plowing or crop growth. Note > 40 mm of subsidence over Lost Hills in 35 days.

Plate 2 The 8-month ascending ERS interferogram with phase converted to range change as in Plate 1. Note that the subsidence scale portrayed in colors is different, and shows > 200 mm of subsidence. Some areas have subsided too much in 8 months to be resolved. Yellow line along California route 46 (CA-46) shows the location of profile across Lost Hills in Plate 3.

Plate 3 West-east profile through the Lost Hills oilfield with the interferometric phase of the 35-day and 8-month pairs converted to range change and divided by the time interval. The graph shows the variation in values (shaded) across a swath through the interferogram that is 200 m wide and the average values (solid lines). Gaps are places where the phase could not be unwrapped in the agricultural areas on both interferograms and the steep deformation gradients in the center of the oilfield on the 8-month interferogram.

Table 1

table notes

bAmbiguity height at mid-swath.

cDescending orbits.

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