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Gravity and gravity gradiometry measurements are commonly used to map density variations in the subsurface. Gravity measurements can characterize gravitational anomalies at long and short wavelengths effectively, but the cost of collecting a sufficiently spatially dense survey to characterize the short wavelengths can be prohibitive. Gravity gradient data can be quickly collected with short-wavelength information at a low noise level, but they have decreasing sensitivity to longer wavelengths. We have described a method to jointly invert gravity and gravity gradient data that takes advantage of the differing frequency contents and noise levels of the two methods to create an improved image of the subsurface. Previous work treated the inversion as a multiple component gravity inversion; however, this can cause unintended errors in the recovered models because each data set is not guaranteed to be fit within its noise level. Our joint inversion methodology ensures that the gravity and gravity gradient data sets are fit within their individual noise levels by incorporating a relative weighting parameter, and we describe how to find that parameter. This method can also be used to create an improved broadband gravity anomaly map that has a reduced noise level at long wavelengths using a joint equivalent source reconstruction. We first build a synthetic model using a Minecraft world editor that has different wavelength anomalies, and find the improvement with joint inversion. These results are also confirmed using a real-world example at the R. J. Smith test range in Kauring, Australia.

Understanding reservoir properties plays a key role in managing a reservoir’s resources and optimizing production. History matching is an important means for characterizing those properties. We developed a method to invert for the distribution of permeability directly from time-lapse gravity data. In this process, we used fluid flow in a porous medium coupled with forward modeling of the time-lapse gravity response as the forward operator, and then we solved a nonlinear inversion to reconstruct the permeability distribution in the reservoir. We were able to formulate the deterministic inversion as a Tikhonov regularization problem because of the relatively low computational cost of forward modeling time-lapse gravity data. The inversion can combine the information from time-lapse gravity and injection-production data sets to determine a static state of the reservoir described by the permeability. The resulting model satisfied all data sets simultaneously while obeying the mechanics of fluid flow through a porous medium. The inverse formulation also enabled the estimation of the uncertainty of the constructed permeability model with respect to the data, and our numerical simulations indicated that the information content in the two dynamic data sets appeared to be sufficiently high to constrain the recovery of permeability distribution.

Objective: To report our experience using a broad spectrum antimicrobial, povidone-iodine, as a novel at-home prescription treatment for molluscum contagiosum. Design/Setting: A systematic review of cases presenting to one of the author’s private dermatology clinics from January to July of 2015 identified 12 patients with molluscum contagiosum seeking treatment. Participants: The population was pediatric, with six males and six female patients included (age range 2–17 years, mean age 6 years). Measurements: Patients were evaluated at baseline and returned to the office for evaluation at four-week intervals until resolution or failure to show for appointments, with number and location of lesions being recorded at each visit. Adverse effects were evaluated at each visit. Results: All 12/12 (100%) patients demonstrated complete or partial resolution. There were a total of 115 lesions treated in the case series, and 103/115 (90%) resolved. Complete resolution occurred in 8/12 (67%) patients. Of the 8/12 with complete resolution, 4/8 (50%) patients showed complete resolution at the four-week follow-up visit and 4/8 (50%) showed complete resolution at the eight-week follow-up. Of the 4/12 (33%) patients who failed to demonstrate complete resolution, 4/4 (100%) showed partial resolution. Conclusion: This case series demonstrates considerable success for treatment of molluscum contagiosum with a dilute povidone-iodine preparation. The treatment was well-tolerated, with minimal side effects.

Compared to other geophysical methods for monitoring subsurface dynamic systems, time-lapse gravity has one important advantage in that the measurements are directly sensitive to the variations in density, which is solely related to the amount of mass changes per volume. In oil and gas reservoirs, such changes are primarily due to fluid movement and substitutions. Thus, while seismic method provides unparalleled structural resolution, time-lapse gravity method has the potential for characterizing the “content” that is the fluid saturation within “containers” delineated by seismic images. There have been significant advances in instrumentation, data acquisition, and quantitative interpretation in time-lapse gravity methods. As a result, we may be on the threshold of a new phase in the application of this method. This paper will focus on the quantitative interpretation techniques for time-lapse gravity data through different inversions and the associated applications in characterizing both the static and dynamic properties of the reservoirs. In particular, we will present and review inversion techniques for recovering time-lapse density distribution in reservoir and joint inversion methods of time-lapse gravity data with production data for imaging the permeability and saturation distribution in reservoirs.

With the ability of gravity gradiometry surveys to be completed quickly relative to a ground based gravity survey with the same spatial resolution, we look to improve upon the far field anomaly recovery of the gradient data. We add gravity to the airborne gravity gradient data in a generalized inversion scheme to improve the far field anomaly recovery. We also estimate the proper DC bias in the relative gravity gradient measurements with the corresponding linear trend in the gravity data. Joint inversion of gravity and gravity gradient data requires a consistent treatment of the two measured data sets. We develop a work-flow to incorporate both data set in a joint inversion and apply the generalized inversion methodology for gravity and gravity gradient data collected at the Kauring Test Site. After ensuring the gravity data are properly reduced consistent with the measured gravity gradient data, we show that the addition of a sparse set of gravity data enhances the model recovered in a joint inversion.

Gravity and gravity gradient data inherently have different frequency contents based on the differing decay rates with distance from the source and differing signal to noise ratios. Gravity contains more low frequency content while more sensitive to deeper structures, and gravity gradient contains relatively more high frequency content while more sensitive to near surface features. We apply techniques for jointly inverting the two data sets using a 3D binary formulation to the SEG/EAGE salt body model. The inversion algorithm is able to recover a meaningful model of the salt body because the density contrast profile is known a priori. The recovered models also help to highlight the interaction between the two data sets and the information they contain.

Gravity and gravity gradient data inherently have different frequency contents based on the differing decay rates with distance from the source and differing signal to noise ratios. Gravity contains more low frequency content, and gravity gradient contains relatively more high frequency content. We develope an algorithm to jointly invert the two data sets using a generalized 3D inversion to obtain a model that benefits from both differing frequency contents of the data sets and test the methodology on two synthetic cases: a simple block model and a more realistic basin and range model with a vertical intrusion. The models improve at depth with the added gravity data and the joint inversion reconstructs more meaningful models. The algorithm helps to highlight the difference in information content in data and is applicable for integrated interpretation of two data set in practice.

The Leyden mine artificial aquifer storage and recovery system was originally monitored by time-lapse gravity from 2004 to 2005 during the water injection period. We now continue that survey seven years later to assess the effectiveness of water storage. In order to do so we must remove sources of noise associated with a long term time-lapse gravity survey in an area with large anthropogenic effects. Missing time-lapse stations were located and reoccupied by using a combination of differential GPS and satellite image referencing. To correct for effects due to a surface quarry and landfill, surface change corrections are calculated by using digital elevation models from different time periods, analogous to a time-lapse terrain correction. After removing these effects, quantitative analyses by means of binary inversion and surface inversion are used to compare to previous work and map the current distribution of water. Comparisons based on surface inversions suggest that no water has left the system, but rather the water has redistributed itself slightly throughout the mine.