Seismically Informed High-Resolution Geometric Gravity Inversion and Forward Modeling of Paleozoic Basement in Rock Valley, NV

Morphology of the basement and Hormuz salt distribution in offshore Abu Dhabi from constrained 3-D inversion of gravity and magnetic data

SUMMARY We present and apply a pseudo trans-dimensional inversion method for 3-D geometrical gravity inversion, in which the number of rock units, their geometry and their density can vary during sampling. The method is designed for efficient exploration of the model space and to infer the presence and properties of units not directly observable but detectable with geophysical data. Sampling relies on a non-reversible Metropolis-Hastings algorithm, during which rock units can be added or removed from the model, interface geometries are perturbed using random fields, and densities are sampled from distributions informed by prior information. To visualize the space of sampled models and to aid interpretation, a workflow is proposed that combines dimensionality reduction with the clustering of models in families. The capabilities of the inversion method are evaluated using two synthetic cases. The first is a motivating example aimed at recovering an intrusion missing from the prior model. It features a layer-cake where fixed-dimensional inversion fails to adequately fit the data and sample models close to the true model, while the proposed pseudo trans-dimensional approach is much more successful. The second case investigates the recovery of two missing units and the capability to overcome prior model biases. Results show the potential of our method to infer the presence of unseen geological features such as intrusions. However, they suggest that with biased prior geological modelling, it may be challenging to infer with certainty the presence of more than two previously unknown rock units at depth.

Resistivity methods are commonly used in mineral exploration to map lithology, structure, sulphides and alteration. In the Athabasca Basin, resistivity methods are used to detect alteration associated with uranium. At the Midwest deposit, there is an alteration zone in the Athabasca sandstones that is above a uraniferous conductive graphitic fault in the basement and below a conductive lake at surface. Previous geophysical work in this area has yielded resistivity sections that we feel are ambiguous in the area where the alteration is expected. Resolve® and TEMPEST sections yield an indistinct alteration zone, while two-dimensional (2D) inversions of the ground resistivity data show an equivocal smeared conductive feature in the expected location between the conductive graphite and the conductive lake. Forward modelling alone cannot identify features in the pseudosections that are clearly associated with alteration, as the section is dominated by the feature associated with the near-surface conductive lake; inverse modelling alone produces sections that are smeared and equivocal. We advocate an approach that uses a combination of forward and inverse modelling. We generate a forward model from a synthetic geoelectric section; this forward data is then inverse modelled and compared with the inverse model generated from the field data using the same inversion parameters. The synthetic geoelectric section is then adjusted until the synthetic inverse model closely matches the field inverse model. We found that this modelling process required a conductive alteration zone in the sandstone above the graphite, as removing the alteration zone from the sandstone created an inverse section very dissimilar to the inverse section derived from the field data. We therefore conclude that the resistivity method is able to identify conductive alteration at Midwest even though it is below a conductive lake and above a conductive graphitic fault. We also concluded that resistivity inversions suggest a conductive paleoweathering surface on the top of the basement rocks at the basin/basement unconformity.

Process Compensated Resonance Testing (PCRT) is a nondestructive evaluation (NDE) method based on the fundamentals of Resonant Ultrasound Spectroscopy (RUS). PCRT is used for material characterization, defect detection, process control and life monitoring of critical gas turbine engine and aircraft components. Forward modeling and model inversion for PCRT have the potential to greatly increase the method’s material characterization capability while reducing its dependence on compiling a large population of physical resonance measurements. This paper presents progress on forward modeling studies for damage mechanisms and defects in common to structural materials for gas turbine engines. Finite element method (FEM) models of single crystal (SX) Ni-based superalloy Mar-M247 dog bones and Ti-6Al-4V cylindrical bars were created, and FEM modal analyses calculated the resonance frequencies for the samples in their baseline condition. Then the frequency effects of superalloy creep (high-temperature plastic deformation) and macroscopic texture (preferred crystallographic orientation of grains detrimental to fatigue properties) were evaluated. A PCRT sorting module for creep damage in Mar-M247 was trained with a virtual database made entirely of modeled design points. The sorting module demonstrated successful discrimination of design points with as little as 1% creep strain in the gauge section from a population of acceptable design points with a range of material and geometric variation. The resonance frequency effects of macro-scale texture in Ti-6Al-4V were quantified with forward models of cylinder samples. FEM-based model inversion was demonstrated for Mar-M247 bulk material properties and variations in crystallographic orientation. PCRT uncertainty quantification (UQ) was performed using Monte Carlo studies for Mar-M247 that quantified the overall uncertainty in resonance frequencies resulting from coupled variation in geometry, material properties, crystallographic orientation and creep damage. A model calibration process was also developed that evaluates inversion fitting to differences from a designated reference sample rather than absolute property values, yielding a reduction in fit error.

The Lower Shire Karoo Basin architecture using 3-D gravity inversion modelling

A new structural analysis is presented for the Browse Basin of the Australian North West Margin, integrating new observations based on a regional 2D seismic data-set and potential field data. Previously published plate reconstructions and gravity inversion modelling were used to understand the mega-regional context of this interpretation and propose a new history of basin evolution. Key basin-forming northeast to southwest structural elements were developed during Carboniferous to Permian rifting, inherited fabrics from relaxed Proterozoic fold belts. Long-lived highs formed during this time delineated the structure of the basin through later Mesozoic rifting. Rifting was accommodated initially by inheritance of large basin-bounding Paleozoic listric faults and then development of new planar faults in the basin. This led to the formation of both rotated syn-rift sediment wedges and tilted fault block geometries. Structures related to several phases of inversion have been mapped, including a previously little-documented Early Cretaceous event. The influence of inherited structural trends and location of inversion structures is discussed. This work provides a new understanding of structural inheritance and rift architecture, and highlights the complexity of the inversion history of the Browse Basin. It has implications for petroleum systems development and the timing of potential hydrocarbon trap formation.

The structural setting of the Ischia resurgent caldera and its magmatic system has been investigated by a joint interpretation of a 3D inversion of previously collected gravimetric data and all the available geological, geophysical and petrological data. Starting from the available Bouguer gravity map of the Neapolitan volcanic area and a previous 2.5D modelling, a selection of on land and offshore gravity data has been used to perform a 3D inversion, adapting and merging the basic ideas of two already tested methods, used to detect isolated bodies and layered discontinuities respectively. The base of the map is a set of gravity values, covering the whole Neapolitan volcanic area and the Gulf of Naples, which results from the union of 862 offshore and about 2000 on land extant gravity data, made uniform and re-analysed. The final model proposed here allows us to outline a very detailed and well-constrained structural setting of the crustal sector beneath Ischia. In particular, the 3D gravity inversion allowed us to outline a body with negative density contrast under Mt Epomeo, interpreted as the resurgent block, and to describe the magmatic system underneath it as a complex system of intrusions, rather than a uniformly distributed laccolithic body.

Today there are still many challenges in the quantitative interpretation of downhole distributed temperature measurements to diagnose multistage fracture treatments in horizontal wells. These challenges include handling enormous amount of data measured by the sensors continuously in time and space domain, a readily-to-be-used fast but robust forward model to simulate temperature behavior, and an efficient algorithm to inverse the parameters that are of interest. Because multistage fracturing involves many uncertain parameters; ranging from reservoir properties to treatment design, to fracture geometries and conductivity; the problem is extremely complex when inverse the measured temperature to a downhole flow profile. This study presents an approach to combine forward and inversion models to interpret downhole temperature data. The goal is to improve computational efficiency. Examples use the field data from a gas well in Marcellus shale formation to illustrate the feasibility of quantitative interpretation of temperature measurement for fracture diagnosis. The forward model uses the fast marching method. The forward simulation is order-of-magnitude faster than even the semi-analytical model, which is the essential contribution to apply the method in the field case successfully. The inversion procedure starts with a sensitivity study to select the inversion parameters among various parameters such as fracture half-length, fracture conductivity, and determine the impact of their uncertainty on inversion. The inversion model uses the initial analysis on temperature gradient to identify the zones with significant temperature changes for interpretation and eliminates the rest of the data from interpretation. Thus, we obtain a prior estimation of the selected inversion parameters, which will be used as an initial guess of the inversion process. This prior estimation saves significant computation. The inversion is performed fracture by fracture either using parallel computing or sequential computing based on the sensor locations. We first show a synthetic example with multiple fractures to illustrate the approach, test the procedure accuracy and computation speed. The primary inversion parameter is flow rate, and either fracture length or fracture conductivity, with all other parameters as an additional constraint. With an adequate initial guess, the inverted parameters match the reference "true value" properly. The inversion process converges with limited iterations for each fracture. The operation time highlights the advantages of the inversion model. The guided initial guess ensures the gradient inversion method converge and avoid local minimization. Finally, a field application is performed using this inversion model and shows encouraging results. The results of the paper illustrate the feasibility and procedure of using temperature date to diagnose multistage fracture treatment. The proposed inversion model is fast and reliable which provides a promising tool that can be used to interpret downhole temperature data quantitatively.

The North Australian Craton 3D Gravity and Magnetic Inversion Models: A trial for first pass modelling of the entire Australian continent

Prediction of lithology distribution is critical for development of oilfield and is also one of the basic tasks of geological modeling. Stochastic simulation has been proved to be an effective method for simulation the distribution of lithology. While stochastic simulation technique is theoretically a mathematical method, the result of simulation will be strongly affected by many factors, such as the quantity, quality, and distribution of well data, and so on. In the area or oilfield with limited wells and insufficient data, the uncertainty of simulation result will be very high, and the reliability of the result will be very low. This result with high uncertainty and low reliability will lead to very poor prediction of sand and shale. Further, the reliability of the result of petrophysical modeling will be low. This article introduces a new method by using constraint condition with high quality to improve the simulation result of lithology distribution and decrease the uncertainty of simulation result. Stratigraphic forward modeling is an effective approach to simulate the process of deposition, and this approach can characterize the geometry and distribution of complex sedimentation. But the resolution of the simulation result of this approach is lower than the requirement of development stage of oilfield. Seismic inversion has been proved to be an effective way with high resolution to describe the distribution of lithology by using high-quality seismic data, while seismic inversion is difficult to reflect the geological process and pattern. The combination of these two methods can provide good constraint condition for stochastic simulation. By using the results of stratigraphic forward modeling and seismic inversion, we can build the trend models for different lithology. The trend models can be used in stochastic simulation, and the trend models can improve the result of stochastic simulation. This paper took A oilfield in Oriente Basin in Ecuador as an example to show the process of this method. We built the stratigraphic forward modeling model based on the geological understanding and completed the research of seismic inversion of M1 layer of Napo Formation. The result of serigraphic forward modeling and seismic inversion was resampled into the geological model. Based on these two results, the trend models of sand and shale of M1 layer have been completed. The trend models have been used to constrain the stochastic simulation of lithology with sequential indicator simulation algorithm. This method can effectively decrease the uncertainty of simulation result caused by insufficient well data and improve the reliability of lithological model which further improves the result of petrophysical modeling.

Magnetotelluric (MT) inversion and forward modeling are closely linked. The optimization and iteration processes of the inverse algorithm require frequent calls to forward modeling. However, traditional numerical simulations for forward modeling are computationally expensive; here, deep learning (DL) networks can simulate forward modeling and significantly improve forward speed. Applying DL for forward modeling in inversion problems requires a high-precision network capable of responding to fine changes in the model to achieve high accuracy in inversion optimization. Most existing MT studies have used a convolutional neural network, but this method is limited by the receptive field and cannot extract global feature information. In contrast, the Mix Transformer has the ability to globally model and extract features. In this study, we used a Mix Transformer to hierarchically extract feature information, adopted a multiscale approach to restore feature information to the decoder, and eliminated the skip connection between the encoder and decoder. We designed a forward modeling network model (MT-MitNet) oriented toward inversion. A sample dataset required for DL forward was established using the forward data generated from the traditional inverse calculation iteration process. The trained network quickly and accurately calculates the forward response. The experimental results indicate a high agreement between the forward results of MT-MitNet and those obtained with traditional methods. When MT-MitNet replaces the forward computation in traditional inversion, the inversion results obtained with it are also highly in agreement with the traditional inversion results. Importantly, under the premise of ensuring high accuracy, the forward speed of MT-MitNet is hundreds of times faster than that of traditional inversion methods in the same process.

For large-scale magnetotelluric (MT) forward modeling using vector finite-element methods, iterative solvers are commonly applied. However, as frequency decreases close to zero, the iterative solution process struggles to converge. This is mainly caused by the fact that the weak conductivity term in the curl-curl equation governing the electromagnetic (EM) diffusion in the earth fades during the iterative solution for EM fields. This can lead to violation of the divergence-free condition for current and false jumps in the calculated fields. We develop a regularization technique for vector finite-element MT forward modeling, in which a scaled grad-div operator for electrical fields is included in the curl-curl equation to enforce the divergence-free condition explicitly. Because of its use of basis functions, the direct edge element discretization of the scaled term can lead to zero coefficients. To address this, an equivalent substitute of the scaled grad-div operator based on potential representation of electrical fields is used, discretized with node elements. For one specific element, this is finally reduced to a scaled gradient of the surface integral of current across all the surfaces of the element, resulting in better connectivity of the linear system of equations. The correctness of our algorithm is verified with two synthetic models and an inversion model from real data. The numerical performance is compared to the traditional iterative divergence correction technique (and without the application of the divergence correction for one case) for each of the three models. The results indicate that our algorithm is generally more efficient and stable compared to the traditional technique for all models at all periods considered, with significant improvement at long periods.

The inversion technique of Nowack and Lutter (1988a) and Lutter et al. (1990) has been applied to first arrival seismic refraction data collected along Line A of the 1986 Lake Superior GLIMPCE experiment, permitting comparison of the inversion image with an independently derived forward model (Trehu et al., 1991; Shay and Trehu, in press). For this study, the inversion method was expanded to allow variable grid spacing for the bicubic spline parameterization of velocity. The variable grid spacing improved model delineation and data fit by permitting model parameters to be clustered at features of interest. Over 800 first‐arrival travel‐times were fit with a final RMS error of 0.045 s. The inversion model images a low velocity central graben and smaller flanking half‐grabens of the Midcontinent Rift, and higher velocity regions (+0.5 to +0.75 km/s) associated with the Isle Royale and Keweenaw faults, which bound the central graben. Although the forward modeling interpretation gives finer details associated with the near surface expression of the two faults because of the inclusion of secondary reflections and refractions that were not included in the inversion, the inversion model reproduces the primary features of the forward model.

Geophysical systematic errors inevitably occur during acquisition and processing of data because of noise and discretization as well as incorrect geophysical forward modeling. In this paper, a new technology is proposed to enhance the geophysical inversion model without introducing any additional information. The relationship between the inversion model resolution matrix and the enhancing model is described. We suggest that more information could be extracted from inversion results by using the blind deconvolution method. Then, a mix‐norm TV regularization enhancement algorithm is proposed. Finally, we use the 1D and 2D magnetotelluric inversion models to prove the correctness and the effectiveness of the proposed methods. The results show that the proposed algorithm can increase geophysical model precision by 88.57%.

A novel inversion approach for fracture parameters and inflow rates diagnosis in multistage fractured horizontal wells