2D inversion of gravity data in bedrock identification (case study: a part of Qotrum plain in Yazd province)

The gravity method measures the vertical component of the acceleration at the Earth’s surface. The earth’s gravity field is affected by the density of different rocks and structures. Therefore, this method can be used in mineral exploration or studying the subsurface cavities and structures such as bedrocks, channels, and dikes.Inverse modeling is useful in understanding the physical phenomena on earth and applies to various fields of earth science, including geophysical exploration, groundwater hydrology, and seismology. In forward modeling, we assume that all physical parameters are known, and various models can be simulated through physical laws and scientific relationships. Despite the direct measuring of unknown parameters in inverse modeling, we would like to know their spatial distribution.Recognition of bedrock depth and geometry in aquifers, is the first stage of groundwater investigation. Geophysical methods play a significant role in the investigation of aquifers because they are the only way to detect deep subsurface structures at much lower costs than the most direct methods like drilling. Due to the complexity of alluvial sediments in terms of type and grading as well as difference between type and depth of bedrock, geophysical modeling approach and achieving the expected result are very important. Undetermined inverse problems that the unknown parameters are more than the measured values, can be solved using problem physics in the partial differential equation (PDE) system. Inverse modeling is one of the useful solutions to create a logical model with relationships between observed and measured values.

In this research, a template is presented to solve undetermined inverse problems using COMSOL multiphysics’ optimization that can be used in modelling a wide range of physical systems governed by the partial differential equation laws. The results indicated that this method, while high in computational speed, can accurately discriminate between low-density contrast regions and the background. Flexible and fast processing is an advantage of this method.

In this paper, gravity forward modeling will be implemented by solving Poisson’s equations with the appropriate boundary conditions, and then a methodology is presented for solving gravity inversion problems using COMSOL Multiphysics. COMSOL multiphysics does not include a gravity calculation module. However, since gravity and electrostatics are both governed by Poisson’s equation, a gravity model can be created in the electrostatics module by changing the electrical permittivity value.In inverse problems, if the number of unknown parameters is more than that of measurement values, the inverse problem is called underdetermined. The objective function for an underground inverse problem is the sum of a fitness and penalty term: The first term is equivalent to a weighted data-fitting criterion, and the second term measures the smoothness of the field relative to the given variogram. The penalty term distinguishes between solutions with comparable fitness values in problems where the number of parameters, exceeds the number of measurement values.We will apply this technique to a 2D synthetic gravity model using the AC/DC module of COMSOL. In the gravity field, a common inverse problem is estimating the density of subsurface structure givenmeasurements from the vertical component of gravitational acceleration. First of all, 2D inversion of gravity data has been run and validated in COMSOL software using some synthetic models and synthetic data in a forward modeling process. Afterwards, using real gravity data surveyed along two cross-sections in a part of Qotrum plain, the bedrock lateral structure was estimated and inverted density values cross-correlated with existing well logs.

Undetermined inverse problems in which the unknown parameters are more than the measured values can be solved using problem physics in the partial differential equation (PDE) system. This research, presented a template to solve undetermined inverse problems of 2D gravity data using COMSOL multiphysics’ optimization applying in 2D or 3D modeling of a wide range of different underdetermined inverse geophysical problems. Despite the most inversion codes designed for a particular application, this method applies to a broad range of physical systems governed by PDEs.The main benefit of COMSOL for solving inverse problems is that, once a user is comfortable with the software, it can solve a wide range of physical problems. Additionally, COMSOL’s ‘‘Multiphysics’’ capabilities allow coupling intrinsically to several physical equations.