Constrained inversion of magnetotelluric data using parallel simulated annealing algorithm and its application

2D magnetotelluric inversion based on ResNet

Data processing is one of the essential steps to obtain optimum response function of the Earth’s subsurface. The MT Data processing is based on the Fast Fourier Transform (FFT) algorithm which converts the time series data into its frequency domain counterpart. The FFT combined with statistical algorithm constitute the Robust Processing algorithm which is widely implemented in MT data processing software. The Robust Processing has three variants, i.e. No Weight (NW), Rho Variance (RV), and Ordinary Coherency (OC). The RV and OC options allow for denoising the data but in many cases the Robust Processing still results in not so smooth sounding curve due to strong noise presence during measurement, such that the Crosspower (XPR) analysis must be conducted in the data processing. The XPR analysis is very time consuming step within the data processing. The collaboration of B-Spline algorithm and Qualitative Spectral Analysis in the frequency domain could be of advantages as an alternative for these steps. The technique is started by using the best coherency from the Robust Processing results. In the Qualitative Spectral Analysis one can determine which part of the data based on frequency that is more or less reliable, then the next process invokes B-Spline algorithm for data smoothing. This algorithm would select the best fit of the data trend in the frequency domain. The smooth apparent resistivity and phase sounding curves can be considered as more appropriate to represent the subsurface. This algorithm has been applied to the real MT data from several survey and give satisfactory results.

Magnetotellurics (MT) images electrical conductivity, a property influenced by fluids, alteration, graphite, and partial melt. Because many different subsurface configurations can explain the MT responses observed in the field, the preferred subsurface conductivity model estimated through inversion is often ambiguous. A central challenge is that a robust stochastic model exploration in 3D, while conceptually the best way to expose such ambiguity, is too computationally demanding to be used as a standard practice. Consequently, most studies report a single deterministic model, which obscures the range of alternative geological structures that are equally consistent with the data.In this work we propose a practical approach to stochastic model exploration in 3D MT inversion. Drawing inspiration from annealing methods, we adopt a Very Fast Simulated Annealing (VFSA) framework, with sparse parameterization that makes the optimisation feasible for large-scale problems. Our inversion algorithm is built around the widely used ModEM forward solver, ensuring compatibility with existing workflows. Instead of producing one definitive model, the workflow can generate a set of plausible models that explain the data equally well. From this ensemble one can compute statistical summaries: a mean model that captures the most consistent structures and quantitative measures of variability that highlight where geometry, depth, or connectivity remain uncertain. This representation enables geologists to make interpretations while being explicitly aware of the uncertainty inherent in the inversion. We demonstrate that the approach works at regional scale using a large-area subset of USArray MT data from Cascadia. This dataset has been extensively studied and previously modelled with deterministic 3D inversion, which allows us to benchmark our results.

In order to improve the performance of simulated annealing (SA) algorithm while solving the large scale vehicle routing problem with time window(VRPTW), we propose a parallel SA(PSA) algorithm based on GPU-acceleration, which maps parallel SA algorithm to thread block executing on consumer-level graphics cards. The analytical results demonstrate that the method we proposed increases the population size, speeds up its execution and provides ordinary users with a feasible PSA solution.KeywordsVRPTWPSAGPUCUDA

In Magnetotelluric (MT) data processing, poor signal-to-noire ratio usually biaces the impedance tensor Z elements estimates. Strong electromagnetic (EM) noise may thus render the MT method impracticable in industrial areas. Noise due to periodic sources (i.e. power line harmonies) is easily removed by analog filtering in the field; but non-periodic EM noise (see e.g. Szarka, 1988, for an exhaustive list) should be handled more accurately in MT data processing.

In this work we propose a highly optimized version of a simulated annealing (SA) algorithm adapted to the more recently developed graphic processor units (GPUs). The programming has been carried out with compute unified device architecture (CUDA) toolkit, specially designed for Nvidia GPUs. For this purpose, efficient versions of SA have been first analyzed and adapted to GPUs. Thus, an appropriate sequential SA algorithm has been developed as starting point. Next, a straightforward asynchronous parallel version has been implemented and then a specific and more efficient synchronous version has been developed. A wide appropriate benchmark to illustrate the performance properties of the implementation has been considered. Among all tests, a classical sample problem provided by the minimization of the normalized Schwefel function has been selected to compare the behavior of the sequential, asynchronous and synchronous versions, the last one being more advantageous in terms of balance between convergence, accuracy and computational cost. Also the implementation of a hybrid method combining SA with a local minimizer method has been developed. Note that the generic feature of the SA algorithm allows its application in a wide set of real problems arising in a large variety of fields, such as biology, physics, engineering, finance and industrial processes.

A combined strategy of an improved simulated annealing (SA) algorithm and genetic algorithm is presented, with the goal of reducing the computational expenses. The improvements made on the SA algorithm include two parts, i.e., the adaptive regulating for the step vector, and the dynamic testing for the equilibrium of the Metropolis process. The proposed strategy has both the advantage of SA algorithm, the ability to avoid being trapped in a local optimum, and that of genetic algorithm, the ability to use the information about the searched states for the next iteration. A practical application on geometry optimization of pole shoes in large salient pole synchronous generators is effectively implemented using the strategy. The numerical results show that the number of iterations used by executing the combined strategy are only about 75% of those by executing basic SA algorithm.

ABSTRACTWe present results from the resolution and sensitivity analysis of 1D DC resistivity and IP sounding data using a non‐linear inversion. The inversion scheme uses a theoretically correct Metropolis–Gibbs' sampling technique and an approximate method using numerous models sampled by a global optimization algorithm called very fast simulated annealing (VFSA). VFSA has recently been found to be computationally efficient in several geophysical parameter estimation problems. Unlike conventional simulated annealing (SA), in VFSA the perturbations are generated from the model parameters according to a Cauchy‐like distribution whose shape changes with each iteration. This results in an algorithm that converges much faster than a standard SA. In the course of finding the optimal solution, VFSA samples several models from the search space. All these models can be used to obtain estimates of uncertainty in the derived solution. This method makes no assumptions about the shape of an a posteriori probability density function in the model space. Here, we carry out a VFSA‐based sensitivity analysis with several synthetic and field sounding data sets for resistivity and IP. The resolution capability of the VFSA algorithm as seen from the sensitivity analysis is satisfactory. The interpretation of VES and IP sounding data by VFSA, incorporating resolution, sensitivity and uncertainty of layer parameters, would generally be more useful than the conventional best‐fit techniques.

We present electrical resistivity models of the crust and upper mantle from two‐dimensional (2‐D) inversion of magnetotelluric (MT) data collected in the Rio Grande rift, New Mexico, USA. Previous geophysical studies of the lithosphere beneath the rift identified a low‐velocity zone several hundred kilometers wide, suggesting that the upper mantle is characterized by a very broad zone of modified lithosphere. In contrast, the surface expression of the rift (e.g., high‐angle normal faults and synrift sedimentary units) is confined to a narrow region a few tens of kilometers wide about the rift axis. MT data are uniquely suited to probing the depths of the lithosphere that fill the gap between surface geology and body wave seismic tomography, namely the middle to lower crust and uppermost mantle. We model the electrical resistivity structure of the lithosphere along two east‐west trending profiles straddling the rift axis at the latitudes of 36.2 and 32.0°N. We present results from both isotropic and anisotropic 2‐D inversions of MT data along these profiles, with a strong preference for the latter in our interpretation. A key feature of the anisotropic resistivity modeling is a broad (~200‐km wide) zone of enhanced conductivity (<20 Ωm) in the middle to lower crust imaged beneath both profiles. We attribute this lower crustal conductor to the accumulation of free saline fluids and partial melt, a direct result of magmatic activity along the rift. High‐conductivity anomalies in the midcrust and upper mantle are interpreted as fault zone alteration and partial melt, respectively.

We collected long-period magnetotelluric (LMT) data on the 64 stations by using a remotely controlled measurement system in northwestern Anatolia, Türkiye. The data was collected along four nearly parallel 300-km-long lines. In our previous project, we already collected broadband magnetotelluric(MT) data on 358 stations along those four lines. These lines are crossing main tectonic traverses such as North Anatolia Fault Zones, and Intra-Pontid Suture zones.  The remotely controlled MT measurement system provides us to control data quality during measurement and we can change the station location if the data quality is not good in the current stations.  This ensures the good data quality of all MT sites. After the time series analysis and main data processing procedure such as phase tensor decomposition and static shift correction, we interpreted each line's data set by using a two-dimensional inversion algorithm. We also inverted LMT data by using a three-dimensional inversion algorithm. The three-dimensional resistivity model also showed us to main tectonic units as two-dimensional resistivity models. Additionally, crust lithosphere relations were also revealed. We obtained upper and lower crust boundaries by using magnetic data and crust al depth by using gravity data. Those results also validated our resistivity models obtained from MT data inversion. We are going to give preliminary interpretation results of the lithosphere structure of northwest Anatolia in this presentation.Acknowledgement:  This study is supported by TUBITAK (The Scientific and Technological Research Council of Turkey) Project with Grant Number 119Y197. We thanks TUBITAK.

This paper investigates the optimal access point (AP) placement (OAPP) in simultaneous broadcast system using orthogonal frequency division multiplexing (OFDM) for high data rate indoor wireless LAN. We aim to determine the best combination of multiple AP placements that minimizes average bit error rate (BER) of terminals when in put information including an indoor configuration, a number APs, and total transmission power is given a priori. Since OAPP is categorized as a hard combinatorial problem with many variables and constraints, we applied a nonlinear optimization scheme called uniform design simulated annealing (UDSA) to search for an approximate optimal solution and analyzed its performance in detail. The simulation results demonstrate that the UDSA algorithm has been successfully applied to OAPP and its effectiveness was also confirmed in comparison with very fast simulated annealing (VFSA) and local search (LS) algorithms.

Joint inversion is an important quantitative interpretation tool for integrated geophysics. The present study situation and progress of joint inversion using gravity and seismic data are reviewed and discussed in the paper first. Then, the improved very fast simulated annealing algorithm (VFSA) with its obvious advantage of finding overall optimal solution in inverse problems is applied. So the constrained synchronous joint inversion of gravity and seismic data using the improved VFSA is put forward. The model with uncommon interface of density and velocity is designed. Through the model test and field observed data processing and interpretation, this method is proved effective and practicable, especially the application in Xuwen area shows that the density and velocity structures of the underground complicated interfaces could be exactly determined and revealed. With the constrained known information, this joint inversion method is clearly superior to the single inversion of gravity data.

Rayleigh wave inversion using heat-bath simulated annealing algorithm

Joint inversion of PP and PS reflection data has been hindered by the difficult task of registration or correlation of PP & PS events and joint inversion method. It can perhaps be achieved by registering the events during inversion, but the resulting algorithm is generally computationally intensive and lower accuracy. In this paper, we propose a stochastic inversion of PP and PS data which have been registered to the same PP time scale using a new interval velocity analysis technique. The prestack PP and PS wave joint stochastic inversion is achieved by using the PP and PS wave angle gathers using a very fast simulated annealing (VFSA) algorithm. The objective function attempts to match both PP and PS data; the starting models are drawn from fractional Gaussian distribution constructed from interpolated well logs. The proposed method has been applied to synthetic and real data; the inverted results from synthetic data inversion compare very well with model data, and inverted results for real data inversion are consistent with seismic data and log data. These also show that the proposed method has a higher accuracy for estimating rock physics parameters while it circumvents the horizon registration problem in the data interpretation. We also estimate uncertainty in our estimated results from multiple VFSA derived models.

This paper introduces a new class of D-dimensional density probability functions to be used in Simulated Annealing algorithms and derives an appropriate cooling schedule that is proved to be inversely proportional to a previously chosen power n of time. This generates a new algorithm, the nFast Simulated Annealing (nFSA), from which the Fast Simulated Annealing (FSA) is a particular case. As will be shown, this new algorithm achieves results with an accuracy that increases with n, at the expense of an initial convergence speed that decreases with n. This drawback is solved by the use of an adaptive algorithm, the Adaptive nFast Simulated Annealing (AnFSA), where the parameter n starts at small value, producing a fast initial convergence, and is raised as the algorithm runs, finding global minima points quickly and with great accuracy.