Gravity Data Analysis Based on Optimum Upward Continuation Filter and 3D Inverse Modelling (Case Study at Sedimentary Basin in Volcanic Region Malang and Its Surrounding Area, East Java)

The study on the fore-arc sedimentary basin for hydrocarbon exploration is rare because of the more complicated geological structures, and conventional seismic methods cannot optimally penetrate the rock layers as there are many volcanic and limestone rocks. One of the natural resources potential in the Southern part of the East Java region, especially in Malang and its surrounding areas is the possibility of hydrocarbons in the fore-arc basin, so research is needed to know the existence of these sedimentary basins. The gravity method is one of the geophysical methods used to assess sedimentary basins based on physical parameters of mass density. The aims of this research are to delineate the sedimentary sub-basin, to find out its structure pattern, interpret subsurface geological and basement configuration. The data analysis approach used in this study involves spectral analysis, upward continuation filter, and 3D inverse modeling. The maximum height for the optimum upward continuation filter is 3000 m, which results in regional and residual anomalies. There were five sedimentary sub-basins identified based on residual gravity anomaly, and the gravity anomalies can also detect structure patterns such as basement high, lineament, and fault pattern. The bedrock is supposed as an intermediate igneous rock with a mass density of around 2.7 gr/cc according to the results of 3D inverse modeling. Deposition from bottom to upward is Mandalika, Nampol, and Wonosari Formations and completed by the uppermost are quaternary volcanic rocks. The inversion modeling results show that the Malang and surrounding areas have thick sedimentary rocks covered by volcanic deposits, which is impressive for further investigation to explore the possibility of the hydrocarbon existence in these areas.

Low-Latitude Reduction-to-the-Pole and Upward Continuation between Arbitrary Surfaces based on the Partial Differential Equation Framework

Summary Magnetic surveys conducted in complex conditions, such as low magnetic latitudes, uneven observation surfaces, or above high-susceptibility sources, pose significant challenges for obtaining stable solutions for reduction-to-the-pole (RTP) and upward-continuation processing on arbitrary surfaces. To tackle these challenges, in this study, we propose constructing an equivalent-susceptibility model based on the partial differential equation (PDE) framework in the space domain. A multilayer equivalent-susceptibility method was employed for RTP and upward-continuation operations, thus allowing for application on undulating observation surfaces and strong self-demagnetisation effect in a non-uniform mesh. A novel positivity constraint is introduced to improve the accuracy and efficiency of the inversion. We analysed the effect of the depth-weighting function in the inversion of equivalent susceptibility for RTP and upward-continuation reproduction. Iterative and direct solvers were utilised and compared in solving the large, sparse, nonsymmetric, and ill-conditioned system of linear equations produced by PDE-based equivalent-source construction. Two synthetic models were used to illustrate the efficiency and accuracy of the proposed method in processing both ground and airborne magnetic data. Aeromagnetic, ground data, and prior magnetic orebody information collected in Brazil at a low magnetic latitude region were used to validate the proposed method for processing RTP and upward-continuation operations on magnetic data sets with strong self-demagnetisation.

Understanding the Geology of the Philippines through Gravity Anomalies

The Philippine Archipelago is a complex island arc system, where many regions still lack geopotential studies. This study aims to present a general discussion of the Philippine gravity anomaly distribution. The high-resolution isostatic anomaly digital grid from the World Gravity Map (WGM) was processed and correlated with the Philippines’ established geology and tectonics. This study also investigated the gravity signatures that correspond to the regional features, e.g., geology, structures, sedimentary basins, and basement rocks of the study area. Upward continuation, high-pass, and gradient filters (i.e., first vertical derivative, horizontal gradient) were applied using the Geosoft Oasis Montaj software. The interpreted gravity maps’ results highlighted the known geologic features (e.g., trench manifestation, ophiolite distribution, basin thickness). They revealed new gravity anomalies with tectonic significance (e.g., basement characterization). The isostatic gravity anomaly map delineates the negative zones. These zones represent the thick sedimentary accumulations along the trenches surrounding the Philippine Mobile Belt (PMB). The Philippine island arc system is characterized by different gravity anomaly signatures, which signify the density contrast of subsurface geology. The negative anomalies (< 0 mGal) represent the thick sedimentary basins, and the moderate signatures (0 to 80 mGal) correspond to the metamorphic belts. The distinct very high gravity anomalies (> 80 mGal) typify the ophiolitic basement rocks. The gravity data’s upward continuation revealed contrasting deep gravity signatures; the central Philippines of continental affinity (20 – 35 mGal) was distinguished from the remaining regions of oceanic affinity (45 – 200 mGal). Local geologic features (e.g., limestone, ophiolitic rocks) and structures (e.g., North Bohol Fault, East Bohol Fault) were also delineated downward continuation and gravity gradient maps of Bohol Island. The WGM dataset’s effectiveness for geologic investigation was achieved by comparing the established geologic features and interpreted gravity anomalies. The processed gravity digital grids provided an efficient and innovative way of investigating the Philippines’ regional geology and tectonics.

An upward continuation method based on spherical harmonic analysis and its application in the calibration of satellite gravity gradiometry data

The ground gravity anomalies can be used to calibrate and validate the satellite gravity gradiometry data. In this study, an upward continuation method of ground gravity data based on spherical harmonic analysis is proposed, which can be applied to the calibration of satellite observations from the European Space Agency's Gravity Field and Steady-State Ocean Circulation Explorer (GOCE). Here, the following process was conducted to apply this method. The accuracy of the upward continuation method based on spherical harmonic analysis was verified using simulated ground gravity anomalies. The DTU13 global gravity anomaly data were used to determine the calibration parameters of the GOCE gravitational gradients based on the spherical harmonic analysis method. The trace and the tensor invariants I2, I3 of the gravitational gradients were used to verify the calibration results. The results revealed that the upward continuation errors based on spherical harmonic analysis were much smaller than the noise level in the measurement bandwidth of the GOCE gravity gradiometer. The scale factors of the Vxx, Vyy, Vzz, and Vyz components were determined at an order of magnitude of approximately 10−2, the Vxz component was approximately 10−3, and the Vxy component was approximately 10−1. The traces of gravitational gradients after calibration were improved when compared with the traces before calibration and were slightly better than the EGG_TRF_2 data released by the European Space Agency (ESA). In addition, the relative errors of the tensor invariants I2, I3 of the gravitational gradients after calibration were significantly better than those before calibration. In conclusion, the upward continuation method based on spherical harmonic analysis could meet the external calibration accuracy requirements of the gradiometer.

Comparative Results of Regional and Residual Anomalies with the Upward Continuation, Moving Average, and Polynomial Methods for Magnetic Data

Geophysics programing of regional and residual anomaly separation on Magnetic data has been carried out with the results compared with the upward continuation method in the OasisMontaj software. Separation of anomalies with moving average and polynomial methods is processed using Matlab programming. The orders used in the polynomial method are first-order, second-order and third-order. Comparison is done by calculating the match value. The chosen matching method is autocorrelation. Correlation of residual magnetic anomalies resulting from upward continuation (Magpick) to moving averages, 1st-order polynomials, 2nd-order polynomials and 3rd-order polynomials. Correlation values obtained for the moving average method are 0.9604, first order polynomial 0.9072, 2nd order polynomial 0.9482 and third order polynomial 0.6057. The moving average and second order polynomial methods can be used as a substitute method if we do not use the upward continuation method.

Evaluating the accuracy of equivalent-source predictions using cross-validation

&lt;p&gt;We investigate the use of cross-validation (CV) techniques to estimate the accuracy of equivalent-source (also known as equivalent-layer) models for interpolation and processing of potential-field data. Our preliminary results indicate that some common CV algorithms (e.g., random permutations and k-folds) tend to overestimate the accuracy. We have found that blocked CV methods, where the data are split along spatial blocks instead of randomly, provide more conservative and realistic accuracy estimates. Beyond evaluating an equivalent-source model's performance, cross-validation can be used to automatically determine configuration parameters, like source depth and amount of regularization, that maximize prediction accuracy and avoid over-fitting.&lt;/p&gt;&lt;p&gt;Widely used in gravity and magnetic data processing, the equivalent-source technique consists of a linear model (usually point sources) used to predict the observed field at arbitrary locations. Upward-continuation, interpolation, gradient calculations, leveling, and reduction-to-the-pole can be performed simultaneously by using the model to make predictions (i.e., forward modelling). Likewise, the use of linear models to make predictions is the backbone of many machine learning (ML) applications. The predictive performance of ML models is usually evaluated through cross-validation, in which the data are split (usually randomly) into a training set and a validation set. Models are fit on the training set and their predictions are evaluated using the validation set using a goodness-of-fit metric, like the mean square error or the R&amp;#178; coefficient of determination. Many cross-validation methods exist in the literature, varying in how the data are split and how this process is repeated. Prior research from the statistical modelling of ecological data suggests that prediction accuracy is usually overestimated by traditional CV methods when the data are spatially auto-correlated. This issue can be mitigated by splitting the data along spatial blocks rather than randomly. We conducted experiments on synthetic gravity data to investigate the use of traditional and blocked CV methods in equivalent-source interpolation. We found that the overestimation problem also occurs and that more conservative accuracy estimates are obtained when applying blocked versions of random permutations and k-fold. Further studies need to be conducted to generalize these findings to upward-continuation, reduction-to-the-pole, and derivative calculation.&lt;/p&gt;&lt;p&gt;Open-source software implementations of the equivalent-source and blocked cross-validation (in progress) methods are available in the Python libraries Harmonica and Verde, which are part of the Fatiando a Terra project (www.fatiando.org).&lt;/p&gt;

The Method of Curvature Attribute applied in the Depth Inversion of the Geological Bodies Edge by Potential Field Data

&lt;p&gt;It is vital to quickly and effectively determine the extent and depth of geological body by using potential field data in gravity and magnetic survey. In this study, three key techniques studying the extent and depth of geological sources based on curvature attribute are studied: the optimal solutions to the objective function, the edge of geological bodies and picking out solutions. Firstly, the optimal solution to the objective function is studied, that is, the key extraction algorithm about the curvature attribute. The Huber norm is introduced into the extraction algorithm of curvature attribute, which more accurately detect the depth of edge of the geological bodies. Secondly, the normalized vertical derivative of the total horizontal derivative (NVDR-THDR) technique is introduced into curvature attribute, which shows more continuous results about the edge position of the geological bodies and more sensitive to the small-scale tectonic structure. Finally, we study the way to pick out the inversion solution, that is, to solve the multi-solution equations in the inversion. The upward continuation of a certain height with strict physical significance was introduced into the inversion method, which was used to suppress the noise, and the final and actual inversion depth was equal to the inversion depth minus the height of upward continuation. And the average value of threshold limitation technology of the potential fields data was also introduced into this method. Using the two technologies, solutions of non-field source edge positions were eliminated, and make the inversion solutions closer to the actual situation. Through the above three key techniques, the accuracy, continuity and recognition to the small-scale structure of the inversion result are optimized. The theoretical models are used to verify the effectiveness of the above key technologies, the results show that the three key technologies have achieved good results, and the combined models are used to verify the effectiveness of the optimized inversion method. The measured aeromagnetic data were used to inversing the edge depth of the intrusive rock in a mining area, and the inversion results are in good agreement with the rock depth revealed by borehole.&lt;/p&gt;

Pemodelan 2D dan 3D Metode Geomagnet untuk Interpretasi Litologi dan Analisis Patahan di Jalur Sesar Oyo

Gempa susulan setelah gempabumi Yogyakarta Tahun 2006 memiliki hiposenter bukan di sepanjang Sesar Opak tapi cenderung di sekitar unidentified fault yang berjarak 10 – 15 km sebelah timur pegunungan Gunung Kidul. Unidentified fault tersebut berkorelasi dengan keberadaan jalur Sesar Oyo. Metode geofisika yang dapat diterapkan untuk mengidentifikasi keberadaan jalur sesar adalah metode geomagnet. Penelitian ini bertujuan untuk mengetahui pola sebaran anomali medan magnet di sekitar jalur Sesar Oyo, mengetahui susunan formasi dan jalur Sesar Oyo berdasarkan pemodelan geomagnet. Pengambilan data dilakukan menggunakan PPM dengan 35 titik pengamatan dan spasi antar titik pengamatan 1,5 km. Pengolahan data dilakukan dengan koreksi variasi harian, koreksi IGRF(International Geomagnetics Reference Field), RTP (Reduction to Pole) dan Upward Continuation. Pemodelan dilakukan dengan menganalisis anomali medan magnet yang telah direduksi ke kutub dan kontinuasi ke atas dengan ketinggian 2500 m. Hasil analisa menunjukkan rentang nilai anomali medan magnet di kawasan penelitian adalah 180 nT – 660 nT, yang menunjukkan kontras keberadaan blok sesar. Hasil pemodelan 2D menunjukkan kawasan penelitian didominasi oleh 3 formasi batuan utama yaitu batubasalt-andesitik Formasi Nglanggran, batupasir Formasi Sambipitu, dan batugamping Formasi Wonosari. Hasil pemodelan 3D menunjukkan Sesar Oyo merupakan sesar geser dengan kedalaman 150 – 300 m, jalur sesar tersebut terbagi menjadi 2 segmen yaitu dengan arah N120°E sepanjang 5,8 km dan N160°E dengan panjang 2,5 km.