Wavefield downward‐continuation method for inversion of refraction data using finite differences

1994 ◽  
Author(s):  
Gerd Liebhardt ◽  
Karl‐Josef Sandmeir
Keyword(s):  
Finite Differences ◽  
Continuation Method ◽  
Downward Continuation ◽  
Refraction Data

A NOTE ON DOWNWARD CONTINUATION OF GRAVITY

Geophysics ◽  
1954 ◽  
Vol 19 (1) ◽  
pp. 71-75 ◽  
Author(s):  
César A. Trejo
Keyword(s):  
Finite Differences ◽  
Downward Continuation ◽  
Upward Continuation ◽  
Finite Differences Method ◽  
Downward Continuation Of Gravity

Comparing calculated and exact values in an ideal example, it is shown that Peters’ proposed method of downward continuation of gravity is far less suitable than a combination of Peters’ procedure for upward continuation and a finite differences method for downward continuation. It is shown also how Peters’ method can be substantially improved by considering only the closest values in the downward step of a continuation process.

A novel method for computing the vertical gradients of the potential field: Application to downward continuation

2019 ◽  
Author(s):  
Kha Van Tran ◽  
Trung Nhu Nguyen
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Potential Field ◽  
Continuation Method ◽  
Taylor Series Expansion ◽  
Expansion Method ◽  
Downward Continuation ◽  
Source Distribution ◽  
Vertical Derivative ◽  
Series Expansion Method

Summary Downward continuation is a very useful technique in the interpretation of potential field data. It would enhance the short wavelength of the gravity anomalies or accentuate the details of the source distribution. Taylor series expansion method has been proposed to be one of the best downward continued methods. However, the method using high-order vertical derivatives leads to low accuracy and instability results in many cases. In this paper, we propose a new method using a combination of Taylor series expansion and upward continuation for computing vertical derivatives. This method has been tested on the gravitational anomaly of infinite horizontal cylinder in both cases with and without random noise for higher accurate and stable than Hilbert transform method and Laplace equation method, especially in the case of noise input data. This vertical derivative method is applied successfully to calculate the downward continuation according to Taylor series expansion method. The downward continuation is also tested on both complex synthetic models and real data in the East Vietnam Sea (South China Sea). The results reveal that by calculating this new vertical derivative, the downward continuation method gave higher accurate and stable than the previous downward continuation methods.

Analysis on Convergence of Iteration Method for Potential Fields Downward Continuation and Research on Robust Downward Continuation Method

2009 ◽  
Vol 52 (2) ◽  
pp. 511-518 ◽  
Author(s):  
Hui ZHANG ◽  
Long-Wei CHEN ◽  
Zhi-Xin REN ◽  
Mei-Ping WU ◽  
Shi-Tu LUO ◽  
...  
Keyword(s):  
Iteration Method ◽  
Continuation Method ◽  
Downward Continuation ◽  
Potential Fields

Interpretation Method of GATEM Data based on PID Controller Iteration Downward Continuation Method

2021 ◽  
Vol 36 (6) ◽  
pp. 622-631
Author(s):  
Shanshan Guan ◽  
Bingxuan Du ◽  
Dongsheng Li ◽  
Yuan Wang ◽  
Yu Zhu ◽  
...  
Keyword(s):  
Pid Controller ◽  
High Efficiency ◽  
Continuation Method ◽  
Synthetic Data ◽  
Downward Continuation ◽  
Shanxi Province ◽  
Electromagnetic Response ◽  
Ground Source ◽  
The Impact ◽  
Interpretation Method

The Ground-source Airborne Time-domain Electromagnetic (GATEM) system has advantages for high efficiency and complex areas such as mountainous zone. Because of ignoring the impact of flight height, the section interpretation method seriously affects the interpretation and imaging accuracy of shallow anomalies. The PID controller iteration downward continuation method is proposed. Based on the original iteration continuation method, the differential coefficient and integral coefficient are added. The result shows that the new method remarkably decreases the iteration number, and the accuracy are verified by comparison with the numerical integration solution. The PID controller iteration downward continuation method is applied to the interpretation of GATEM data. For synthetic data, the interpretation results of continued electromagnetic response are closer to the true model than the z = 30 m interpretation results. The method is also applied to GATEM field data in Yangquan City, Shanxi Province, China. The interpretation results perform reliability using PID controller iteration downward continuation method in a GATEM field.

scholarly journals A Magnetic Potential-field Downward Continuation Method Based on Accelerated Landweber Iteration

2021 ◽  
Vol 1885 (4) ◽  
pp. 042003
Author(s):  
Ze Wang ◽  
Qi Zhang ◽  
Mengchun Pan ◽  
Dixiang Chen ◽  
Zhongyan Liu ◽  
...  
Keyword(s):  
Potential Field ◽  
Continuation Method ◽  
Magnetic Potential ◽  
Downward Continuation

scholarly journals Application of the normalized largest eigenvalue of structure tensor in the interpretation of potential field tensor data

2020 ◽  
Vol 72 (1) ◽  
Author(s):  
Yuan Yuan ◽  
Xiangyu Zhang ◽  
Wenna Zhou ◽  
Guochao Wu ◽  
Weidong Luo
Keyword(s):  
Potential Field ◽  
Continuation Method ◽  
Structure Tensor ◽  
Downward Continuation ◽  
Southwest Indian Ridge ◽  
Magnetic Data ◽  
Depth Information ◽  
Field Tensor ◽  
Largest Eigenvalue ◽  
Tensor Data

Abstract Obtaining horizontal edges and the buried depths of geological bodies, using potential field tensor data directly is an outstanding question. The largest eigenvalue of the structure tensor is one of the commonly used edge detectors for delineating the horizontal edges without depth information of the potential field tensor data. In this study, we presented a normalized largest eigenvalue of structure tensor method based on the normalized downward continuation (NDC) to invert the source location parameters without any priori information. To improve the stability and accuracy of the NDC calculation, the Chebyshev–Pade´ approximation downward continuation method was introduced to obtain the potential field data on different depth levels. The new approach was tested on various models data with and without noise, which validated that it can simultaneously obtain the horizontal edges and the buried depths of the geological bodies. The satisfactory results demonstrated that the normalized largest eigenvalue of structure tensor can describe the locations of geological sources and decrease the noise interference magnified by the downward continuation. Finally, the method was applied to the gravity data over the Humble salt dome in USA, and the near-bottom magnetic data over the Southwest Indian Ridge. The results show a good correspondence to the results of previous work.

An improved and stable downward continuation of potential field data: The truncated Taylor series iterative downward continuation method

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. J75-J86 ◽  
Author(s):  
HengLei Zhang ◽  
Dhananjay Ravat ◽  
XiangYun Hu
Keyword(s):  
Taylor Series ◽  
Potential Field ◽  
Field Data ◽  
Memory Performance ◽  
Continuation Method ◽  
Taylor Series Expansion ◽  
Downward Continuation ◽  
Continuation Methods ◽  
Potential Field Data ◽  
The Difference

We present a stable downward continuation strategy based on combining the ideas of the Taylor series expansion and the iterative downward continuation methods in a single method with better downward continuation and/or computer time/memory performance for potential field data containing noise. In the new truncated Taylor series iterative downward continuation (TTSIDC) method, a correction is made on the continuing plane by downward continuing the difference between the observed and the calculated field. The process is iteratively repeated until the difference meets the convergence conditions. It is tested on synthetic and field data and compared to other downward continuation methods. The proposed method yields sharper images and estimates more accurate amplitudes than most of the existing methods, especially for downward continuation over larger distances. The TTSIDC method also gives comparable results to the method of downward continuation using the least-squares inversion (DCLSI); however, the DCLSI method’s requirements of computer memory and time are substantially greater than our TTSIDC method, rendering the DCLSI method impractical for data sets of routine size on desktop computers commonly available today.

scholarly journals Interpretation Method of GATEM Data Based on PID Controller Iteration Downward Continuation Method  

2020 ◽  
Author(s):  
Shanshan Guan ◽  
Yu Zhu ◽  
Bingxuan Du ◽  
Dongsheng Li ◽  
Yuan Wang ◽  
...  
Keyword(s):  
Pid Controller ◽  
High Efficiency ◽  
Continuation Method ◽  
Synthetic Data ◽  
Downward Continuation ◽  
Shanxi Province ◽  
Ground Source ◽  
Time Domain Electromagnetic ◽  
The Impact ◽  
Interpretation Method

Abstract The Ground-source Airborne Time-domain Electromagnetic (GATEM) system has advantages for high efficiency and complex areas such as mountainous zone. The widely used section interpretation method, ignoring the impact of flight height, which seriously affects the interpretation and imaging accuracy of shallow anomalies. The PID controller iteration downward continuation method is proposed. Based on the original continuation iteration method, the differential coefficient and integral coefficient are added. The result shows that the new method remarkably decreases the iteration number and the accuracy are verified by comparison with the numerical integration solution. The PID controller iteration downward continuation method is applied to the interpretation of GATEM data. For synthetic data, the after continuation interpretation results are closer to the true model than the z = 30 m interpretation results. The method is also applied to GATEM field data in Yangquan City, Shanxi Province, China. The interpretation performs using PID controller iteration downward continuation results in a reliable GATEM field.

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