The moments of the impulse response, a new paradigm for the interpretation of transient electromagnetic data

2002 ◽  
Author(s):  
Richard S. Smith ◽  
Terry J. Lee
Keyword(s):  
Impulse Response ◽  
New Paradigm ◽  
Electromagnetic Data ◽  
Transient Electromagnetic

scholarly journals Wiener estimation of the Green’s function

Geophysics ◽  
2013 ◽  
Vol 78 (5) ◽  
pp. W31-W44 ◽  
Author(s):  
Anton Ziolkowski
Keyword(s):  
Green’S Function ◽  
Impulse Response ◽  
Green's Function ◽  
Seismic Data ◽  
Wiener Filter ◽  
Electromagnetic Data ◽  
Transient Electromagnetic ◽  
Marine Seismic ◽  
Measured Response

I consider the problem of finding the impulse response, or Green’s function, from a measured response including noise, given an estimate of the source time function. This process is usually known as signature deconvolution. Classical signature deconvolution provides no measure of the quality of the result and does not separate signal from noise. Recovery of the earth impulse response is here formulated as the calculation of a Wiener filter in which the estimated source signature is the input and the measured response is the desired output. Convolution of this filter with the estimated source signature is the part of the measured response that is correlated with the estimated signature. Subtraction of the correlated part from the measured response yields the estimated noise, or the uncorrelated part. The fraction of energy not contained in this uncorrelated component is defined as the quality of the filter. If the estimated source signature contains errors, the estimated earth impulse response is incomplete, and the estimated noise contains signal, recognizable as trace-to-trace correlation. The method can be applied to many types of geophysical data, including earthquake seismic data, exploration seismic data, and controlled source electromagnetic data; it is illustrated here with examples of marine seismic and marine transient electromagnetic data.

The moments of the impulse response: A new paradigm for the interpretation of transient electromagnetic data

Geophysics ◽  
2002 ◽  
Vol 67 (4) ◽  
pp. 1095-1103 ◽  
Author(s):  
Richard S. Smith ◽  
Terry J. Lee
Keyword(s):  
Frequency Domain ◽  
Impulse Response ◽  
Time Constant ◽  
Delta Function ◽  
Late Time ◽  
New Paradigm ◽  
Time Data ◽  
Transient Electromagnetic ◽  
First Moment ◽  
Spherical Conductor

We define the nth moment of the transient electromagnetic impulse response as the definite integral with respect to time of the “quadrature” magnetic‐field impulse response weighted by time to the nth power. In this context, the quadrature response is defined as the full impulse response with the in‐phase component (i.e., the delta function component at zero time) removed. The low‐order moments are equivalent to familiar quantities: the zeroth moment (n = 0) is numerically equal to the frequency‐domain inductive limit, and the first moment is the resistive‐limit response. The higher order moments can be of particular benefit: successively they put greater emphasis on the late‐time data, and hence can bring out features in the data that are more conductive or deeper. An advantage of calculating moments (and hence the inductive and resistive limit) is that these data are not strongly dependent on any distortion of the waveform from an ideal impulse. Hence, it is not critical to deconvolve the data prior to estimating the moments. If a conductor has a single exponential decay, the nth moment of the decay is proportional to the nth power of the time constant of the exponential. Thus, it is relatively easy to estimate the time constant from the moments. For a conductive sphere model, the expressions for the moments are more complicated, but are still simpler than the full transient solution or the frequency‐domain solution. In a field example, the high‐order moments emphasize local highly conductive features, but also show the noise present in the late‐time data. A discrete feature on the profile evident in moments 3 through 10 has been modeled as a spherical conductor with its center at 90 m depth, a radius of 45 m, and a conductivity of 9.4 S/m.

scholarly journals An Express Algorithm for Transient Electromagnetic Data Interpretation

Electronics ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 354 ◽  
Author(s):  
Roman Kaminskyj ◽  
Nataliya Shakhovska ◽  
Gregus Michal ◽  
Borys Ladanivskyy ◽  
Lidia Savkiv
Keyword(s):  
Experimental Data ◽  
Spline Approximation ◽  
Numerical Differentiation ◽  
Data Interpretation ◽  
Continuous Functions ◽  
Electromagnetic Data ◽  
Polynomial Coefficients ◽  
Transient Electromagnetic ◽  
1D Model ◽  
Tem Method

The transient electromagnetic (TEM) method is a time-domain, controlled source, electromagnetic (EM) geophysical technique which is often applied to image the subsurface conductivity distributions of shallow layers due to its effectiveness and adaptability to complex site working conditions. The means for an express analysis of such experimental data in several practical cases have advantages and are suitable for use. We developed our approach for determining the approximate one-dimensional (1D) model of background conductivity based on the formal transformation of the TEM experimental data and the mathematical analysis of continuous functions. Our algorithm, which allows the 1D model’s parameters to be obtained in terms of a layer’s thickness and resistivity, widely utilizes the numerical differentiation of experimental curves as well as of transformed ones. Since the noise level increases with time in the attenuating TEM signals and differentiation even enhances it, special procedures are required to calculate the derivative values. We applied the piecewise cubic spline approximation to solve this problem. In that case, the derivatives are obtained using polynomial coefficients which are available for each node. The application of the created facilities is demonstrated using real experimental data of the TEM soundings.

Sign in / Sign up

Export Citation Format

Share Document