Electromagnetic seismograph constants by least-squares inversion

1969 ◽  
Vol 59 (3) ◽  
pp. 1335-1348
Author(s):  
B. J. Mitchell ◽  
M. Landisman
Keyword(s):  
Least Squares ◽  
Love Wave ◽  
Least Squares Method ◽  
Linear Trend ◽  
Wave Train ◽  
Vertical Component ◽  
Long Period ◽  
Electromagnetic Seismograph ◽  
Before And After

abstract A least-squares method has been developed to determine the free periods and damping constants of an electromagnetic seismograph from its calibration pulse. The resulting values are correct to within a few tenths of one per cent for synthetic calibration pulses, even when moderate levels of microseismic noise are present. The seismograph constants of the long-period vertical component at Dallas, Texas were determined from in situ measurements and compared with those calculated from the calibration pulse. The results agreed to within four per cent or better for the free periods and damping constants, after correcting for the linear trend and the base coordinate system of the observed pulse. The values differed by as much as 30 per cent when the linear trend and base coordinate corrections were ignored. Two sets of instrumental constants from an unmatched pair of horizontal seismographs were determined from their calibration pulses. Directions of particle motion for a Love wave train recorded on the same instruments were computed before and after instrumental corrections; the results differed by as much as 8 degrees.

Temperature effects on long-period seismographs: an accurate method to determine the transfer function

1976 ◽  
Vol 66 (4) ◽  
pp. 1405-1412
Author(s):  
Walter Mitronovas
Keyword(s):  
Transfer Function ◽  
Least Squares ◽  
Vertical Component ◽  
Direct Determination ◽  
Phase Response ◽  
Calibration Data ◽  
Seasonal Temperature ◽  
Simple Method ◽  
Long Period

abstract A simple method for monitoring the transfer function of a long-period (LP) seismograph as a function of time is described. This method makes it possible, under certain restrictions, to estimate quite accurately (one order of magnitude better than the least-squares inversion of the calibration pulse) changes in the transfer function of a system using only the maximum amplitude information of the transient calibration pulses. The restrictions of this method are: (1) no change in the period of the horizontal seismometers (TS) and galvanometers (TG): (2) length of the spring of a vertical seismometer (boom position) is a function of temperature only; and (3) magnetic field is uniform in the range of expected boom (coil) excursions. In other words, the system parameters are affected only by temperature. Briefly, temperature affects mainly the resistance of the coils (copper) of seismometer (RS) and galvanometer (RG), which changes the current flowing in the circuit and hence the amplitude of the calibration pulse. The expected changes in the damping of the seismometer (hS), galvanometer (hG) and in the seismometer period (vertical component) have only negligible additional effect on the amplitude. Therefore, from the observed daily variation in the amplitude of the calibration pulses, it is simple to calculate changes in RS and RG and, hence, the in situ temperature as a function of time. The effect of temperature on the vertical seismometer boom position, and hence TS, can be determined beforehand (or at any time) for each instrument. From this, TS as a function of time can be inferred. Finally, from the calculated variations in RS and RG, variation in hG can be determined; from variations in RS, RG and TS, variation in hS and then the coupling factor (σ) can be determined. Analysis of the calibration data from a vertical component at Zurich for a 2-year period, 1972–73, is presented as an illustration of the method. The in situ seasonal temperature variation was inferred to be around ±4 C. In terms of the variation in the system phase response (delay), this amounts to about ±0.20 sec (at most) at a period of 100 sec, and less at shorter periods. This estimate is in good agreement with direct determination of the differences in phase delay for a similar system under controlled temperature conditions. It is also consistent with the fact that no systematic variation in phase response as a function of time was detected using the least-squares inversion of the calibration pulse (method not accurate enough). This indicates that the temperature effect on the phase response is fairly small and that under normal conditions modern LP instruments satisfy to a good approximation the requirements of this calibration method.

Densities determined from surface and subsurface gravity measurements

Geophysics ◽  
1981 ◽  
Vol 46 (11) ◽  
pp. 1568-1571 ◽  
Author(s):  
B. A. Sissons
Keyword(s):  
Least Squares ◽  
Least Squares Method ◽  
Average Density ◽  
Laboratory Measurements ◽  
Density Estimates ◽  
Direct Inversion ◽  
Gravity Measurements ◽  
The Difference ◽  
Made In

A least‐squares method for the direct inversion of surface and subsurface gravity measurements to obtain in situ density estimates is presented. The method is applied to a set of measurements made in a tunnel through the flank of an andesitic volcano. Densities obtained are [Formula: see text] for material in the top 100 m increasing to [Formula: see text] at about 200 m depth. The average density for rocks penetrated by the tunnel is, from laboratory measurements, [Formula: see text] i.e., about 4 percent higher. The difference is ascribed to joints and voids present in situ and not sampled in the laboratory specimens.

scholarly journals Stability of milking order in goat over a long period (short communication)

2004 ◽  
Vol 47 (2) ◽  
pp. 203-208
Author(s):  
M. T. Górecki ◽  
J. Wójtowski
Keyword(s):  
Body Weight ◽  
Social Status ◽  
Least Squares ◽  
Milk Yield ◽  
Short Communication ◽  
Least Squares Method ◽  
Rank Correlation ◽  
Milk Productivity ◽  
Long Period ◽  
Spearman’S Rank Correlation

Abstract. The aim of this paper was to assess if goat milking order was stabile over a long period and if milking order is influenced by horned ness, age, body weight, breed, social status and milk productivity. Milking order was studied in three periods: the second half of 1999, and the first and second halves of 2000. To verify the results statistically, a variance analysis (ANOVA), the least squares method and Spearman's rank correlation were used. The observed milking order of goats was non-random and very similar in the two consecutive years. Milk yield correlated with the milking order in two of the three periods (higher–yielding goats entered the milking parlour first). Social status as well as age affected milking order only in one period (dominant and younger animals came to the milking parlour earlier). In one period it was observed that body weight influenced the milking order at a marginally significant level (p = 0.0598). Heavier goats were milked before lighter ones. It can be suggested, that milk productivity is the strongest predictor of the animal position in the milking order. However, habits seems to influence milking order stronger than measurable traits. The own results were compared with other studies on milking order in cattle, sheep and goats.

scholarly journals Analisis Trend Produksi Padi Organik dan Anorganik pada Lahan Rawa di Kabupaten Hulu Sungai Utara

2017 ◽  
Vol 7 (1) ◽  
pp. 472-478
Author(s):  
Ahmad Suhaimi ◽  
Rezka Yulia
Keyword(s):  
Least Squares ◽  
Research Method ◽  
Least Squares Method ◽  
Linear Trend ◽  
Secondary Data ◽  
Rice Production ◽  
Food Crops

       This study aims to find out (i) fluctuations in production trends, (ii) forecasting projections, and (iii) volumes of organic and inorganic paddy production from 2016-2021 at wetland in Hulu Sungai Utara Regency. The study was conducted from March to July 2016. The research method used was descriptive with secondary data obtained from the Office of Food Crops and Horticulture of Hulu Sungai Utara Regency, data obtained from 2010 to 2015. The analysis used in this study was linear trend with the least squares method which aims to predict or predict the development of organic and inorganic rice production in swamps in North Hulu Sungai Regency, South Kalimantan Province. The results showed fluctuations in production trends, forecasting projections and production of organic and inorganic paddy each year has increased

‘Least squares’ method—theorem or law?

1980 ◽  
Vol 59 (9) ◽  
pp. 8
Author(s):  
D.E. Turnbull
Keyword(s):  
Least Squares ◽  
Least Squares Method

An Augmented Iteratively Re-weighted and Refined Least Squares Method for lp Minimization Problem in Inverse Modeling of Potential Field Magnetic Data

2020 ◽  
Vol 1 (3) ◽  
Author(s):  
Maysam Abedi
Keyword(s):  
Magnetic Field ◽  
Magnetic Susceptibility ◽  
Least Squares ◽  
Minimization Problem ◽  
Potential Field ◽  
Field Data ◽  
Least Squares Method ◽  
Porphyry Copper ◽  
Magnetic Data ◽  
Magnetic Field Data

The presented work examines application of an Augmented Iteratively Re-weighted and Refined Least Squares method (AIRRLS) to construct a 3D magnetic susceptibility property from potential field magnetic anomalies. This algorithm replaces an lp minimization problem by a sequence of weighted linear systems in which the retrieved magnetic susceptibility model is successively converged to an optimum solution, while the regularization parameter is the stopping iteration numbers. To avoid the natural tendency of causative magnetic sources to concentrate at shallow depth, a prior depth weighting function is incorporated in the original formulation of the objective function. The speed of lp minimization problem is increased by inserting a pre-conditioner conjugate gradient method (PCCG) to solve the central system of equation in cases of large scale magnetic field data. It is assumed that there is no remanent magnetization since this study focuses on inversion of a geological structure with low magnetic susceptibility property. The method is applied on a multi-source noise-corrupted synthetic magnetic field data to demonstrate its suitability for 3D inversion, and then is applied to a real data pertaining to a geologically plausible porphyry copper unit.  The real case study located in  Semnan province of  Iran  consists  of  an arc-shaped  porphyry  andesite  covered  by  sedimentary  units  which  may  have  potential  of  mineral  occurrences, especially  porphyry copper. It is demonstrated that such structure extends down at depth, and consequently exploratory drilling is highly recommended for acquiring more pieces of information about its potential for ore-bearing mineralization.

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