Analysis of Zonal Field Morphology and Data Quality for a Global Set of Magnetic Observatory Daily Mean Values*

Transcription

1 J. Geomag. Geoelectr., 35, , 1983 Analysis of Zonal Field Morphology and Data Quality for a Global Set of Magnetic Observatory Daily Mean Values* A. SCHULTZ1 and J. C. LARSEN2 1Geophysics Program WḆ10 2PMEL, Univ. Washington, Seattle WA, USA, NOAA, 7600 Sand Pt. Wy. NE, Seattle WA, USA (Received August 15, 1983) Geomagnetic induction studies of the electrical conductivity of the sublithospheric mantle are currently underway at the University of Washington. This work is based upon the analysis of magnetic time variations in the frequency range 0.01 cpd to 0.2 cpd. The data are obtained from a set of 76 magnetic observatories distributed as uniformly as possible over the earth's surface. Pioneering work by Banks and others has shown that the P01 spherical harmonic adequately describes the major part of magnetic field variations in the above range of frequencies. The dominance of the zonal ring current term has been exploited by a number of workers in attempts to determine the global distribution of electrical conductivity. The magnetovariational transfer function, i.e. the vertical over horizontal ratio of the I-ourier components of the field variations, is estimated. This function can be related to the magnetotelluric impedance function, and hence can be inverted to yield conductivity structures. Application of one-dimensional Backus-Gilbert inverse theory to data obtained at Tucson and Honolulu has shown a resolvable difference in conductivity structures at the two sites. This work serves as the basis for the current effort to delineate lateral mantle conductivity variations using the world-wide distribution of magnetic observatory data. The data for this work consists of 1358 station years. Each station-year contains up to 366 daily mean values for each of the three magnetic components H, D and Z. Much of these data exist as simultaneous timeseries from sites distributed around the globe. The simultaneity of data will allow us to test the validity of the P01 assumption and identify and remove noise. A statistical basis for the treatment of spurious data will also be discussed. 1. Introduction Considerable interest has been expressed lately in the determination of a deep global electrical conductivity reference model. This effort would be greatly *Contribution 652 from the NOAA/ERL Pacific Marine Environmental Laboratory USA., Seattle WA, 835

2 836 A. SCHULTZ and J. C. LARSEN aided by the estimation of lateral changes in the sublithospheric electrical conductivity structure. This paper will describe the status of our investigations, which are directed toward these ends. It was the goal of early investigators in this field to estimate the electrical conductivity distribution of the earth assuming a radially symmetric structure (CHAPMAN, 1919; LAHIRI and PRICE, 1939; PRICE, 1967). More recent studies have shown the assumption of radial symmetry to be suspect even at substantial depths. It is our intent to cast aside this notion of a globally one-dimensional earth, and instead to assume there are resolvable lateral conductivity variations. It is necessary therefore to estimate the conductivity structure at a substantial number of sites well distributed over the earth's surface. It is of paramount importance that careful attention be paid to the effects of spurious, noisy and incomplete data on the estimation of magnetovariational transfer functions. It is our contention that earlier efforts at modeling earth conductivities by examination of magnetic observatory data have been significantly hampered by the influence of data quality and uncertainty in identifying the frequency range in which magnetic field variations are zonal. By zonal variations we mean a source field which is polarized in the H direction and dependent only on latitude. 2. Magnetovariational Responses The following is a description of the preliminary results of the analysis of magnetic field variations at two sites in the USA-Tucson Arizona and Ewa Beach Hawaii. A magnetovariational response function was calculated for each of these sites: (1) colatitude. See Cox et al. (1968) for the derivation of the equivalent magnetotelluric response. The zonal assumption is found to apply to the frequency range 0.01 cpd to 0.2 cpd. The low frequency limit is high enough to exclude the semi-annual variation. Preliminary analysis of the Tucson and Honolulu observatory data shows that the responses at the two sites differ significantly within the resolution kernels

3 Analysis of Zonal Field Morphology 837 of the data. The conductivity structures resulting from the inversion of the response curves reveal realistic deep conductivity structures that are significantly different between Tucson and Honolulu. A zone of enhanced conductivity has been resolved beneath Tucson at a depth range of km that is absent beneath Honolulu. It is this difference between these stations that has prompted us to extend this study to a large distribution of magnetic observatories located in as many different tectonic regimes as possible. 3. The Global Magnetic Database Three component magnetic field variations at a total of 76 magnetic observatories have been assembled into an on-line computer database. These stations have a good global distribution and this can be seen in Fig. 1. These data are Fig. 1. Global distribution of magnetic observatories used in this study. Each circle represents a radius of 5 degrees on the surface of the earth. This is a distance of approximately 500km which is the skin depth for a period of 10 days and a conductivity of approximately 1S/M. This gives an indication of the volume of earth sampled for a typical period and conductivity. Note that Europe is the only region densely covered and that the oceans are poorly covered.

4 838 A. SCHULTZ and J. C. LARSEN a compendium of digitized data from World Data Center A, tapes supplied by the United States Geological Survey, and daily mean values read from magnetic observatory published yearbooks and microfilms. A substantial portion of these data have never before been available in digital form. The total number of daily as few as a single station and as many as 49 simultaneous stations. The distribution of the number of stations in the database as a function of time can be seen in Fig. 2. The data is organized according to station name, year, latitude and longitude, and the data may be extracted from the database by specifying any combination of these parameters. 4. Data Quality A number of factors influence the suitability of assuming a zonal source term for geomagnetic variations. These factors may be divided into two categories; Those factors resulting from errors, gaps and noise in the data; and those factors relating to the morphology of the magnetic field. We shall consider each topic separately. 4.1 Erroneous Data It has become apparent during this investigation that errors are introduced into the data both during the initial data reduction at the observatory and during the keypunching of digitized data. Data entry errors most often manifest themselves as delta-like functions in the timeseries. Observatory errors are usually manifested as box-car-like or Heaviside-like functions and result from erroneous baseline Fig. 2. Distribution of number of stations in database vs. time. Note that data was preferentially gathered for the time periods and

5 Analysis of Zonal Field Morphology 839 values. Compounding these problems may be the presence of numerous gaps in the data, and the existence of instrumental and environmental noise. Lack of attention to the above-mentioned problems will result in incorrect spectral estimates and erroneous transfer functions. We have found it efficacious to examine the forward differences of the magnetic components in the time domain. where B, is a magnetic field component at station i. In this space of forward differences, an erroneous datapoint of large amplitude will appear as a sharp spike of a given polarity followed by another spike of opposite polarity. A Heaviside-like function in the time domain (a bad baseline value) will appear as a single spike (see Fig. 3). The effects of secular changes and long term instrument drift will be reduced. It might be justifiable to state that the forward difference of a magnetic field component can never exceed some threshold value, say 1000nT. We could then eliminate all first differences greater than this threshold and integrate the remaining first difference series to obtain a timeseries free from delta functions, boxcars and Heaviside functions. Of course, some sophistication in filling in the deleted first differences by interpolation between neighboring points prior to integration is desirable so that small baseline changes are not introduced into the data. An example of the removal of large first differences can be seen in Fig. 4. The above method may be modified in such a way as to allow a statistical justification for the determination of threshold values. This elaboration on the (3) Fig. 3. H component timeseries and it's first-difference from WATHER00 for 1924 showing the effects of bad baseline values in the first-difference of data.

6 840 A. SCHULTZ and J. C. LARSEN Fig. 4. H component vs. time for the decade inclusive. Stations are sorted by geographic latitude. The curves are scaled at 185nT. per 10 degrees latitude. The plot on the left shows the unprocessed H component data. The plot on the right shows the same data after first-differences greater than 1000nT, have been removed and a linear trend has been removed from each year. Note the strong correlation between timeseries after the data has been processed. technique takes advantage of the simultaneous nature of the data from most stations and the fact that the fields are mainly describable by a single zonal (4) coherent with B'i(t), i.e. the uncorrelated noise. We solve for the Transient Projection Function by finding the L2 norm which minimizes the misfit (6)

7 Analysis of Zonal Field Morphology 841 (8) (10) where (12)

8 842 A. SCHULTZ and J. C. LARSEN of the matrix is a process that gives us a firm statistical basis for the identification and rejection of spikes and offsets in the data. This allows a more accurate computation of c, uncontaminated by outliers in the first differences. 4.2 Zonal assumption It is advisable to test the data for the applicability of the assumption of a zonal harmonic source term prior to more sophisticated analysis. It has been long recognized that a number of magnetic observatories are anomalous and that these anomalies are due to local effects such as proximity to oceans and local conductivity anomalies that can cause rotation of the axis of the components away from global geomagnetic north. In addition, the poles of the global zonal variations may not correspond to the global geomagnetic poles. Analysis of these data without removal of anomalous effects can lead to erroneous transfer functions and erroneous spherical harmonic field representations. We introduce a test self-consistent with the zonal assumption: Assume the local magnetic basis is rotated with respect to the global zonal poles. We shall refer to this global coordinate system as the "zonal basis". This rotation may be due to a local anomaly. Let the H and D magnetic field components be related to the X and Y components by X=HcosD Y=HsinD (13) where X is the North-South component and Y is the East-West component, both in the local basis. If the magnetic field were truly zonal, there would be no East-West component of the global zonal fields. We therefore apply a rotational transformation to the local basis such that the sum of the squares of Y in the zonal basis are minimized. (14) basis. Once the rotation angle is found, the data can be transformed into the zonal

9 Analysis of Zonal Field Morphology 843 The identical transformation can be performed in the frequency domain. The advantage of this is that individual basis rotation angles are found as a function of frequency. If the source term were zonal, we would expect the same rotation angle for all of the frequencies. If a deviation from some constant rotation angle were found for some range of frequencies, it would be inferred that the source term violates the zonal assumption for those frequencies. Therefore (16) (17) plex conjugate. Some results of the coordinate transformation can be seen in Fig. 5. Two sites, Dombas and Toledo for two years, 1958 and 1964 are examined. For the solar active year 1958, the rotations for all frequency bands cluster near the time domain rotation at both stations. There is some noticeable deterioration in the fit between the rotations in the two domains at frequencies above 0.2 cpd. This deterioration is dramatic for the solar quiet year Below each plot of rotation angle vs. frequency is a graph of the ratio in energy in the X component to the energy in the Y component for each frequency band. If the zonal approximation were true, the energy should be completely polarized in the X direction. It is seen that the field polarization deteriorates in the same manner as the rotation angle. This indicates that the rotation angle deterioration is significant and not an artifact of low signal strength in both components. We conclude that the zonal assumption is invalid for the stations examined at frequencies of approximately 0.2cpd and higher. 4.3 Random noise The effects of random noise between magnetic components at one or more stations can be examined in the frequency domain. We consider two magnetic

10 844 A. SCHULTZ and J. C. LARSEN Fig. 5. Rotation angles from geographic coordinates to zonal basis for Dombas and Toledo for Solar Active Year 1958 and Solar Quiet Year Rotation is in time domain (light line) and in discrete frequency bands (heavy lines). The field polarizations are plotted below the basis rotation angles. The variance in basis rotation estimates for the frequency domain and field polarizations is shown as a vertical line in the center of the band. Note that the zonal assumption is generally poor for frequencies greater than approximately 0.2cpd. One could determine the transfer function between rotated X components at two sites and search for statistical outliers by examination of the uncorrelated noise. This process allows us to examine individual frequency bands and enables a further estimation of the applicability of the zonal assumption and local anomalous effects. In particular, the onset of a DST storm is not likely to be describable by a single P01 zonal term and thus will be part of the noise. For the case of a zonal source term, it is expected that the X component at a given station should be coherent with X at any other station. The field variations should merely be scaled to first order by a function of geomagnetic colatitude. This is equivalent to saying that the above transfer function should be real and frequency independent since deep conductivity structure is not expected to be grossly different between sites.

11 Analysis of Zonal Field Morphology 845 Transfer functions and coherencies for a number of stations appear in Fig. 6. It can be seen that the coherence between X components in the zonal basis are high and quasi-frequency dependent. This dependence is significant above Fig. 6. Coherence squared and frequency-band-averaged transfer functions for three pairs of magnetic observatories in The data consists of zonally-rotated and detrended X components. The monovariate transfer functions are defined as X1=X2T+N, where X, and X2 are the complex Fourier coefficients of the X component (rotated H component) at Stations 1 and 2. This shows the high coherency between stations for frequencies below 0.2cpd.

12 846 A. SCHULTZ and J. C. LARSEN approximately 0.2cpd and mirrors the deterioration in fit between rotation angles during transformation to the zonal basis. Similarly, the transfer functions are essentially real and have little frequency dependence below this frequency. This suggests the zonal assumption is appropriate for frequencies below 0.2cpd. 4.4 Data gaps Gaps in the data can be removed by a combination of interpolation and data estimation by the projection of a remote field into the predicted missing field through an iterative transfer function estimation scheme. The reader is referred to a previous work (LARSEN, 1980). 5. Conclusion The results of this paper can be sumarized as follows: Magnetic field morphologies are consistent with the zonal assumption for a frequency range of 0.2 to 0.01cpd and inconsistent with this assumption for higher frequencies. The overall level of random noise is acceptable and the effects of spurious data can be minimized by a statistical treatment of the forward differences of the timeseries. A study of lateral variations in conductivity structures in the sublithosphere is underway. This work involves the analysis of the most comprehensive collection of magnetic observatory daily mean values assembled to date. It is our goal to expand upon our preliminary results for Tucson and Ewa Beach to include this global distribution of magnetic observatories. The authors wish to thank William Paulishak, Ron Buhman and the staff of World Data Center A as well as Joe Cain and Barbara Dodge of the U.S. Geological Survey for the assistance rendered during the data compilation stage of this work. We also wish to thank Linda Sylwester for her tireless assistance in data entry. This material is based upon work supported by the National Science Foundation under Grant No. EAR REFERENCES CHAPMAN, S., The solar and lunar diurnal variations of terrestrial magnetism, Phil. Trans. Roy. Soc. London, A218, 1-118, Cox, C. S., J. H. FILLOux, and J. C. LARSEN, Electromagnetic studies of ocean currents and electrical conductivity beneath the ocean floor, in The Sea, Vol 4, Part 1, edited by Maxwell, , John Wiley & Sons, Inc., New York, LAHIRI, B. N. and A. T. PRICE, Electromagnetic induction in non-uniform conductors, Phil. Trans. Roy. Soc. London, A 237, , LARSEN, J. C., Electromagnetic response functions from interrupted and noisy data, J. Geomag. Geoelectr., 32, Supple. I,S189-SI103, LARSEN, J. C., A new technique for layered-earth magnetotelluric inversion. Geophys, 46, No. 9, , PRICE, A. T., Electromagnetic induction within the earth, in Physics of Geomagnetic Phenomenon, pp , Academic Press, New York, 1967.