Data Reduction

pro-dnces, an

integrated understanding

of the mantle-crust system is impor-

tant.

To achieve

the desired degree

of resolution seYeral

means haYe been

employed. First, core phases

have

been added

to

the

data

set

so that

rays with angles more

nearly

vertical than the

direct P arrivals

can

be used

. These

rays help

constrain the

structure,

especially that which is

deep beneath

south- ern California. Also, a tomographic method of inversion

has been used since

it allows for a detailed inversion.

The

first part

of this

chapter discusses

the data and the reduction

pro-

cedures that have been

applied

to bring

the

data to a

set of travel

time

residu- als. This is followed

by

a description of the details of the tomographic method

of

inversion

needed in

this

specific

application. A

more

general

discussion

of tomography is the

topic

of

Chapter

I. Included are

a

fe,\· examples

of

recon- structions

performed

on artificially created "data" computed from

synthetic

structures.

Finally, the inversion of the actual P

delay data

is

given

and

dis-

cussed

. Chapter III

deals with

the interpretation, modeling, and tectonic significance of the observed features.

---- .. '

\ Figure 11.1. Locations of the 163 events used in this study. Map (a) gives the geographical locations, while (b) displays the same events in ray parameter-azimuth space. In b) the inner circle is 5 sec/deg and the outer circle is 10 sec/deg.

I w 0) I

-37-

0 ,

o - r---

o - 0 t.D

o - 0

L{)

0

(/)

0 -

- ^c

_:::J ^~

0

0 u o -

t<')

•

_I

! II

0 o -

N \,1

I

I I .

I

0

ⁱ

o - _- I

rr TT

r ~~

Tn • ••••••

1.5 .5 0 .5 1.5

delay ( in seconds)

Figure ll.2. Histogram of the 9888 travel time residuals used in this study. Each ray has associated with it one residual, and the residuals have been tallied for each 1 /20th second increment.

l'" CAL TECH-USGS SOUTHERN CALIFORNIA

NETWORK May. 1, 1979

SBS~ _---:...

20'

-38-

oa,~,.

"··

•TIN

OL~~<~~•~

•ewe

J

Figure ll.3. Map of the seismic station locations for the Southern California Array. This particular figure shows the station distribution for May 1, 1979, which is representative of the distribution during the time interval that data used in this study were recorded .

-

39-

the observations are determined by using the I\TEIS

locations and

the

Herrin T

ables (He

rrin

,

19

68). The core phases are

represented by the symbols

·wi

th

epicentral distances greater than 100°, or with slowness less than

4

sec/deg.

The

data are seen to cove

r

all quadrants and range in ray parameter from 0-10 sec/deg

.

The south and northeast directions, however, are much more poorly

represented than the northwest

and southeast directions

. In

all, about

160

events

recorded by the Southern California

Array are used

. The

number of stat

ions

giving usable

records for

any particular event varies, and the

resulting data set

consists of nearly

10,000 rays.

Figure II.2 is a histogram of the data

delay

values. Most of the data deviate from the mean by no more than half a second.

A

station

location

map

is shown

in

Figure Il.3 for

t

he

year

1979.

There has

been some change

in

station distri but

ion

through time, but the cov- erage shown

in Figure II.3 is

typical for the times

from

which t

he

data were

recorded. In t

otal,

158 stations were used in

this study. Each station

recorded

an average of 63 events while each event was recorded by an average of 61 sta- tions

.

To reduce

the data to a set of t

ravel

time delays, seve

ral

standard correc-

tions are appli ed. These corrections are elevation and sediment corrections

(applied

in

the same manner as

R

aikes,

1980) and travel time

corrections

. The

travel time corrections

include reductions

by dT /d..6.. and

d²T / d..6..²

(from the

Herrin T

ab

les). Also, the average

delay for each event

is removed to reduce

the effect of errors

in

the source parameters. The core phases,

PKP

and

PKIKP,

a

re

reduced somewhat differently since reduc

tion by the Herrin

Tables

cons

istently

underestimates dT /d..6..

.

Fortunately, a large event (mb

=

6.1 )

-40-

occurred near the antipode to southern California (£::.. ::::::::: 175°). The Herrin corrections, small for this event, were applied to produce a reference delay map. It >vas then a straightforward matter to adjust dT / d£::.. for each of the other events in order to best match the reference P delay map in a least- squares sense. Since the antipodal travel time residuals indicate the delay

accumulated directly beneath each observation site, and also because this e.-ent was exceptionally >veil recorded, this P delay map has been chosen as an example P wave map (Figure II.4). For comparison, the P delay map resulting from an event of similar magnitude (mb = 5.9) that occurred in Korea

(.6. =

70°) is also shown. Arrivals from this e.-ent are from the \V. 0V, and the general pattern is seen to shift towards the ESE.

In addition to the standard reductions, a correction for variable crustal thickness has been applied. The indiYidual station corrections are calculated from the station P n time-terms of Hearn (198-la). These time terms may be due to variations in either crustal velocity or in Moho depth, but since the time term method is especially sensitive to variations in the ::.1oho depth, this was assumed to be the cause. Corrections are determined by calculating a travel time slab correction v·:ith a slab thickness given by the de•·iation of the ::.1oho from its aYerage depth, as inferred from Hearn's time terms (19 -la), and by using an assumed .-elocity contrast across the ::.Ioho of 1.2 km/sec. The travel time effect on the P delays resulting from varying crustal thickness is less than that produced by varying crustal velocity, and so this is the more conservative of the two approaches. The corrections made in this way are in the range ±0.37 sec. >rith an average deviation of ±0.06 sec.

0 0

delta=175

0

0

rfo

D 0

delta= 82

0

0

',,

0

0

'··· ..

^,

·,

0

0

. .

' ' _'

~

0 " ... '".!

0

.... ···

,-'

" ...

.

^I

___

,_...:

'

',

·.

,-' ' ' '

Figure ll.4. Maps of travel time residuals for two events. The solid triangles represent early arrivals, and the open squares represent late arrivals. The size of the symbol is pro- portional to the value of the delay. The upper map is the result of a nearly antipodal event and thus shows the integrated delay directly beneath each station, while the lower map is for an event in Korea (.b. = 82°, to the WNW) and the delay pattern is shifted to the ESE.

-42-

2.3 Method of Inversion

The method

of tomography

was chosen to invert

the data.

The

major

advantage

offered

with

this app

roach is

the ab

ili

ty to handle a

detailed inver-

sion.

The

theory and methodology are the subjects of Chapter

I, and only a few in

t

roductory comments will

be given

here. T

he statement of the problem

is identical

to that

most

commonly used

in

the generalized

inverse problem

(see,

for example, A

ki et aL (1977)

for a discussion that is particularly relevant

to the geometry of

teleseismic

arrivals).

This involves

dividing the

region in which

one

is in

te

rested into

a

number

of

discrete blocks, and the slowness per-

turbations

to

these blocks that best produce the observations a

re sought.

Th

e geometry of the near

normal incidence of teleseismic r

ays

result in

a

few

spec

ial properties

that can be taken advantage of, eithe

r for

the

purpose of gaining insight

or

to

simplify the calculational

formulas. An important obser- vation can easily be made that the average slowness perturbation of each layer

is

t

he same.

(Since

the

ave

rage delay

has

been removed from

each events set of t

ravel

t

im

es, this

value is zero.) T

here

is no

ability, therefore

.

to resolve the

average vertical structure. Thi

s

is simply a statement that all rays

t

raverse the entire inversion domain

t

hickn

ess and

therefore lack

the

ability to resolve

the

average

vertical

structure,

or equivalently, that the eigenvectors of the

information matrix (LTL,

Chapter

I) do not

span this dimension and are

independent of changes in it.

Two approximations which simplify the computations have been imple- mented. Since

all

rays are fairly v

ertical,

it is "

·ithout significant

loss

of accu-

r

acy

that

one may assign the

ray to one and only one block per layer. If

the

ray happens

to penetrate

more than one block, only the block "·ith the longest ray segment is

used, and

it is

assumed that the

ray

traverses the entire

layer within

that single

block.

This

greatly

simplifies the geometrical considerations that

have

to

be made. Once ray segments are associated with an entire block,

all

ray lengths within

any

block are

approximately equal and equation

I.l

can

be simplified

to

sb

=

~dr /~trb without

perceptible alteration of

the

r r

inverse. Comparison

of the

mverse

constructed

using

this

formulation with

that produced with the

use of

I.l

("·here

in both instances

the one

block

per layer

approximation has

been

used) gives

a

difference in

the

most deviant

blocks between the

two

inverses

of

less

than

1% ,

and most

blocks are unal-

tered to within the four significant places kept in

the data

files.